[{"data":1,"prerenderedAt":7179},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fwichtige-grenzwerte":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fwichtige-grenzwerte":7166},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":556,"category":101,"checks":7076,"conditions":7102,"conditionsHtml":7102,"deprecated":7102,"description":7070,"extension":7103,"figure":7104,"figureCaption":7105,"figureHtml":7134,"formulaId":7135,"latex":7136,"latexHtml":7137,"level":7138,"meta":7139,"navigation":7116,"path":7140,"redirectFrom":7141,"related":7142,"seo":7147,"stem":7148,"subject":588,"summary":7149,"tags":7150,"variables":7155,"__hash__":7165},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fcalculus\u002Fwichtige-grenzwerte.md","Wichtige Grenzwerte",[550,551,552,553,554,555],"Standardgrenzwerte","sin x durch x","Grenzwert sin(x)\u002Fx","n-te Wurzel aus n","bekannte Grenzwerte","(e^x - 1)\u002Fx",{"type":557,"value":558,"toc":7069},"minimark",[559,564,572,1823,1826,2988,2992,3288,3619,4061,4761,5094,5503,5507],[560,561,563],"h2",{"id":562},"erklärung","Erklärung",[565,566,567,568,571],"p",{},"Diese ",[569,570,550],"strong",{}," tauchen beim Ableiten und bei Grenzwertaufgaben ständig auf:",[573,574,575,928,1440],"ul",{},[576,577,578,775,776,829,830,894,895,923,924,927],"li",{},[579,580,583,627],"span",{"className":581},[582],"katex",[579,584,587],{"className":585},[586],"katex-mathml",[588,589,591],"math",{"xmlns":590},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[592,593,594,622],"semantics",{},[595,596,597,615,618],"mrow",{},[598,599,600,613],"mfrac",{},[595,601,602,606,610],{},[603,604,605],"mi",{},"sin",[607,608,609],"mo",{},"⁡",[603,611,612],{},"x",[603,614,612],{},[607,616,617],{},"→",[619,620,621],"mn",{},"1",[623,624,626],"annotation",{"encoding":625},"application\u002Fx-tex","\\frac{\\sin x}{x} \\to 1",[579,628,632,765],{"className":629,"ariaHidden":631},[630],"katex-html","true",[579,633,636,641,754,758,762],{"className":634},[635],"base",[579,637],{"className":638,"style":640},[639],"strut","height:1.2065em;vertical-align:-0.345em;",[579,642,645,650,750],{"className":643},[644],"mord",[579,646],{"className":647},[648,649],"mopen","nulldelimiter",[579,651,653],{"className":652},[598],[579,654,658,741],{"className":655},[656,657],"vlist-t","vlist-t2",[579,659,662,736],{"className":660},[661],"vlist-r",[579,663,667,689,700],{"className":664,"style":666},[665],"vlist","height:0.8615em;",[579,668,670,675],{"style":669},"top:-2.655em;",[579,671],{"className":672,"style":674},[673],"pstrut","height:3em;",[579,676,682],{"className":677},[678,679,680,681],"sizing","reset-size6","size3","mtight",[579,683,685],{"className":684},[644,681],[579,686,612],{"className":687},[644,688,681],"mathnormal",[579,690,692,695],{"style":691},"top:-3.23em;",[579,693],{"className":694,"style":674},[673],[579,696],{"className":697,"style":699},[698],"frac-line","border-bottom-width:0.04em;",[579,701,703,706],{"style":702},"top:-3.394em;",[579,704],{"className":705,"style":674},[673],[579,707,709],{"className":708},[678,679,680,681],[579,710,712,728,733],{"className":711},[644,681],[579,713,716,720,724],{"className":714},[715,681],"mop",[579,717,719],{"className":718},[681],"s",[579,721,723],{"className":722},[681],"i",[579,725,727],{"className":726},[681],"n",[579,729],{"className":730,"style":732},[731,681],"mspace","margin-right:0.1952em;",[579,734,612],{"className":735},[644,688,681],[579,737,740],{"className":738},[739],"vlist-s","​",[579,742,744],{"className":743},[661],[579,745,748],{"className":746,"style":747},[665],"height:0.345em;",[579,749],{},[579,751],{"className":752},[753,649],"mclose",[579,755],{"className":756,"style":757},[731],"margin-right:0.2778em;",[579,759,617],{"className":760},[761],"mrel",[579,763],{"className":764,"style":757},[731],[579,766,768,772],{"className":767},[635],[579,769],{"className":770,"style":771},[639],"height:0.6444em;",[579,773,621],{"className":774},[644]," für ",[579,777,779,798],{"className":778},[582],[579,780,782],{"className":781},[586],[588,783,784],{"xmlns":590},[592,785,786,795],{},[595,787,788,790,792],{},[603,789,612],{},[607,791,617],{},[619,793,794],{},"0",[623,796,797],{"encoding":625},"x \\to 0",[579,799,801,820],{"className":800,"ariaHidden":631},[630],[579,802,804,808,811,814,817],{"className":803},[635],[579,805],{"className":806,"style":807},[639],"height:0.4306em;",[579,809,612],{"className":810},[644,688],[579,812],{"className":813,"style":757},[731],[579,815,617],{"className":816},[761],[579,818],{"className":819,"style":757},[731],[579,821,823,826],{"className":822},[635],[579,824],{"className":825,"style":771},[639],[579,827,794],{"className":828},[644]," liefert die Ableitung des Sinus und die Näherung ",[579,831,833,856],{"className":832},[582],[579,834,836],{"className":835},[586],[588,837,838],{"xmlns":590},[592,839,840,853],{},[595,841,842,844,846,848,851],{},[603,843,605],{},[607,845,609],{},[603,847,612],{},[607,849,850],{},"≈",[603,852,612],{},[623,854,855],{"encoding":625},"\\sin x \\approx x",[579,857,859,885],{"className":858,"ariaHidden":631},[630],[579,860,862,866,869,873,876,879,882],{"className":861},[635],[579,863],{"className":864,"style":865},[639],"height:0.6679em;",[579,867,605],{"className":868},[715],[579,870],{"className":871,"style":872},[731],"margin-right:0.1667em;",[579,874,612],{"className":875},[644,688],[579,877],{"className":878,"style":757},[731],[579,880,850],{"className":881},[761],[579,883],{"className":884,"style":757},[731],[579,886,888,891],{"className":887},[635],[579,889],{"className":890,"style":807},[639],[579,892,612],{"className":893},[644,688]," für kleine ",[579,896,898,911],{"className":897},[582],[579,899,901],{"className":900},[586],[588,902,903],{"xmlns":590},[592,904,905,909],{},[595,906,907],{},[603,908,612],{},[623,910,612],{"encoding":625},[579,912,914],{"className":913,"ariaHidden":631},[630],[579,915,917,920],{"className":916},[635],[579,918],{"className":919,"style":807},[639],[579,921,612],{"className":922},[644,688],". Das gilt nur im ",[569,925,926],{},"Bogenmaß",".",[576,929,930,775,1104,1154,1155,1217,1218,1246,1247,1275,1276,927],{},[579,931,933,968],{"className":932},[582],[579,934,936],{"className":935},[586],[588,937,938],{"xmlns":590},[592,939,940,965],{},[595,941,942,961,963],{},[598,943,944,959],{},[595,945,946,954,957],{},[947,948,949,952],"msup",{},[603,950,951],{},"e",[603,953,612],{},[607,955,956],{},"−",[619,958,621],{},[603,960,612],{},[607,962,617],{},[619,964,621],{},[623,966,967],{"encoding":625},"\\frac{e^x - 1}{x} \\to 1",[579,969,971,1095],{"className":970,"ariaHidden":631},[630],[579,972,974,978,1086,1089,1092],{"className":973},[635],[579,975],{"className":976,"style":977},[639],"height:1.256em;vertical-align:-0.345em;",[579,979,981,984,1083],{"className":980},[644],[579,982],{"className":983},[648,649],[579,985,987],{"className":986},[598],[579,988,990,1075],{"className":989},[656,657],[579,991,993,1072],{"className":992},[661],[579,994,997,1011,1019],{"className":995,"style":996},[665],"height:0.911em;",[579,998,999,1002],{"style":669},[579,1000],{"className":1001,"style":674},[673],[579,1003,1005],{"className":1004},[678,679,680,681],[579,1006,1008],{"className":1007},[644,681],[579,1009,612],{"className":1010},[644,688,681],[579,1012,1013,1016],{"style":691},[579,1014],{"className":1015,"style":674},[673],[579,1017],{"className":1018,"style":699},[698],[579,1020,1021,1024],{"style":702},[579,1022],{"className":1023,"style":674},[673],[579,1025,1027],{"className":1026},[678,679,680,681],[579,1028,1030,1065,1069],{"className":1029},[644,681],[579,1031,1033,1036],{"className":1032},[644,681],[579,1034,951],{"className":1035},[644,688,681],[579,1037,1040],{"className":1038},[1039],"msupsub",[579,1041,1043],{"className":1042},[656],[579,1044,1046],{"className":1045},[661],[579,1047,1050],{"className":1048,"style":1049},[665],"height:0.7385em;",[579,1051,1053,1057],{"style":1052},"top:-2.931em;margin-right:0.0714em;",[579,1054],{"className":1055,"style":1056},[673],"height:2.5em;",[579,1058,1062],{"className":1059},[678,1060,1061,681],"reset-size3","size1",[579,1063,612],{"className":1064},[644,688,681],[579,1066,956],{"className":1067},[1068,681],"mbin",[579,1070,621],{"className":1071},[644,681],[579,1073,740],{"className":1074},[739],[579,1076,1078],{"className":1077},[661],[579,1079,1081],{"className":1080,"style":747},[665],[579,1082],{},[579,1084],{"className":1085},[753,649],[579,1087],{"className":1088,"style":757},[731],[579,1090,617],{"className":1091},[761],[579,1093],{"className":1094,"style":757},[731],[579,1096,1098,1101],{"className":1097},[635],[579,1099],{"className":1100,"style":771},[639],[579,1102,621],{"className":1103},[644],[579,1105,1107,1124],{"className":1106},[582],[579,1108,1110],{"className":1109},[586],[588,1111,1112],{"xmlns":590},[592,1113,1114,1122],{},[595,1115,1116,1118,1120],{},[603,1117,612],{},[607,1119,617],{},[619,1121,794],{},[623,1123,797],{"encoding":625},[579,1125,1127,1145],{"className":1126,"ariaHidden":631},[630],[579,1128,1130,1133,1136,1139,1142],{"className":1129},[635],[579,1131],{"className":1132,"style":807},[639],[579,1134,612],{"className":1135},[644,688],[579,1137],{"className":1138,"style":757},[731],[579,1140,617],{"className":1141},[761],[579,1143],{"className":1144,"style":757},[731],[579,1146,1148,1151],{"className":1147},[635],[579,1149],{"className":1150,"style":771},[639],[579,1152,794],{"className":1153},[644]," ist genau die Aussage, dass ",[579,1156,1158,1176],{"className":1157},[582],[579,1159,1161],{"className":1160},[586],[588,1162,1163],{"xmlns":590},[592,1164,1165,1173],{},[595,1166,1167],{},[947,1168,1169,1171],{},[603,1170,951],{},[603,1172,612],{},[623,1174,1175],{"encoding":625},"e^x",[579,1177,1179],{"className":1178,"ariaHidden":631},[630],[579,1180,1182,1186],{"className":1181},[635],[579,1183],{"className":1184,"style":1185},[639],"height:0.6644em;",[579,1187,1189,1192],{"className":1188},[644],[579,1190,951],{"className":1191},[644,688],[579,1193,1195],{"className":1194},[1039],[579,1196,1198],{"className":1197},[656],[579,1199,1201],{"className":1200},[661],[579,1202,1204],{"className":1203,"style":1185},[665],[579,1205,1207,1211],{"style":1206},"top:-3.063em;margin-right:0.05em;",[579,1208],{"className":1209,"style":1210},[673],"height:2.7em;",[579,1212,1214],{"className":1213},[678,679,680,681],[579,1215,612],{"className":1216},[644,688,681]," bei ",[579,1219,1221,1234],{"className":1220},[582],[579,1222,1224],{"className":1223},[586],[588,1225,1226],{"xmlns":590},[592,1227,1228,1232],{},[595,1229,1230],{},[619,1231,794],{},[623,1233,794],{"encoding":625},[579,1235,1237],{"className":1236,"ariaHidden":631},[630],[579,1238,1240,1243],{"className":1239},[635],[579,1241],{"className":1242,"style":771},[639],[579,1244,794],{"className":1245},[644]," die Steigung ",[579,1248,1250,1263],{"className":1249},[582],[579,1251,1253],{"className":1252},[586],[588,1254,1255],{"xmlns":590},[592,1256,1257,1261],{},[595,1258,1259],{},[619,1260,621],{},[623,1262,621],{"encoding":625},[579,1264,1266],{"className":1265,"ariaHidden":631},[630],[579,1267,1269,1272],{"className":1268},[635],[579,1270],{"className":1271,"style":771},[639],[579,1273,621],{"className":1274},[644]," hat. Gleichwertig ist ",[579,1277,1279,1320],{"className":1278},[582],[579,1280,1282],{"className":1281},[586],[588,1283,1284],{"xmlns":590},[592,1285,1286,1317],{},[595,1287,1288,1313,1315],{},[598,1289,1290,1311],{},[595,1291,1292,1295,1297,1301,1303,1306,1308],{},[603,1293,1294],{},"ln",[607,1296,609],{},[607,1298,1300],{"stretchy":1299},"false","(",[619,1302,621],{},[607,1304,1305],{},"+",[603,1307,612],{},[607,1309,1310],{"stretchy":1299},")",[603,1312,612],{},[607,1314,617],{},[619,1316,621],{},[623,1318,1319],{"encoding":625},"\\frac{\\ln(1 + x)}{x} \\to 1",[579,1321,1323,1431],{"className":1322,"ariaHidden":631},[630],[579,1324,1326,1330,1422,1425,1428],{"className":1325},[635],[579,1327],{"className":1328,"style":1329},[639],"height:1.355em;vertical-align:-0.345em;",[579,1331,1333,1336,1419],{"className":1332},[644],[579,1334],{"className":1335},[648,649],[579,1337,1339],{"className":1338},[598],[579,1340,1342,1411],{"className":1341},[656,657],[579,1343,1345,1408],{"className":1344},[661],[579,1346,1349,1363,1371],{"className":1347,"style":1348},[665],"height:1.01em;",[579,1350,1351,1354],{"style":669},[579,1352],{"className":1353,"style":674},[673],[579,1355,1357],{"className":1356},[678,679,680,681],[579,1358,1360],{"className":1359},[644,681],[579,1361,612],{"className":1362},[644,688,681],[579,1364,1365,1368],{"style":691},[579,1366],{"className":1367,"style":674},[673],[579,1369],{"className":1370,"style":699},[698],[579,1372,1374,1377],{"style":1373},"top:-3.485em;",[579,1375],{"className":1376,"style":674},[673],[579,1378,1380],{"className":1379},[678,679,680,681],[579,1381,1383,1393,1396,1399,1402,1405],{"className":1382},[644,681],[579,1384,1386,1390],{"className":1385},[715,681],[579,1387,1389],{"className":1388},[681],"l",[579,1391,727],{"className":1392},[681],[579,1394,1300],{"className":1395},[648,681],[579,1397,621],{"className":1398},[644,681],[579,1400,1305],{"className":1401},[1068,681],[579,1403,612],{"className":1404},[644,688,681],[579,1406,1310],{"className":1407},[753,681],[579,1409,740],{"className":1410},[739],[579,1412,1414],{"className":1413},[661],[579,1415,1417],{"className":1416,"style":747},[665],[579,1418],{},[579,1420],{"className":1421},[753,649],[579,1423],{"className":1424,"style":757},[731],[579,1426,617],{"className":1427},[761],[579,1429],{"className":1430,"style":757},[731],[579,1432,1434,1437],{"className":1433},[635],[579,1435],{"className":1436,"style":771},[639],[579,1438,621],{"className":1439},[644],[576,1441,1442,775,1589,1642,1643,1769,1770,927],{},[579,1443,1445,1468],{"className":1444},[582],[579,1446,1448],{"className":1447},[586],[588,1449,1450],{"xmlns":590},[592,1451,1452,1465],{},[595,1453,1454,1461,1463],{},[1455,1456,1457,1459],"mroot",{},[603,1458,727],{},[603,1460,727],{},[607,1462,617],{},[619,1464,621],{},[623,1466,1467],{"encoding":625},"\\sqrt[n]{n} \\to 1",[579,1469,1471,1580],{"className":1470,"ariaHidden":631},[630],[579,1472,1474,1478,1571,1574,1577],{"className":1473},[635],[579,1475],{"className":1476,"style":1477},[639],"height:1.04em;vertical-align:-0.2397em;",[579,1479,1482,1511],{"className":1480},[644,1481],"sqrt",[579,1483,1486],{"className":1484},[1485],"root",[579,1487,1489],{"className":1488},[656],[579,1490,1492],{"className":1491},[661],[579,1493,1496],{"className":1494,"style":1495},[665],"height:0.5516em;",[579,1497,1499,1502],{"style":1498},"top:-2.8363em;",[579,1500],{"className":1501,"style":1056},[673],[579,1503,1505],{"className":1504},[678,679,1061,681],[579,1506,1508],{"className":1507},[644,681],[579,1509,727],{"className":1510},[644,688,681],[579,1512,1514,1562],{"className":1513},[656,657],[579,1515,1517,1559],{"className":1516},[661],[579,1518,1521,1536],{"className":1519,"style":1520},[665],"height:0.8003em;",[579,1522,1526,1529],{"className":1523,"style":1525},[1524],"svg-align","top:-3em;",[579,1527],{"className":1528,"style":674},[673],[579,1530,1533],{"className":1531,"style":1532},[644],"padding-left:0.833em;",[579,1534,727],{"className":1535},[644,688],[579,1537,1539,1542],{"style":1538},"top:-2.7603em;",[579,1540],{"className":1541,"style":674},[673],[579,1543,1547],{"className":1544,"style":1546},[1545],"hide-tail","min-width:0.853em;height:1.08em;",[1548,1549,1555],"svg",{"xmlns":1550,"width":1551,"height":1552,"viewBox":1553,"preserveAspectRatio":1554},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[1556,1557],"path",{"d":1558},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[579,1560,740],{"className":1561},[739],[579,1563,1565],{"className":1564},[661],[579,1566,1569],{"className":1567,"style":1568},[665],"height:0.2397em;",[579,1570],{},[579,1572],{"className":1573,"style":757},[731],[579,1575,617],{"className":1576},[761],[579,1578],{"className":1579,"style":757},[731],[579,1581,1583,1586],{"className":1582},[635],[579,1584],{"className":1585,"style":771},[639],[579,1587,621],{"className":1588},[644],[579,1590,1592,1612],{"className":1591},[582],[579,1593,1595],{"className":1594},[586],[588,1596,1597],{"xmlns":590},[592,1598,1599,1609],{},[595,1600,1601,1603,1605],{},[603,1602,727],{},[607,1604,617],{},[603,1606,1608],{"mathvariant":1607},"normal","∞",[623,1610,1611],{"encoding":625},"n \\to \\infty",[579,1613,1615,1633],{"className":1614,"ariaHidden":631},[630],[579,1616,1618,1621,1624,1627,1630],{"className":1617},[635],[579,1619],{"className":1620,"style":807},[639],[579,1622,727],{"className":1623},[644,688],[579,1625],{"className":1626,"style":757},[731],[579,1628,617],{"className":1629},[761],[579,1631],{"className":1632,"style":757},[731],[579,1634,1636,1639],{"className":1635},[635],[579,1637],{"className":1638,"style":807},[639],[579,1640,1608],{"className":1641},[644]," wird beim Wurzelkriterium gebraucht. Ebenso gilt ",[579,1644,1646,1669],{"className":1645},[582],[579,1647,1649],{"className":1648},[586],[588,1650,1651],{"xmlns":590},[592,1652,1653,1666],{},[595,1654,1655,1662,1664],{},[1455,1656,1657,1660],{},[603,1658,1659],{},"c",[603,1661,727],{},[607,1663,617],{},[619,1665,621],{},[623,1667,1668],{"encoding":625},"\\sqrt[n]{c} \\to 1",[579,1670,1672,1760],{"className":1671,"ariaHidden":631},[630],[579,1673,1675,1678,1751,1754,1757],{"className":1674},[635],[579,1676],{"className":1677,"style":1477},[639],[579,1679,1681,1707],{"className":1680},[644,1481],[579,1682,1684],{"className":1683},[1485],[579,1685,1687],{"className":1686},[656],[579,1688,1690],{"className":1689},[661],[579,1691,1693],{"className":1692,"style":1495},[665],[579,1694,1695,1698],{"style":1498},[579,1696],{"className":1697,"style":1056},[673],[579,1699,1701],{"className":1700},[678,679,1061,681],[579,1702,1704],{"className":1703},[644,681],[579,1705,727],{"className":1706},[644,688,681],[579,1708,1710,1743],{"className":1709},[656,657],[579,1711,1713,1740],{"className":1712},[661],[579,1714,1716,1728],{"className":1715,"style":1520},[665],[579,1717,1719,1722],{"className":1718,"style":1525},[1524],[579,1720],{"className":1721,"style":674},[673],[579,1723,1725],{"className":1724,"style":1532},[644],[579,1726,1659],{"className":1727},[644,688],[579,1729,1730,1733],{"style":1538},[579,1731],{"className":1732,"style":674},[673],[579,1734,1736],{"className":1735,"style":1546},[1545],[1548,1737,1738],{"xmlns":1550,"width":1551,"height":1552,"viewBox":1553,"preserveAspectRatio":1554},[1556,1739],{"d":1558},[579,1741,740],{"className":1742},[739],[579,1744,1746],{"className":1745},[661],[579,1747,1749],{"className":1748,"style":1568},[665],[579,1750],{},[579,1752],{"className":1753,"style":757},[731],[579,1755,617],{"className":1756},[761],[579,1758],{"className":1759,"style":757},[731],[579,1761,1763,1766],{"className":1762},[635],[579,1764],{"className":1765,"style":771},[639],[579,1767,621],{"className":1768},[644]," für jedes feste ",[579,1771,1773,1792],{"className":1772},[582],[579,1774,1776],{"className":1775},[586],[588,1777,1778],{"xmlns":590},[592,1779,1780,1789],{},[595,1781,1782,1784,1787],{},[603,1783,1659],{},[607,1785,1786],{},">",[619,1788,794],{},[623,1790,1791],{"encoding":625},"c > 0",[579,1793,1795,1814],{"className":1794,"ariaHidden":631},[630],[579,1796,1798,1802,1805,1808,1811],{"className":1797},[635],[579,1799],{"className":1800,"style":1801},[639],"height:0.5782em;vertical-align:-0.0391em;",[579,1803,1659],{"className":1804},[644,688],[579,1806],{"className":1807,"style":757},[731],[579,1809,1786],{"className":1810},[761],[579,1812],{"className":1813,"style":757},[731],[579,1815,1817,1820],{"className":1816},[635],[579,1818],{"className":1819,"style":771},[639],[579,1821,794],{"className":1822},[644],[565,1824,1825],{},"Weitere wichtige Grenzwerte:",[573,1827,1828,2245,2516,2794],{},[576,1829,1830,2026,2027,927],{},[579,1831,1833,1869],{"className":1832},[582],[579,1834,1836],{"className":1835},[586],[588,1837,1838],{"xmlns":590},[592,1839,1840,1866],{},[595,1841,1842,1862,1864],{},[947,1843,1844,1860],{},[595,1845,1846,1848,1850,1852,1858],{},[607,1847,1300],{"fence":631},[619,1849,621],{},[607,1851,1305],{},[598,1853,1854,1856],{},[619,1855,621],{},[603,1857,727],{},[607,1859,1310],{"fence":631},[603,1861,727],{},[607,1863,617],{},[603,1865,951],{},[623,1867,1868],{"encoding":625},"\\left(1 + \\frac{1}{n}\\right)^n \\to e",[579,1870,1872,2017],{"className":1871,"ariaHidden":631},[630],[579,1873,1875,1879,2008,2011,2014],{"className":1874},[635],[579,1876],{"className":1877,"style":1878},[639],"height:1.2543em;vertical-align:-0.35em;",[579,1880,1883,1983],{"className":1881},[1882],"minner",[579,1884,1886,1895,1898,1902,1905,1908,1977],{"className":1885},[1882],[579,1887,1891],{"className":1888,"style":1890},[648,1889],"delimcenter","top:0em;",[579,1892,1300],{"className":1893},[1894,1061],"delimsizing",[579,1896,621],{"className":1897},[644],[579,1899],{"className":1900,"style":1901},[731],"margin-right:0.2222em;",[579,1903,1305],{"className":1904},[1068],[579,1906],{"className":1907,"style":1901},[731],[579,1909,1911,1914,1974],{"className":1910},[644],[579,1912],{"className":1913},[648,649],[579,1915,1917],{"className":1916},[598],[579,1918,1920,1966],{"className":1919},[656,657],[579,1921,1923,1963],{"className":1922},[661],[579,1924,1927,1941,1949],{"className":1925,"style":1926},[665],"height:0.8451em;",[579,1928,1929,1932],{"style":669},[579,1930],{"className":1931,"style":674},[673],[579,1933,1935],{"className":1934},[678,679,680,681],[579,1936,1938],{"className":1937},[644,681],[579,1939,727],{"className":1940},[644,688,681],[579,1942,1943,1946],{"style":691},[579,1944],{"className":1945,"style":674},[673],[579,1947],{"className":1948,"style":699},[698],[579,1950,1951,1954],{"style":702},[579,1952],{"className":1953,"style":674},[673],[579,1955,1957],{"className":1956},[678,679,680,681],[579,1958,1960],{"className":1959},[644,681],[579,1961,621],{"className":1962},[644,681],[579,1964,740],{"className":1965},[739],[579,1967,1969],{"className":1968},[661],[579,1970,1972],{"className":1971,"style":747},[665],[579,1973],{},[579,1975],{"className":1976},[753,649],[579,1978,1980],{"className":1979,"style":1890},[753,1889],[579,1981,1310],{"className":1982},[1894,1061],[579,1984,1986],{"className":1985},[1039],[579,1987,1989],{"className":1988},[656],[579,1990,1992],{"className":1991},[661],[579,1993,1996],{"className":1994,"style":1995},[665],"height:0.9043em;",[579,1997,1999,2002],{"style":1998},"top:-3.3029em;margin-right:0.05em;",[579,2000],{"className":2001,"style":1210},[673],[579,2003,2005],{"className":2004},[678,679,680,681],[579,2006,727],{"className":2007},[644,688,681],[579,2009],{"className":2010,"style":757},[731],[579,2012,617],{"className":2013},[761],[579,2015],{"className":2016,"style":757},[731],[579,2018,2020,2023],{"className":2019},[635],[579,2021],{"className":2022,"style":807},[639],[579,2024,951],{"className":2025},[644,688]," und allgemeiner ",[579,2028,2030,2070],{"className":2029},[582],[579,2031,2033],{"className":2032},[586],[588,2034,2035],{"xmlns":590},[592,2036,2037,2067],{},[595,2038,2039,2059,2061],{},[947,2040,2041,2057],{},[595,2042,2043,2045,2047,2049,2055],{},[607,2044,1300],{"fence":631},[619,2046,621],{},[607,2048,1305],{},[598,2050,2051,2053],{},[603,2052,612],{},[603,2054,727],{},[607,2056,1310],{"fence":631},[603,2058,727],{},[607,2060,617],{},[947,2062,2063,2065],{},[603,2064,951],{},[603,2066,612],{},[623,2068,2069],{"encoding":625},"\\left(1 + \\frac{x}{n}\\right)^n \\to e^x",[579,2071,2073,2210],{"className":2072,"ariaHidden":631},[630],[579,2074,2076,2079,2201,2204,2207],{"className":2075},[635],[579,2077],{"className":2078,"style":1878},[639],[579,2080,2082,2178],{"className":2081},[1882],[579,2083,2085,2091,2094,2097,2100,2103,2172],{"className":2084},[1882],[579,2086,2088],{"className":2087,"style":1890},[648,1889],[579,2089,1300],{"className":2090},[1894,1061],[579,2092,621],{"className":2093},[644],[579,2095],{"className":2096,"style":1901},[731],[579,2098,1305],{"className":2099},[1068],[579,2101],{"className":2102,"style":1901},[731],[579,2104,2106,2109,2169],{"className":2105},[644],[579,2107],{"className":2108},[648,649],[579,2110,2112],{"className":2111},[598],[579,2113,2115,2161],{"className":2114},[656,657],[579,2116,2118,2158],{"className":2117},[661],[579,2119,2122,2136,2144],{"className":2120,"style":2121},[665],"height:0.6954em;",[579,2123,2124,2127],{"style":669},[579,2125],{"className":2126,"style":674},[673],[579,2128,2130],{"className":2129},[678,679,680,681],[579,2131,2133],{"className":2132},[644,681],[579,2134,727],{"className":2135},[644,688,681],[579,2137,2138,2141],{"style":691},[579,2139],{"className":2140,"style":674},[673],[579,2142],{"className":2143,"style":699},[698],[579,2145,2146,2149],{"style":702},[579,2147],{"className":2148,"style":674},[673],[579,2150,2152],{"className":2151},[678,679,680,681],[579,2153,2155],{"className":2154},[644,681],[579,2156,612],{"className":2157},[644,688,681],[579,2159,740],{"className":2160},[739],[579,2162,2164],{"className":2163},[661],[579,2165,2167],{"className":2166,"style":747},[665],[579,2168],{},[579,2170],{"className":2171},[753,649],[579,2173,2175],{"className":2174,"style":1890},[753,1889],[579,2176,1310],{"className":2177},[1894,1061],[579,2179,2181],{"className":2180},[1039],[579,2182,2184],{"className":2183},[656],[579,2185,2187],{"className":2186},[661],[579,2188,2190],{"className":2189,"style":1995},[665],[579,2191,2192,2195],{"style":1998},[579,2193],{"className":2194,"style":1210},[673],[579,2196,2198],{"className":2197},[678,679,680,681],[579,2199,727],{"className":2200},[644,688,681],[579,2202],{"className":2203,"style":757},[731],[579,2205,617],{"className":2206},[761],[579,2208],{"className":2209,"style":757},[731],[579,2211,2213,2216],{"className":2212},[635],[579,2214],{"className":2215,"style":1185},[639],[579,2217,2219,2222],{"className":2218},[644],[579,2220,951],{"className":2221},[644,688],[579,2223,2225],{"className":2224},[1039],[579,2226,2228],{"className":2227},[656],[579,2229,2231],{"className":2230},[661],[579,2232,2234],{"className":2233,"style":1185},[665],[579,2235,2236,2239],{"style":1206},[579,2237],{"className":2238,"style":1210},[673],[579,2240,2242],{"className":2241},[678,679,680,681],[579,2243,612],{"className":2244},[644,688,681],[576,2246,2247,775,2434,2485,2486,2515],{},[579,2248,2250,2281],{"className":2249},[582],[579,2251,2253],{"className":2252},[586],[588,2254,2255],{"xmlns":590},[592,2256,2257,2278],{},[595,2258,2259,2274,2276],{},[598,2260,2261,2268],{},[947,2262,2263,2265],{},[603,2264,612],{},[603,2266,2267],{},"k",[947,2269,2270,2272],{},[603,2271,951],{},[603,2273,612],{},[607,2275,617],{},[619,2277,794],{},[623,2279,2280],{"encoding":625},"\\frac{x^k}{e^x} \\to 0",[579,2282,2284,2425],{"className":2283,"ariaHidden":631},[630],[579,2285,2287,2291,2416,2419,2422],{"className":2286},[635],[579,2288],{"className":2289,"style":2290},[639],"height:1.3879em;vertical-align:-0.345em;",[579,2292,2294,2297,2413],{"className":2293},[644],[579,2295],{"className":2296},[648,649],[579,2298,2300],{"className":2299},[598],[579,2301,2303,2405],{"className":2302},[656,657],[579,2304,2306,2402],{"className":2305},[661],[579,2307,2310,2352,2360],{"className":2308,"style":2309},[665],"height:1.0429em;",[579,2311,2312,2315],{"style":669},[579,2313],{"className":2314,"style":674},[673],[579,2316,2318],{"className":2317},[678,679,680,681],[579,2319,2321],{"className":2320},[644,681],[579,2322,2324,2327],{"className":2323},[644,681],[579,2325,951],{"className":2326},[644,688,681],[579,2328,2330],{"className":2329},[1039],[579,2331,2333],{"className":2332},[656],[579,2334,2336],{"className":2335},[661],[579,2337,2340],{"className":2338,"style":2339},[665],"height:0.5935em;",[579,2341,2343,2346],{"style":2342},"top:-2.786em;margin-right:0.0714em;",[579,2344],{"className":2345,"style":1056},[673],[579,2347,2349],{"className":2348},[678,1060,1061,681],[579,2350,612],{"className":2351},[644,688,681],[579,2353,2354,2357],{"style":691},[579,2355],{"className":2356,"style":674},[673],[579,2358],{"className":2359,"style":699},[698],[579,2361,2362,2365],{"style":702},[579,2363],{"className":2364,"style":674},[673],[579,2366,2368],{"className":2367},[678,679,680,681],[579,2369,2371],{"className":2370},[644,681],[579,2372,2374,2377],{"className":2373},[644,681],[579,2375,612],{"className":2376},[644,688,681],[579,2378,2380],{"className":2379},[1039],[579,2381,2383],{"className":2382},[656],[579,2384,2386],{"className":2385},[661],[579,2387,2390],{"className":2388,"style":2389},[665],"height:0.927em;",[579,2391,2392,2395],{"style":1052},[579,2393],{"className":2394,"style":1056},[673],[579,2396,2398],{"className":2397},[678,1060,1061,681],[579,2399,2267],{"className":2400,"style":2401},[644,688,681],"margin-right:0.0315em;",[579,2403,740],{"className":2404},[739],[579,2406,2408],{"className":2407},[661],[579,2409,2411],{"className":2410,"style":747},[665],[579,2412],{},[579,2414],{"className":2415},[753,649],[579,2417],{"className":2418,"style":757},[731],[579,2420,617],{"className":2421},[761],[579,2423],{"className":2424,"style":757},[731],[579,2426,2428,2431],{"className":2427},[635],[579,2429],{"className":2430,"style":771},[639],[579,2432,794],{"className":2433},[644],[579,2435,2437,2455],{"className":2436},[582],[579,2438,2440],{"className":2439},[586],[588,2441,2442],{"xmlns":590},[592,2443,2444,2452],{},[595,2445,2446,2448,2450],{},[603,2447,612],{},[607,2449,617],{},[603,2451,1608],{"mathvariant":1607},[623,2453,2454],{"encoding":625},"x \\to \\infty",[579,2456,2458,2476],{"className":2457,"ariaHidden":631},[630],[579,2459,2461,2464,2467,2470,2473],{"className":2460},[635],[579,2462],{"className":2463,"style":807},[639],[579,2465,612],{"className":2466},[644,688],[579,2468],{"className":2469,"style":757},[731],[579,2471,617],{"className":2472},[761],[579,2474],{"className":2475,"style":757},[731],[579,2477,2479,2482],{"className":2478},[635],[579,2480],{"className":2481,"style":807},[639],[579,2483,1608],{"className":2484},[644]," und jedes ",[579,2487,2489,2502],{"className":2488},[582],[579,2490,2492],{"className":2491},[586],[588,2493,2494],{"xmlns":590},[592,2495,2496,2500],{},[595,2497,2498],{},[603,2499,2267],{},[623,2501,2267],{"encoding":625},[579,2503,2505],{"className":2504,"ariaHidden":631},[630],[579,2506,2508,2512],{"className":2507},[635],[579,2509],{"className":2510,"style":2511},[639],"height:0.6944em;",[579,2513,2267],{"className":2514,"style":2401},[644,688],": Die Exponentialfunktion wächst schneller als jede Potenz.",[576,2517,2518,775,2691,2485,2741,2793],{},[579,2519,2521,2553],{"className":2520},[582],[579,2522,2524],{"className":2523},[586],[588,2525,2526],{"xmlns":590},[592,2527,2528,2550],{},[595,2529,2530,2546,2548],{},[598,2531,2532,2540],{},[595,2533,2534,2536,2538],{},[603,2535,1294],{},[607,2537,609],{},[603,2539,612],{},[947,2541,2542,2544],{},[603,2543,612],{},[603,2545,2267],{},[607,2547,617],{},[619,2549,794],{},[623,2551,2552],{"encoding":625},"\\frac{\\ln x}{x^k} \\to 0",[579,2554,2556,2682],{"className":2555,"ariaHidden":631},[630],[579,2557,2559,2563,2673,2676,2679],{"className":2558},[635],[579,2560],{"className":2561,"style":2562},[639],"height:1.2375em;vertical-align:-0.3574em;",[579,2564,2566,2569,2670],{"className":2565},[644],[579,2567],{"className":2568},[648,649],[579,2570,2572],{"className":2571},[598],[579,2573,2575,2661],{"className":2574},[656,657],[579,2576,2578,2658],{"className":2577},[661],[579,2579,2582,2624,2632],{"className":2580,"style":2581},[665],"height:0.8801em;",[579,2583,2585,2588],{"style":2584},"top:-2.6426em;",[579,2586],{"className":2587,"style":674},[673],[579,2589,2591],{"className":2590},[678,679,680,681],[579,2592,2594],{"className":2593},[644,681],[579,2595,2597,2600],{"className":2596},[644,681],[579,2598,612],{"className":2599},[644,688,681],[579,2601,2603],{"className":2602},[1039],[579,2604,2606],{"className":2605},[656],[579,2607,2609],{"className":2608},[661],[579,2610,2613],{"className":2611,"style":2612},[665],"height:0.782em;",[579,2614,2615,2618],{"style":2342},[579,2616],{"className":2617,"style":1056},[673],[579,2619,2621],{"className":2620},[678,1060,1061,681],[579,2622,2267],{"className":2623,"style":2401},[644,688,681],[579,2625,2626,2629],{"style":691},[579,2627],{"className":2628,"style":674},[673],[579,2630],{"className":2631,"style":699},[698],[579,2633,2634,2637],{"style":702},[579,2635],{"className":2636,"style":674},[673],[579,2638,2640],{"className":2639},[678,679,680,681],[579,2641,2643,2652,2655],{"className":2642},[644,681],[579,2644,2646,2649],{"className":2645},[715,681],[579,2647,1389],{"className":2648},[681],[579,2650,727],{"className":2651},[681],[579,2653],{"className":2654,"style":732},[731,681],[579,2656,612],{"className":2657},[644,688,681],[579,2659,740],{"className":2660},[739],[579,2662,2664],{"className":2663},[661],[579,2665,2668],{"className":2666,"style":2667},[665],"height:0.3574em;",[579,2669],{},[579,2671],{"className":2672},[753,649],[579,2674],{"className":2675,"style":757},[731],[579,2677,617],{"className":2678},[761],[579,2680],{"className":2681,"style":757},[731],[579,2683,2685,2688],{"className":2684},[635],[579,2686],{"className":2687,"style":771},[639],[579,2689,794],{"className":2690},[644],[579,2692,2694,2711],{"className":2693},[582],[579,2695,2697],{"className":2696},[586],[588,2698,2699],{"xmlns":590},[592,2700,2701,2709],{},[595,2702,2703,2705,2707],{},[603,2704,612],{},[607,2706,617],{},[603,2708,1608],{"mathvariant":1607},[623,2710,2454],{"encoding":625},[579,2712,2714,2732],{"className":2713,"ariaHidden":631},[630],[579,2715,2717,2720,2723,2726,2729],{"className":2716},[635],[579,2718],{"className":2719,"style":807},[639],[579,2721,612],{"className":2722},[644,688],[579,2724],{"className":2725,"style":757},[731],[579,2727,617],{"className":2728},[761],[579,2730],{"className":2731,"style":757},[731],[579,2733,2735,2738],{"className":2734},[635],[579,2736],{"className":2737,"style":807},[639],[579,2739,1608],{"className":2740},[644],[579,2742,2744,2762],{"className":2743},[582],[579,2745,2747],{"className":2746},[586],[588,2748,2749],{"xmlns":590},[592,2750,2751,2759],{},[595,2752,2753,2755,2757],{},[603,2754,2267],{},[607,2756,1786],{},[619,2758,794],{},[623,2760,2761],{"encoding":625},"k > 0",[579,2763,2765,2784],{"className":2764,"ariaHidden":631},[630],[579,2766,2768,2772,2775,2778,2781],{"className":2767},[635],[579,2769],{"className":2770,"style":2771},[639],"height:0.7335em;vertical-align:-0.0391em;",[579,2773,2267],{"className":2774,"style":2401},[644,688],[579,2776],{"className":2777,"style":757},[731],[579,2779,1786],{"className":2780},[761],[579,2782],{"className":2783,"style":757},[731],[579,2785,2787,2790],{"className":2786},[635],[579,2788],{"className":2789,"style":771},[639],[579,2791,794],{"className":2792},[644],": Der Logarithmus wächst langsamer als jede Potenz.",[576,2795,2796,1769,2959,927],{},[579,2797,2799,2831],{"className":2798},[582],[579,2800,2802],{"className":2801},[586],[588,2803,2804],{"xmlns":590},[592,2805,2806,2828],{},[595,2807,2808,2824,2826],{},[598,2809,2810,2817],{},[947,2811,2812,2815],{},[603,2813,2814],{},"q",[603,2816,727],{},[595,2818,2819,2821],{},[603,2820,727],{},[607,2822,2823],{"stretchy":1299},"!",[607,2825,617],{},[619,2827,794],{},[623,2829,2830],{"encoding":625},"\\frac{q^n}{n!} \\to 0",[579,2832,2834,2950],{"className":2833,"ariaHidden":631},[630],[579,2835,2837,2841,2941,2944,2947],{"className":2836},[635],[579,2838],{"className":2839,"style":2840},[639],"height:1.3081em;vertical-align:-0.345em;",[579,2842,2844,2847,2938],{"className":2843},[644],[579,2845],{"className":2846},[648,649],[579,2848,2850],{"className":2849},[598],[579,2851,2853,2930],{"className":2852},[656,657],[579,2854,2856,2927],{"className":2855},[661],[579,2857,2860,2877,2885],{"className":2858,"style":2859},[665],"height:0.9631em;",[579,2861,2862,2865],{"style":669},[579,2863],{"className":2864,"style":674},[673],[579,2866,2868],{"className":2867},[678,679,680,681],[579,2869,2871,2874],{"className":2870},[644,681],[579,2872,727],{"className":2873},[644,688,681],[579,2875,2823],{"className":2876},[753,681],[579,2878,2879,2882],{"style":691},[579,2880],{"className":2881,"style":674},[673],[579,2883],{"className":2884,"style":699},[698],[579,2886,2888,2891],{"style":2887},"top:-3.4461em;",[579,2889],{"className":2890,"style":674},[673],[579,2892,2894],{"className":2893},[678,679,680,681],[579,2895,2897],{"className":2896},[644,681],[579,2898,2900,2904],{"className":2899},[644,681],[579,2901,2814],{"className":2902,"style":2903},[644,688,681],"margin-right:0.0359em;",[579,2905,2907],{"className":2906},[1039],[579,2908,2910],{"className":2909},[656],[579,2911,2913],{"className":2912},[661],[579,2914,2916],{"className":2915,"style":1049},[665],[579,2917,2918,2921],{"style":1052},[579,2919],{"className":2920,"style":1056},[673],[579,2922,2924],{"className":2923},[678,1060,1061,681],[579,2925,727],{"className":2926},[644,688,681],[579,2928,740],{"className":2929},[739],[579,2931,2933],{"className":2932},[661],[579,2934,2936],{"className":2935,"style":747},[665],[579,2937],{},[579,2939],{"className":2940},[753,649],[579,2942],{"className":2943,"style":757},[731],[579,2945,617],{"className":2946},[761],[579,2948],{"className":2949,"style":757},[731],[579,2951,2953,2956],{"className":2952},[635],[579,2954],{"className":2955,"style":771},[639],[579,2957,794],{"className":2958},[644],[579,2960,2962,2975],{"className":2961},[582],[579,2963,2965],{"className":2964},[586],[588,2966,2967],{"xmlns":590},[592,2968,2969,2973],{},[595,2970,2971],{},[603,2972,2814],{},[623,2974,2814],{"encoding":625},[579,2976,2978],{"className":2977,"ariaHidden":631},[630],[579,2979,2981,2985],{"className":2980},[635],[579,2982],{"className":2983,"style":2984},[639],"height:0.625em;vertical-align:-0.1944em;",[579,2986,2814],{"className":2987,"style":2903},[644,688],[560,2989,2991],{"id":2990},"beispiele","Beispiele",[565,2993,2994,3199,3200,3228,3229,3287],{},[579,2995,2997,3046],{"className":2996},[582],[579,2998,3000],{"className":2999},[586],[588,3001,3002],{"xmlns":590},[592,3003,3004,3043],{},[595,3005,3006,3024],{},[3007,3008,3009,3016],"msub",{},[595,3010,3011,3014],{},[603,3012,3013],{},"lim",[607,3015,609],{},[595,3017,3018,3020,3022],{},[603,3019,612],{},[607,3021,617],{},[619,3023,794],{},[598,3025,3026,3041],{},[595,3027,3028,3030,3032,3034,3037,3039],{},[603,3029,605],{},[607,3031,609],{},[607,3033,1300],{"stretchy":1299},[619,3035,3036],{},"3",[603,3038,612],{},[607,3040,1310],{"stretchy":1299},[603,3042,612],{},[623,3044,3045],{"encoding":625},"\\lim_{x \\to 0} \\frac{\\sin(3x)}{x}",[579,3047,3049],{"className":3048,"ariaHidden":631},[630],[579,3050,3052,3055,3107,3110],{"className":3051},[635],[579,3053],{"className":3054,"style":1329},[639],[579,3056,3058,3061],{"className":3057},[715],[579,3059,3013],{"className":3060},[715],[579,3062,3064],{"className":3063},[1039],[579,3065,3067,3098],{"className":3066},[656,657],[579,3068,3070,3095],{"className":3069},[661],[579,3071,3074],{"className":3072,"style":3073},[665],"height:0.3011em;",[579,3075,3077,3080],{"style":3076},"top:-2.55em;margin-right:0.05em;",[579,3078],{"className":3079,"style":1210},[673],[579,3081,3083],{"className":3082},[678,679,680,681],[579,3084,3086,3089,3092],{"className":3085},[644,681],[579,3087,612],{"className":3088},[644,688,681],[579,3090,617],{"className":3091},[761,681],[579,3093,794],{"className":3094},[644,681],[579,3096,740],{"className":3097},[739],[579,3099,3101],{"className":3100},[661],[579,3102,3105],{"className":3103,"style":3104},[665],"height:0.15em;",[579,3106],{},[579,3108],{"className":3109,"style":872},[731],[579,3111,3113,3116,3196],{"className":3112},[644],[579,3114],{"className":3115},[648,649],[579,3117,3119],{"className":3118},[598],[579,3120,3122,3188],{"className":3121},[656,657],[579,3123,3125,3185],{"className":3124},[661],[579,3126,3128,3142,3150],{"className":3127,"style":1348},[665],[579,3129,3130,3133],{"style":669},[579,3131],{"className":3132,"style":674},[673],[579,3134,3136],{"className":3135},[678,679,680,681],[579,3137,3139],{"className":3138},[644,681],[579,3140,612],{"className":3141},[644,688,681],[579,3143,3144,3147],{"style":691},[579,3145],{"className":3146,"style":674},[673],[579,3148],{"className":3149,"style":699},[698],[579,3151,3152,3155],{"style":1373},[579,3153],{"className":3154,"style":674},[673],[579,3156,3158],{"className":3157},[678,679,680,681],[579,3159,3161,3173,3176,3179,3182],{"className":3160},[644,681],[579,3162,3164,3167,3170],{"className":3163},[715,681],[579,3165,719],{"className":3166},[681],[579,3168,723],{"className":3169},[681],[579,3171,727],{"className":3172},[681],[579,3174,1300],{"className":3175},[648,681],[579,3177,3036],{"className":3178},[644,681],[579,3180,612],{"className":3181},[644,688,681],[579,3183,1310],{"className":3184},[753,681],[579,3186,740],{"className":3187},[739],[579,3189,3191],{"className":3190},[661],[579,3192,3194],{"className":3193,"style":747},[665],[579,3195],{},[579,3197],{"className":3198},[753,649],": Man erweitert mit ",[579,3201,3203,3216],{"className":3202},[582],[579,3204,3206],{"className":3205},[586],[588,3207,3208],{"xmlns":590},[592,3209,3210,3214],{},[595,3211,3212],{},[619,3213,3036],{},[623,3215,3036],{"encoding":625},[579,3217,3219],{"className":3218,"ariaHidden":631},[630],[579,3220,3222,3225],{"className":3221},[635],[579,3223],{"className":3224,"style":771},[639],[579,3226,3036],{"className":3227},[644]," und setzt ",[579,3230,3232,3254],{"className":3231},[582],[579,3233,3235],{"className":3234},[586],[588,3236,3237],{"xmlns":590},[592,3238,3239,3251],{},[595,3240,3241,3244,3247,3249],{},[603,3242,3243],{},"u",[607,3245,3246],{},"=",[619,3248,3036],{},[603,3250,612],{},[623,3252,3253],{"encoding":625},"u = 3x",[579,3255,3257,3275],{"className":3256,"ariaHidden":631},[630],[579,3258,3260,3263,3266,3269,3272],{"className":3259},[635],[579,3261],{"className":3262,"style":807},[639],[579,3264,3243],{"className":3265},[644,688],[579,3267],{"className":3268,"style":757},[731],[579,3270,3246],{"className":3271},[761],[579,3273],{"className":3274,"style":757},[731],[579,3276,3278,3281,3284],{"className":3277},[635],[579,3279],{"className":3280,"style":771},[639],[579,3282,3036],{"className":3283},[644],[579,3285,612],{"className":3286},[644,688],":",[579,3289,3292],{"className":3290},[3291],"katex-display",[579,3293,3295,3367],{"className":3294},[582],[579,3296,3298],{"className":3297},[586],[588,3299,3301],{"xmlns":590,"display":3300},"block",[592,3302,3303,3364],{},[595,3304,3305,3323,3325,3327,3330,3352,3354,3356,3358,3360,3362],{},[598,3306,3307,3321],{},[595,3308,3309,3311,3313,3315,3317,3319],{},[603,3310,605],{},[607,3312,609],{},[607,3314,1300],{"stretchy":1299},[619,3316,3036],{},[603,3318,612],{},[607,3320,1310],{"stretchy":1299},[603,3322,612],{},[607,3324,3246],{},[619,3326,3036],{},[607,3328,3329],{},"⋅",[598,3331,3332,3346],{},[595,3333,3334,3336,3338,3340,3342,3344],{},[603,3335,605],{},[607,3337,609],{},[607,3339,1300],{"stretchy":1299},[619,3341,3036],{},[603,3343,612],{},[607,3345,1310],{"stretchy":1299},[595,3347,3348,3350],{},[619,3349,3036],{},[603,3351,612],{},[607,3353,617],{},[619,3355,3036],{},[607,3357,3329],{},[619,3359,621],{},[607,3361,3246],{},[619,3363,3036],{},[623,3365,3366],{"encoding":625},"\\frac{\\sin(3x)}{x} = 3 \\cdot \\frac{\\sin(3x)}{3x} \\to 3 \\cdot 1 = 3",[579,3368,3370,3464,3482,3574,3592,3610],{"className":3369,"ariaHidden":631},[630],[579,3371,3373,3377,3455,3458,3461],{"className":3372},[635],[579,3374],{"className":3375,"style":3376},[639],"height:2.113em;vertical-align:-0.686em;",[579,3378,3380,3383,3452],{"className":3379},[644],[579,3381],{"className":3382},[648,649],[579,3384,3386],{"className":3385},[598],[579,3387,3389,3443],{"className":3388},[656,657],[579,3390,3392,3440],{"className":3391},[661],[579,3393,3396,3408,3416],{"className":3394,"style":3395},[665],"height:1.427em;",[579,3397,3399,3402],{"style":3398},"top:-2.314em;",[579,3400],{"className":3401,"style":674},[673],[579,3403,3405],{"className":3404},[644],[579,3406,612],{"className":3407},[644,688],[579,3409,3410,3413],{"style":691},[579,3411],{"className":3412,"style":674},[673],[579,3414],{"className":3415,"style":699},[698],[579,3417,3419,3422],{"style":3418},"top:-3.677em;",[579,3420],{"className":3421,"style":674},[673],[579,3423,3425,3428,3431,3434,3437],{"className":3424},[644],[579,3426,605],{"className":3427},[715],[579,3429,1300],{"className":3430},[648],[579,3432,3036],{"className":3433},[644],[579,3435,612],{"className":3436},[644,688],[579,3438,1310],{"className":3439},[753],[579,3441,740],{"className":3442},[739],[579,3444,3446],{"className":3445},[661],[579,3447,3450],{"className":3448,"style":3449},[665],"height:0.686em;",[579,3451],{},[579,3453],{"className":3454},[753,649],[579,3456],{"className":3457,"style":757},[731],[579,3459,3246],{"className":3460},[761],[579,3462],{"className":3463,"style":757},[731],[579,3465,3467,3470,3473,3476,3479],{"className":3466},[635],[579,3468],{"className":3469,"style":771},[639],[579,3471,3036],{"className":3472},[644],[579,3474],{"className":3475,"style":1901},[731],[579,3477,3329],{"className":3478},[1068],[579,3480],{"className":3481,"style":1901},[731],[579,3483,3485,3488,3565,3568,3571],{"className":3484},[635],[579,3486],{"className":3487,"style":3376},[639],[579,3489,3491,3494,3562],{"className":3490},[644],[579,3492],{"className":3493},[648,649],[579,3495,3497],{"className":3496},[598],[579,3498,3500,3554],{"className":3499},[656,657],[579,3501,3503,3551],{"className":3502},[661],[579,3504,3506,3520,3528],{"className":3505,"style":3395},[665],[579,3507,3508,3511],{"style":3398},[579,3509],{"className":3510,"style":674},[673],[579,3512,3514,3517],{"className":3513},[644],[579,3515,3036],{"className":3516},[644],[579,3518,612],{"className":3519},[644,688],[579,3521,3522,3525],{"style":691},[579,3523],{"className":3524,"style":674},[673],[579,3526],{"className":3527,"style":699},[698],[579,3529,3530,3533],{"style":3418},[579,3531],{"className":3532,"style":674},[673],[579,3534,3536,3539,3542,3545,3548],{"className":3535},[644],[579,3537,605],{"className":3538},[715],[579,3540,1300],{"className":3541},[648],[579,3543,3036],{"className":3544},[644],[579,3546,612],{"className":3547},[644,688],[579,3549,1310],{"className":3550},[753],[579,3552,740],{"className":3553},[739],[579,3555,3557],{"className":3556},[661],[579,3558,3560],{"className":3559,"style":3449},[665],[579,3561],{},[579,3563],{"className":3564},[753,649],[579,3566],{"className":3567,"style":757},[731],[579,3569,617],{"className":3570},[761],[579,3572],{"className":3573,"style":757},[731],[579,3575,3577,3580,3583,3586,3589],{"className":3576},[635],[579,3578],{"className":3579,"style":771},[639],[579,3581,3036],{"className":3582},[644],[579,3584],{"className":3585,"style":1901},[731],[579,3587,3329],{"className":3588},[1068],[579,3590],{"className":3591,"style":1901},[731],[579,3593,3595,3598,3601,3604,3607],{"className":3594},[635],[579,3596],{"className":3597,"style":771},[639],[579,3599,621],{"className":3600},[644],[579,3602],{"className":3603,"style":757},[731],[579,3605,3246],{"className":3606},[761],[579,3608],{"className":3609,"style":757},[731],[579,3611,3613,3616],{"className":3612},[635],[579,3614],{"className":3615,"style":771},[639],[579,3617,3036],{"className":3618},[644],[565,3620,3621,3853,3854,4060],{},[579,3622,3624,3674],{"className":3623},[582],[579,3625,3627],{"className":3626},[586],[588,3628,3629],{"xmlns":590},[592,3630,3631,3671],{},[595,3632,3633,3649],{},[3007,3634,3635,3641],{},[595,3636,3637,3639],{},[603,3638,3013],{},[607,3640,609],{},[595,3642,3643,3645,3647],{},[603,3644,612],{},[607,3646,617],{},[619,3648,794],{},[598,3650,3651,3664],{},[595,3652,3653,3655,3657,3660,3662],{},[619,3654,621],{},[607,3656,956],{},[603,3658,3659],{},"cos",[607,3661,609],{},[603,3663,612],{},[947,3665,3666,3668],{},[603,3667,612],{},[619,3669,3670],{},"2",[623,3672,3673],{"encoding":625},"\\lim_{x \\to 0} \\frac{1 - \\cos x}{x^2}",[579,3675,3677],{"className":3676,"ariaHidden":631},[630],[579,3678,3680,3684,3733,3736],{"className":3679},[635],[579,3681],{"className":3682,"style":3683},[639],"height:1.1901em;vertical-align:-0.345em;",[579,3685,3687,3690],{"className":3686},[715],[579,3688,3013],{"className":3689},[715],[579,3691,3693],{"className":3692},[1039],[579,3694,3696,3725],{"className":3695},[656,657],[579,3697,3699,3722],{"className":3698},[661],[579,3700,3702],{"className":3701,"style":3073},[665],[579,3703,3704,3707],{"style":3076},[579,3705],{"className":3706,"style":1210},[673],[579,3708,3710],{"className":3709},[678,679,680,681],[579,3711,3713,3716,3719],{"className":3712},[644,681],[579,3714,612],{"className":3715},[644,688,681],[579,3717,617],{"className":3718},[761,681],[579,3720,794],{"className":3721},[644,681],[579,3723,740],{"className":3724},[739],[579,3726,3728],{"className":3727},[661],[579,3729,3731],{"className":3730,"style":3104},[665],[579,3732],{},[579,3734],{"className":3735,"style":872},[731],[579,3737,3739,3742,3850],{"className":3738},[644],[579,3740],{"className":3741},[648,649],[579,3743,3745],{"className":3744},[598],[579,3746,3748,3842],{"className":3747},[656,657],[579,3749,3751,3839],{"className":3750},[661],[579,3752,3754,3795,3803],{"className":3753,"style":1926},[665],[579,3755,3756,3759],{"style":669},[579,3757],{"className":3758,"style":674},[673],[579,3760,3762],{"className":3761},[678,679,680,681],[579,3763,3765],{"className":3764},[644,681],[579,3766,3768,3771],{"className":3767},[644,681],[579,3769,612],{"className":3770},[644,688,681],[579,3772,3774],{"className":3773},[1039],[579,3775,3777],{"className":3776},[656],[579,3778,3780],{"className":3779},[661],[579,3781,3784],{"className":3782,"style":3783},[665],"height:0.7463em;",[579,3785,3786,3789],{"style":2342},[579,3787],{"className":3788,"style":1056},[673],[579,3790,3792],{"className":3791},[678,1060,1061,681],[579,3793,3670],{"className":3794},[644,681],[579,3796,3797,3800],{"style":691},[579,3798],{"className":3799,"style":674},[673],[579,3801],{"className":3802,"style":699},[698],[579,3804,3805,3808],{"style":702},[579,3806],{"className":3807,"style":674},[673],[579,3809,3811],{"className":3810},[678,679,680,681],[579,3812,3814,3817,3820,3833,3836],{"className":3813},[644,681],[579,3815,621],{"className":3816},[644,681],[579,3818,956],{"className":3819},[1068,681],[579,3821,3823,3826,3830],{"className":3822},[715,681],[579,3824,1659],{"className":3825},[681],[579,3827,3829],{"className":3828},[681],"o",[579,3831,719],{"className":3832},[681],[579,3834],{"className":3835,"style":732},[731,681],[579,3837,612],{"className":3838},[644,688,681],[579,3840,740],{"className":3841},[739],[579,3843,3845],{"className":3844},[661],[579,3846,3848],{"className":3847,"style":747},[665],[579,3849],{},[579,3851],{"className":3852},[753,649],": Mit ",[579,3855,3857,3899],{"className":3856},[582],[579,3858,3860],{"className":3859},[586],[588,3861,3862],{"xmlns":590},[592,3863,3864,3896],{},[595,3865,3866,3868,3870,3872,3874,3876,3878,3880,3890],{},[619,3867,621],{},[607,3869,956],{},[603,3871,3659],{},[607,3873,609],{},[603,3875,612],{},[607,3877,3246],{},[619,3879,3670],{},[947,3881,3882,3888],{},[595,3883,3884,3886],{},[603,3885,605],{},[607,3887,609],{},[619,3889,3670],{},[598,3891,3892,3894],{},[603,3893,612],{},[619,3895,3670],{},[623,3897,3898],{"encoding":625},"1 - \\cos x = 2\\sin^2\\frac{x}{2}",[579,3900,3902,3921,3945],{"className":3901,"ariaHidden":631},[630],[579,3903,3905,3909,3912,3915,3918],{"className":3904},[635],[579,3906],{"className":3907,"style":3908},[639],"height:0.7278em;vertical-align:-0.0833em;",[579,3910,621],{"className":3911},[644],[579,3913],{"className":3914,"style":1901},[731],[579,3916,956],{"className":3917},[1068],[579,3919],{"className":3920,"style":1901},[731],[579,3922,3924,3927,3930,3933,3936,3939,3942],{"className":3923},[635],[579,3925],{"className":3926,"style":807},[639],[579,3928,3659],{"className":3929},[715],[579,3931],{"className":3932,"style":872},[731],[579,3934,612],{"className":3935},[644,688],[579,3937],{"className":3938,"style":757},[731],[579,3940,3246],{"className":3941},[761],[579,3943],{"className":3944,"style":757},[731],[579,3946,3948,3952,3955,3958,3989,3992],{"className":3947},[635],[579,3949],{"className":3950,"style":3951},[639],"height:1.2169em;vertical-align:-0.345em;",[579,3953,3670],{"className":3954},[644],[579,3956],{"className":3957,"style":872},[731],[579,3959,3961,3964],{"className":3960},[715],[579,3962,605],{"className":3963},[715],[579,3965,3967],{"className":3966},[1039],[579,3968,3970],{"className":3969},[656],[579,3971,3973],{"className":3972},[661],[579,3974,3977],{"className":3975,"style":3976},[665],"height:0.8719em;",[579,3978,3980,3983],{"style":3979},"top:-3.1208em;margin-right:0.05em;",[579,3981],{"className":3982,"style":1210},[673],[579,3984,3986],{"className":3985},[678,679,680,681],[579,3987,3670],{"className":3988},[644,681],[579,3990],{"className":3991,"style":872},[731],[579,3993,3995,3998,4057],{"className":3994},[644],[579,3996],{"className":3997},[648,649],[579,3999,4001],{"className":4000},[598],[579,4002,4004,4049],{"className":4003},[656,657],[579,4005,4007,4046],{"className":4006},[661],[579,4008,4010,4024,4032],{"className":4009,"style":2121},[665],[579,4011,4012,4015],{"style":669},[579,4013],{"className":4014,"style":674},[673],[579,4016,4018],{"className":4017},[678,679,680,681],[579,4019,4021],{"className":4020},[644,681],[579,4022,3670],{"className":4023},[644,681],[579,4025,4026,4029],{"style":691},[579,4027],{"className":4028,"style":674},[673],[579,4030],{"className":4031,"style":699},[698],[579,4033,4034,4037],{"style":702},[579,4035],{"className":4036,"style":674},[673],[579,4038,4040],{"className":4039},[678,679,680,681],[579,4041,4043],{"className":4042},[644,681],[579,4044,612],{"className":4045},[644,688,681],[579,4047,740],{"className":4048},[739],[579,4050,4052],{"className":4051},[661],[579,4053,4055],{"className":4054,"style":747},[665],[579,4056],{},[579,4058],{"className":4059},[753,649]," wird daraus",[579,4062,4064],{"className":4063},[3291],[579,4065,4067,4153],{"className":4066},[582],[579,4068,4070],{"className":4069},[586],[588,4071,4072],{"xmlns":590,"display":3300},[592,4073,4074,4150],{},[595,4075,4076,4104,4106,4112,4142,4144],{},[598,4077,4078,4098],{},[595,4079,4080,4082,4092],{},[619,4081,3670],{},[947,4083,4084,4090],{},[595,4085,4086,4088],{},[603,4087,605],{},[607,4089,609],{},[619,4091,3670],{},[598,4093,4094,4096],{},[603,4095,612],{},[619,4097,3670],{},[947,4099,4100,4102],{},[603,4101,612],{},[619,4103,3670],{},[607,4105,3246],{},[598,4107,4108,4110],{},[619,4109,621],{},[619,4111,3670],{},[947,4113,4114,4140],{},[595,4115,4116,4118,4138],{},[607,4117,1300],{"fence":631},[598,4119,4120,4132],{},[595,4121,4122,4124,4126],{},[603,4123,605],{},[607,4125,609],{},[598,4127,4128,4130],{},[603,4129,612],{},[619,4131,3670],{},[598,4133,4134,4136],{},[603,4135,612],{},[619,4137,3670],{},[607,4139,1310],{"fence":631},[619,4141,3670],{},[607,4143,617],{},[598,4145,4146,4148],{},[619,4147,621],{},[619,4149,3670],{},[623,4151,4152],{"encoding":625},"\\frac{2\\sin^2 \\frac{x}{2}}{x^2} = \\frac{1}{2} \\left( \\frac{\\sin \\frac{x}{2}}{\\frac{x}{2}} \\right)^2 \\to \\frac{1}{2}",[579,4154,4156,4367,4692],{"className":4155,"ariaHidden":631},[630],[579,4157,4159,4163,4358,4361,4364],{"className":4158},[635],[579,4160],{"className":4161,"style":4162},[639],"height:2.2929em;vertical-align:-0.686em;",[579,4164,4166,4169,4355],{"className":4165},[644],[579,4167],{"className":4168},[648,649],[579,4170,4172],{"className":4171},[598],[579,4173,4175,4347],{"className":4174},[656,657],[579,4176,4178,4344],{"className":4177},[661],[579,4179,4182,4221,4229],{"className":4180,"style":4181},[665],"height:1.6069em;",[579,4183,4184,4187],{"style":3398},[579,4185],{"className":4186,"style":674},[673],[579,4188,4190],{"className":4189},[644],[579,4191,4193,4196],{"className":4192},[644],[579,4194,612],{"className":4195},[644,688],[579,4197,4199],{"className":4198},[1039],[579,4200,4202],{"className":4201},[656],[579,4203,4205],{"className":4204},[661],[579,4206,4209],{"className":4207,"style":4208},[665],"height:0.7401em;",[579,4210,4212,4215],{"style":4211},"top:-2.989em;margin-right:0.05em;",[579,4213],{"className":4214,"style":1210},[673],[579,4216,4218],{"className":4217},[678,679,680,681],[579,4219,3670],{"className":4220},[644,681],[579,4222,4223,4226],{"style":691},[579,4224],{"className":4225,"style":674},[673],[579,4227],{"className":4228,"style":699},[698],[579,4230,4232,4235],{"style":4231},"top:-3.735em;",[579,4233],{"className":4234,"style":674},[673],[579,4236,4238,4241,4244,4273,4276],{"className":4237},[644],[579,4239,3670],{"className":4240},[644],[579,4242],{"className":4243,"style":872},[731],[579,4245,4247,4250],{"className":4246},[715],[579,4248,605],{"className":4249},[715],[579,4251,4253],{"className":4252},[1039],[579,4254,4256],{"className":4255},[656],[579,4257,4259],{"className":4258},[661],[579,4260,4262],{"className":4261,"style":3976},[665],[579,4263,4264,4267],{"style":3979},[579,4265],{"className":4266,"style":1210},[673],[579,4268,4270],{"className":4269},[678,679,680,681],[579,4271,3670],{"className":4272},[644,681],[579,4274],{"className":4275,"style":872},[731],[579,4277,4279,4282,4341],{"className":4278},[644],[579,4280],{"className":4281},[648,649],[579,4283,4285],{"className":4284},[598],[579,4286,4288,4333],{"className":4287},[656,657],[579,4289,4291,4330],{"className":4290},[661],[579,4292,4294,4308,4316],{"className":4293,"style":2121},[665],[579,4295,4296,4299],{"style":669},[579,4297],{"className":4298,"style":674},[673],[579,4300,4302],{"className":4301},[678,679,680,681],[579,4303,4305],{"className":4304},[644,681],[579,4306,3670],{"className":4307},[644,681],[579,4309,4310,4313],{"style":691},[579,4311],{"className":4312,"style":674},[673],[579,4314],{"className":4315,"style":699},[698],[579,4317,4318,4321],{"style":702},[579,4319],{"className":4320,"style":674},[673],[579,4322,4324],{"className":4323},[678,679,680,681],[579,4325,4327],{"className":4326},[644,681],[579,4328,612],{"className":4329},[644,688,681],[579,4331,740],{"className":4332},[739],[579,4334,4336],{"className":4335},[661],[579,4337,4339],{"className":4338,"style":747},[665],[579,4340],{},[579,4342],{"className":4343},[753,649],[579,4345,740],{"className":4346},[739],[579,4348,4350],{"className":4349},[661],[579,4351,4353],{"className":4352,"style":3449},[665],[579,4354],{},[579,4356],{"className":4357},[753,649],[579,4359],{"className":4360,"style":757},[731],[579,4362,3246],{"className":4363},[761],[579,4365],{"className":4366,"style":757},[731],[579,4368,4370,4374,4437,4440,4683,4686,4689],{"className":4369},[635],[579,4371],{"className":4372,"style":4373},[639],"height:2.685em;vertical-align:-1.031em;",[579,4375,4377,4380,4434],{"className":4376},[644],[579,4378],{"className":4379},[648,649],[579,4381,4383],{"className":4382},[598],[579,4384,4386,4426],{"className":4385},[656,657],[579,4387,4389,4423],{"className":4388},[661],[579,4390,4393,4404,4412],{"className":4391,"style":4392},[665],"height:1.3214em;",[579,4394,4395,4398],{"style":3398},[579,4396],{"className":4397,"style":674},[673],[579,4399,4401],{"className":4400},[644],[579,4402,3670],{"className":4403},[644],[579,4405,4406,4409],{"style":691},[579,4407],{"className":4408,"style":674},[673],[579,4410],{"className":4411,"style":699},[698],[579,4413,4414,4417],{"style":3418},[579,4415],{"className":4416,"style":674},[673],[579,4418,4420],{"className":4419},[644],[579,4421,621],{"className":4422},[644],[579,4424,740],{"className":4425},[739],[579,4427,4429],{"className":4428},[661],[579,4430,4432],{"className":4431,"style":3449},[665],[579,4433],{},[579,4435],{"className":4436},[753,649],[579,4438],{"className":4439,"style":872},[731],[579,4441,4443,4658],{"className":4442},[1882],[579,4444,4446,4452,4652],{"className":4445},[1882],[579,4447,4449],{"className":4448,"style":1890},[648,1889],[579,4450,1300],{"className":4451},[1894,680],[579,4453,4455,4458,4649],{"className":4454},[644],[579,4456],{"className":4457},[648,649],[579,4459,4461],{"className":4460},[598],[579,4462,4464,4640],{"className":4463},[656,657],[579,4465,4467,4637],{"className":4466},[661],[579,4468,4471,4547,4555],{"className":4469,"style":4470},[665],"height:1.4304em;",[579,4472,4473,4476],{"style":3398},[579,4474],{"className":4475,"style":674},[673],[579,4477,4479],{"className":4478},[644],[579,4480,4482,4485,4544],{"className":4481},[644],[579,4483],{"className":4484},[648,649],[579,4486,4488],{"className":4487},[598],[579,4489,4491,4536],{"className":4490},[656,657],[579,4492,4494,4533],{"className":4493},[661],[579,4495,4497,4511,4519],{"className":4496,"style":2121},[665],[579,4498,4499,4502],{"style":669},[579,4500],{"className":4501,"style":674},[673],[579,4503,4505],{"className":4504},[678,679,680,681],[579,4506,4508],{"className":4507},[644,681],[579,4509,3670],{"className":4510},[644,681],[579,4512,4513,4516],{"style":691},[579,4514],{"className":4515,"style":674},[673],[579,4517],{"className":4518,"style":699},[698],[579,4520,4521,4524],{"style":702},[579,4522],{"className":4523,"style":674},[673],[579,4525,4527],{"className":4526},[678,679,680,681],[579,4528,4530],{"className":4529},[644,681],[579,4531,612],{"className":4532},[644,688,681],[579,4534,740],{"className":4535},[739],[579,4537,4539],{"className":4538},[661],[579,4540,4542],{"className":4541,"style":747},[665],[579,4543],{},[579,4545],{"className":4546},[753,649],[579,4548,4549,4552],{"style":691},[579,4550],{"className":4551,"style":674},[673],[579,4553],{"className":4554,"style":699},[698],[579,4556,4557,4560],{"style":4231},[579,4558],{"className":4559,"style":674},[673],[579,4561,4563,4566,4569],{"className":4562},[644],[579,4564,605],{"className":4565},[715],[579,4567],{"className":4568,"style":872},[731],[579,4570,4572,4575,4634],{"className":4571},[644],[579,4573],{"className":4574},[648,649],[579,4576,4578],{"className":4577},[598],[579,4579,4581,4626],{"className":4580},[656,657],[579,4582,4584,4623],{"className":4583},[661],[579,4585,4587,4601,4609],{"className":4586,"style":2121},[665],[579,4588,4589,4592],{"style":669},[579,4590],{"className":4591,"style":674},[673],[579,4593,4595],{"className":4594},[678,679,680,681],[579,4596,4598],{"className":4597},[644,681],[579,4599,3670],{"className":4600},[644,681],[579,4602,4603,4606],{"style":691},[579,4604],{"className":4605,"style":674},[673],[579,4607],{"className":4608,"style":699},[698],[579,4610,4611,4614],{"style":702},[579,4612],{"className":4613,"style":674},[673],[579,4615,4617],{"className":4616},[678,679,680,681],[579,4618,4620],{"className":4619},[644,681],[579,4621,612],{"className":4622},[644,688,681],[579,4624,740],{"className":4625},[739],[579,4627,4629],{"className":4628},[661],[579,4630,4632],{"className":4631,"style":747},[665],[579,4633],{},[579,4635],{"className":4636},[753,649],[579,4638,740],{"className":4639},[739],[579,4641,4643],{"className":4642},[661],[579,4644,4647],{"className":4645,"style":4646},[665],"height:1.031em;",[579,4648],{},[579,4650],{"className":4651},[753,649],[579,4653,4655],{"className":4654,"style":1890},[753,1889],[579,4656,1310],{"className":4657},[1894,680],[579,4659,4661],{"className":4660},[1039],[579,4662,4664],{"className":4663},[656],[579,4665,4667],{"className":4666},[661],[579,4668,4671],{"className":4669,"style":4670},[665],"height:1.654em;",[579,4672,4674,4677],{"style":4673},"top:-3.9029em;margin-right:0.05em;",[579,4675],{"className":4676,"style":1210},[673],[579,4678,4680],{"className":4679},[678,679,680,681],[579,4681,3670],{"className":4682},[644,681],[579,4684],{"className":4685,"style":757},[731],[579,4687,617],{"className":4688},[761],[579,4690],{"className":4691,"style":757},[731],[579,4693,4695,4699],{"className":4694},[635],[579,4696],{"className":4697,"style":4698},[639],"height:2.0074em;vertical-align:-0.686em;",[579,4700,4702,4705,4758],{"className":4701},[644],[579,4703],{"className":4704},[648,649],[579,4706,4708],{"className":4707},[598],[579,4709,4711,4750],{"className":4710},[656,657],[579,4712,4714,4747],{"className":4713},[661],[579,4715,4717,4728,4736],{"className":4716,"style":4392},[665],[579,4718,4719,4722],{"style":3398},[579,4720],{"className":4721,"style":674},[673],[579,4723,4725],{"className":4724},[644],[579,4726,3670],{"className":4727},[644],[579,4729,4730,4733],{"style":691},[579,4731],{"className":4732,"style":674},[673],[579,4734],{"className":4735,"style":699},[698],[579,4737,4738,4741],{"style":3418},[579,4739],{"className":4740,"style":674},[673],[579,4742,4744],{"className":4743},[644],[579,4745,621],{"className":4746},[644],[579,4748,740],{"className":4749},[739],[579,4751,4753],{"className":4752},[661],[579,4754,4756],{"className":4755,"style":3449},[665],[579,4757],{},[579,4759],{"className":4760},[753,649],[565,4762,4763,4866,4867,4895,4896,4948,4949,927],{},[579,4764,4766,4784],{"className":4765},[582],[579,4767,4769],{"className":4768},[586],[588,4770,4771],{"xmlns":590},[592,4772,4773,4781],{},[595,4774,4775],{},[1455,4776,4777,4779],{},[603,4778,727],{},[603,4780,727],{},[623,4782,4783],{"encoding":625},"\\sqrt[n]{n}",[579,4785,4787],{"className":4786,"ariaHidden":631},[630],[579,4788,4790,4793],{"className":4789},[635],[579,4791],{"className":4792,"style":1477},[639],[579,4794,4796,4822],{"className":4795},[644,1481],[579,4797,4799],{"className":4798},[1485],[579,4800,4802],{"className":4801},[656],[579,4803,4805],{"className":4804},[661],[579,4806,4808],{"className":4807,"style":1495},[665],[579,4809,4810,4813],{"style":1498},[579,4811],{"className":4812,"style":1056},[673],[579,4814,4816],{"className":4815},[678,679,1061,681],[579,4817,4819],{"className":4818},[644,681],[579,4820,727],{"className":4821},[644,688,681],[579,4823,4825,4858],{"className":4824},[656,657],[579,4826,4828,4855],{"className":4827},[661],[579,4829,4831,4843],{"className":4830,"style":1520},[665],[579,4832,4834,4837],{"className":4833,"style":1525},[1524],[579,4835],{"className":4836,"style":674},[673],[579,4838,4840],{"className":4839,"style":1532},[644],[579,4841,727],{"className":4842},[644,688],[579,4844,4845,4848],{"style":1538},[579,4846],{"className":4847,"style":674},[673],[579,4849,4851],{"className":4850,"style":1546},[1545],[1548,4852,4853],{"xmlns":1550,"width":1551,"height":1552,"viewBox":1553,"preserveAspectRatio":1554},[1556,4854],{"d":1558},[579,4856,740],{"className":4857},[739],[579,4859,4861],{"className":4860},[661],[579,4862,4864],{"className":4863,"style":1568},[665],[579,4865],{}," nähert sich ",[579,4868,4870,4883],{"className":4869},[582],[579,4871,4873],{"className":4872},[586],[588,4874,4875],{"xmlns":590},[592,4876,4877,4881],{},[595,4878,4879],{},[619,4880,621],{},[623,4882,621],{"encoding":625},[579,4884,4886],{"className":4885,"ariaHidden":631},[630],[579,4887,4889,4892],{"className":4888},[635],[579,4890],{"className":4891,"style":771},[639],[579,4893,621],{"className":4894},[644]," nur langsam: Für ",[579,4897,4899,4918],{"className":4898},[582],[579,4900,4902],{"className":4901},[586],[588,4903,4904],{"xmlns":590},[592,4905,4906,4915],{},[595,4907,4908,4910,4912],{},[603,4909,727],{},[607,4911,3246],{},[619,4913,4914],{},"1000",[623,4916,4917],{"encoding":625},"n = 1000",[579,4919,4921,4939],{"className":4920,"ariaHidden":631},[630],[579,4922,4924,4927,4930,4933,4936],{"className":4923},[635],[579,4925],{"className":4926,"style":807},[639],[579,4928,727],{"className":4929},[644,688],[579,4931],{"className":4932,"style":757},[731],[579,4934,3246],{"className":4935},[761],[579,4937],{"className":4938,"style":757},[731],[579,4940,4942,4945],{"className":4941},[635],[579,4943],{"className":4944,"style":771},[639],[579,4946,4914],{"className":4947},[644]," ist ",[579,4950,4952,4975],{"className":4951},[582],[579,4953,4955],{"className":4954},[586],[588,4956,4957],{"xmlns":590},[592,4958,4959,4972],{},[595,4960,4961,4967,4969],{},[1455,4962,4963,4965],{},[619,4964,4914],{},[619,4966,4914],{},[607,4968,850],{},[619,4970,4971],{},"1,0069",[623,4973,4974],{"encoding":625},"\\sqrt[1000]{1000} \\approx 1{,}0069",[579,4976,4978,5072],{"className":4977,"ariaHidden":631},[630],[579,4979,4981,4985,5063,5066,5069],{"className":4980},[635],[579,4982],{"className":4983,"style":4984},[639],"height:1.04em;vertical-align:-0.1328em;",[579,4986,4988,5016],{"className":4987},[644,1481],[579,4989,4991],{"className":4990},[1485],[579,4992,4994],{"className":4993},[656],[579,4995,4997],{"className":4996},[661],[579,4998,5001],{"className":4999,"style":5000},[665],"height:0.7869em;",[579,5002,5004,5007],{"style":5003},"top:-2.9647em;",[579,5005],{"className":5006,"style":1056},[673],[579,5008,5010],{"className":5009},[678,679,1061,681],[579,5011,5013],{"className":5012},[644,681],[579,5014,4914],{"className":5015},[644,681],[579,5017,5019,5054],{"className":5018},[656,657],[579,5020,5022,5051],{"className":5021},[661],[579,5023,5026,5038],{"className":5024,"style":5025},[665],"height:0.9072em;",[579,5027,5029,5032],{"className":5028,"style":1525},[1524],[579,5030],{"className":5031,"style":674},[673],[579,5033,5035],{"className":5034,"style":1532},[644],[579,5036,4914],{"className":5037},[644],[579,5039,5041,5044],{"style":5040},"top:-2.8672em;",[579,5042],{"className":5043,"style":674},[673],[579,5045,5047],{"className":5046,"style":1546},[1545],[1548,5048,5049],{"xmlns":1550,"width":1551,"height":1552,"viewBox":1553,"preserveAspectRatio":1554},[1556,5050],{"d":1558},[579,5052,740],{"className":5053},[739],[579,5055,5057],{"className":5056},[661],[579,5058,5061],{"className":5059,"style":5060},[665],"height:0.1328em;",[579,5062],{},[579,5064],{"className":5065,"style":757},[731],[579,5067,850],{"className":5068},[761],[579,5070],{"className":5071,"style":757},[731],[579,5073,5075,5079,5082,5090],{"className":5074},[635],[579,5076],{"className":5077,"style":5078},[639],"height:0.8389em;vertical-align:-0.1944em;",[579,5080,621],{"className":5081},[644],[579,5083,5085],{"className":5084},[644],[579,5086,5089],{"className":5087},[5088],"mpunct",",",[579,5091,5093],{"className":5092},[644],"0069",[565,5095,5096,5257,5258,5310,5311,5386,5387,5502],{},[579,5097,5099,5125],{"className":5098},[582],[579,5100,5102],{"className":5101},[586],[588,5103,5104],{"xmlns":590},[592,5105,5106,5122],{},[595,5107,5108],{},[598,5109,5110,5116],{},[947,5111,5112,5114],{},[603,5113,612],{},[619,5115,3036],{},[947,5117,5118,5120],{},[603,5119,951],{},[603,5121,612],{},[623,5123,5124],{"encoding":625},"\\frac{x^3}{e^x}",[579,5126,5128],{"className":5127,"ariaHidden":631},[630],[579,5129,5131,5135],{"className":5130},[635],[579,5132],{"className":5133,"style":5134},[639],"height:1.3629em;vertical-align:-0.345em;",[579,5136,5138,5141,5254],{"className":5137},[644],[579,5139],{"className":5140},[648,649],[579,5142,5144],{"className":5143},[598],[579,5145,5147,5246],{"className":5146},[656,657],[579,5148,5150,5243],{"className":5149},[661],[579,5151,5154,5194,5202],{"className":5152,"style":5153},[665],"height:1.0179em;",[579,5155,5156,5159],{"style":669},[579,5157],{"className":5158,"style":674},[673],[579,5160,5162],{"className":5161},[678,679,680,681],[579,5163,5165],{"className":5164},[644,681],[579,5166,5168,5171],{"className":5167},[644,681],[579,5169,951],{"className":5170},[644,688,681],[579,5172,5174],{"className":5173},[1039],[579,5175,5177],{"className":5176},[656],[579,5178,5180],{"className":5179},[661],[579,5181,5183],{"className":5182,"style":2339},[665],[579,5184,5185,5188],{"style":2342},[579,5186],{"className":5187,"style":1056},[673],[579,5189,5191],{"className":5190},[678,1060,1061,681],[579,5192,612],{"className":5193},[644,688,681],[579,5195,5196,5199],{"style":691},[579,5197],{"className":5198,"style":674},[673],[579,5200],{"className":5201,"style":699},[698],[579,5203,5204,5207],{"style":702},[579,5205],{"className":5206,"style":674},[673],[579,5208,5210],{"className":5209},[678,679,680,681],[579,5211,5213],{"className":5212},[644,681],[579,5214,5216,5219],{"className":5215},[644,681],[579,5217,612],{"className":5218},[644,688,681],[579,5220,5222],{"className":5221},[1039],[579,5223,5225],{"className":5224},[656],[579,5226,5228],{"className":5227},[661],[579,5229,5232],{"className":5230,"style":5231},[665],"height:0.8913em;",[579,5233,5234,5237],{"style":1052},[579,5235],{"className":5236,"style":1056},[673],[579,5238,5240],{"className":5239},[678,1060,1061,681],[579,5241,3036],{"className":5242},[644,681],[579,5244,740],{"className":5245},[739],[579,5247,5249],{"className":5248},[661],[579,5250,5252],{"className":5251,"style":747},[665],[579,5253],{},[579,5255],{"className":5256},[753,649]," ist für ",[579,5259,5261,5280],{"className":5260},[582],[579,5262,5264],{"className":5263},[586],[588,5265,5266],{"xmlns":590},[592,5267,5268,5277],{},[595,5269,5270,5272,5274],{},[603,5271,612],{},[607,5273,3246],{},[619,5275,5276],{},"100",[623,5278,5279],{"encoding":625},"x = 100",[579,5281,5283,5301],{"className":5282,"ariaHidden":631},[630],[579,5284,5286,5289,5292,5295,5298],{"className":5285},[635],[579,5287],{"className":5288,"style":807},[639],[579,5290,612],{"className":5291},[644,688],[579,5293],{"className":5294,"style":757},[731],[579,5296,3246],{"className":5297},[761],[579,5299],{"className":5300,"style":757},[731],[579,5302,5304,5307],{"className":5303},[635],[579,5305],{"className":5306,"style":771},[639],[579,5308,5276],{"className":5309},[644]," schon kleiner als ",[579,5312,5314,5338],{"className":5313},[582],[579,5315,5317],{"className":5316},[586],[588,5318,5319],{"xmlns":590},[592,5320,5321,5335],{},[595,5322,5323],{},[947,5324,5325,5328],{},[619,5326,5327],{},"10",[595,5329,5330,5332],{},[607,5331,956],{},[619,5333,5334],{},"30",[623,5336,5337],{"encoding":625},"10^{-30}",[579,5339,5341],{"className":5340,"ariaHidden":631},[630],[579,5342,5344,5348,5351],{"className":5343},[635],[579,5345],{"className":5346,"style":5347},[639],"height:0.8141em;",[579,5349,621],{"className":5350},[644],[579,5352,5354,5357],{"className":5353},[644],[579,5355,794],{"className":5356},[644],[579,5358,5360],{"className":5359},[1039],[579,5361,5363],{"className":5362},[656],[579,5364,5366],{"className":5365},[661],[579,5367,5369],{"className":5368,"style":5347},[665],[579,5370,5371,5374],{"style":1206},[579,5372],{"className":5373,"style":1210},[673],[579,5375,5377],{"className":5376},[678,679,680,681],[579,5378,5380,5383],{"className":5379},[644,681],[579,5381,956],{"className":5382},[644,681],[579,5384,5334],{"className":5385},[644,681],", obwohl ",[579,5388,5390,5417],{"className":5389},[582],[579,5391,5393],{"className":5392},[586],[588,5394,5395],{"xmlns":590},[592,5396,5397,5414],{},[595,5398,5399,5405,5407],{},[947,5400,5401,5403],{},[603,5402,612],{},[619,5404,3036],{},[607,5406,3246],{},[947,5408,5409,5411],{},[619,5410,5327],{},[619,5412,5413],{},"6",[623,5415,5416],{"encoding":625},"x^3 = 10^6",[579,5418,5420,5464],{"className":5419,"ariaHidden":631},[630],[579,5421,5423,5426,5455,5458,5461],{"className":5422},[635],[579,5424],{"className":5425,"style":5347},[639],[579,5427,5429,5432],{"className":5428},[644],[579,5430,612],{"className":5431},[644,688],[579,5433,5435],{"className":5434},[1039],[579,5436,5438],{"className":5437},[656],[579,5439,5441],{"className":5440},[661],[579,5442,5444],{"className":5443,"style":5347},[665],[579,5445,5446,5449],{"style":1206},[579,5447],{"className":5448,"style":1210},[673],[579,5450,5452],{"className":5451},[678,679,680,681],[579,5453,3036],{"className":5454},[644,681],[579,5456],{"className":5457,"style":757},[731],[579,5459,3246],{"className":5460},[761],[579,5462],{"className":5463,"style":757},[731],[579,5465,5467,5470,5473],{"className":5466},[635],[579,5468],{"className":5469,"style":5347},[639],[579,5471,621],{"className":5472},[644],[579,5474,5476,5479],{"className":5475},[644],[579,5477,794],{"className":5478},[644],[579,5480,5482],{"className":5481},[1039],[579,5483,5485],{"className":5484},[656],[579,5486,5488],{"className":5487},[661],[579,5489,5491],{"className":5490,"style":5347},[665],[579,5492,5493,5496],{"style":1206},[579,5494],{"className":5495,"style":1210},[673],[579,5497,5499],{"className":5498},[678,679,680,681],[579,5500,5413],{"className":5501},[644,681]," ist.",[560,5504,5506],{"id":5505},"typische-fehler","Typische Fehler",[573,5508,5509,5921,6257,6876],{},[576,5510,5511,5630,5631,4948,5686,5768,5769,5891,5892,5920],{},[579,5512,5514,5538],{"className":5513},[582],[579,5515,5517],{"className":5516},[586],[588,5518,5519],{"xmlns":590},[592,5520,5521,5535],{},[595,5522,5523],{},[598,5524,5525,5533],{},[595,5526,5527,5529,5531],{},[603,5528,605],{},[607,5530,609],{},[603,5532,612],{},[603,5534,612],{},[623,5536,5537],{"encoding":625},"\\frac{\\sin x}{x}",[579,5539,5541],{"className":5540,"ariaHidden":631},[630],[579,5542,5544,5547],{"className":5543},[635],[579,5545],{"className":5546,"style":640},[639],[579,5548,5550,5553,5627],{"className":5549},[644],[579,5551],{"className":5552},[648,649],[579,5554,5556],{"className":5555},[598],[579,5557,5559,5619],{"className":5558},[656,657],[579,5560,5562,5616],{"className":5561},[661],[579,5563,5565,5579,5587],{"className":5564,"style":666},[665],[579,5566,5567,5570],{"style":669},[579,5568],{"className":5569,"style":674},[673],[579,5571,5573],{"className":5572},[678,679,680,681],[579,5574,5576],{"className":5575},[644,681],[579,5577,612],{"className":5578},[644,688,681],[579,5580,5581,5584],{"style":691},[579,5582],{"className":5583,"style":674},[673],[579,5585],{"className":5586,"style":699},[698],[579,5588,5589,5592],{"style":702},[579,5590],{"className":5591,"style":674},[673],[579,5593,5595],{"className":5594},[678,679,680,681],[579,5596,5598,5610,5613],{"className":5597},[644,681],[579,5599,5601,5604,5607],{"className":5600},[715,681],[579,5602,719],{"className":5603},[681],[579,5605,723],{"className":5606},[681],[579,5608,727],{"className":5609},[681],[579,5611],{"className":5612,"style":732},[731,681],[579,5614,612],{"className":5615},[644,688,681],[579,5617,740],{"className":5618},[739],[579,5620,5622],{"className":5621},[661],[579,5623,5625],{"className":5624,"style":747},[665],[579,5626],{},[579,5628],{"className":5629},[753,649]," im Gradmaß auswerten. Für ",[579,5632,5634,5655],{"className":5633},[582],[579,5635,5637],{"className":5636},[586],[588,5638,5639],{"xmlns":590},[592,5640,5641,5652],{},[595,5642,5643,5645,5647,5649],{},[603,5644,612],{},[607,5646,3246],{},[619,5648,621],{},[603,5650,5651],{"mathvariant":1607},"°",[623,5653,5654],{"encoding":625},"x = 1°",[579,5656,5658,5676],{"className":5657,"ariaHidden":631},[630],[579,5659,5661,5664,5667,5670,5673],{"className":5660},[635],[579,5662],{"className":5663,"style":807},[639],[579,5665,612],{"className":5666},[644,688],[579,5668],{"className":5669,"style":757},[731],[579,5671,3246],{"className":5672},[761],[579,5674],{"className":5675,"style":757},[731],[579,5677,5679,5682],{"className":5678},[635],[579,5680],{"className":5681,"style":2511},[639],[579,5683,5685],{"className":5684},[644],"1°",[579,5687,5689,5718],{"className":5688},[582],[579,5690,5692],{"className":5691},[586],[588,5693,5694],{"xmlns":590},[592,5695,5696,5715],{},[595,5697,5698,5700,5702,5704,5706,5708,5710,5712],{},[603,5699,605],{},[607,5701,609],{},[607,5703,1300],{"stretchy":1299},[619,5705,621],{},[603,5707,5651],{"mathvariant":1607},[607,5709,1310],{"stretchy":1299},[607,5711,850],{},[619,5713,5714],{},"0,0175",[623,5716,5717],{"encoding":625},"\\sin(1°) \\approx 0{,}0175",[579,5719,5721,5749],{"className":5720,"ariaHidden":631},[630],[579,5722,5724,5728,5731,5734,5737,5740,5743,5746],{"className":5723},[635],[579,5725],{"className":5726,"style":5727},[639],"height:1em;vertical-align:-0.25em;",[579,5729,605],{"className":5730},[715],[579,5732,1300],{"className":5733},[648],[579,5735,5685],{"className":5736},[644],[579,5738,1310],{"className":5739},[753],[579,5741],{"className":5742,"style":757},[731],[579,5744,850],{"className":5745},[761],[579,5747],{"className":5748,"style":757},[731],[579,5750,5752,5755,5758,5764],{"className":5751},[635],[579,5753],{"className":5754,"style":5078},[639],[579,5756,794],{"className":5757},[644],[579,5759,5761],{"className":5760},[644],[579,5762,5089],{"className":5763},[5088],[579,5765,5767],{"className":5766},[644],"0175",", der Quotient ",[579,5770,5772,5798],{"className":5771},[582],[579,5773,5775],{"className":5774},[586],[588,5776,5777],{"xmlns":590},[592,5778,5779,5795],{},[595,5780,5781],{},[598,5782,5783,5793],{},[595,5784,5785,5787,5789,5791],{},[603,5786,605],{},[607,5788,609],{},[619,5790,621],{},[603,5792,5651],{"mathvariant":1607},[619,5794,621],{},[623,5796,5797],{"encoding":625},"\\frac{\\sin 1°}{1}",[579,5799,5801],{"className":5800,"ariaHidden":631},[630],[579,5802,5804,5808],{"className":5803},[635],[579,5805],{"className":5806,"style":5807},[639],"height:1.2251em;vertical-align:-0.345em;",[579,5809,5811,5814,5888],{"className":5810},[644],[579,5812],{"className":5813},[648,649],[579,5815,5817],{"className":5816},[598],[579,5818,5820,5880],{"className":5819},[656,657],[579,5821,5823,5877],{"className":5822},[661],[579,5824,5826,5840,5848],{"className":5825,"style":2581},[665],[579,5827,5828,5831],{"style":669},[579,5829],{"className":5830,"style":674},[673],[579,5832,5834],{"className":5833},[678,679,680,681],[579,5835,5837],{"className":5836},[644,681],[579,5838,621],{"className":5839},[644,681],[579,5841,5842,5845],{"style":691},[579,5843],{"className":5844,"style":674},[673],[579,5846],{"className":5847,"style":699},[698],[579,5849,5850,5853],{"style":702},[579,5851],{"className":5852,"style":674},[673],[579,5854,5856],{"className":5855},[678,679,680,681],[579,5857,5859,5871,5874],{"className":5858},[644,681],[579,5860,5862,5865,5868],{"className":5861},[715,681],[579,5863,719],{"className":5864},[681],[579,5866,723],{"className":5867},[681],[579,5869,727],{"className":5870},[681],[579,5872],{"className":5873,"style":732},[731,681],[579,5875,5685],{"className":5876},[644,681],[579,5878,740],{"className":5879},[739],[579,5881,5883],{"className":5882},[661],[579,5884,5886],{"className":5885,"style":747},[665],[579,5887],{},[579,5889],{"className":5890},[753,649]," ist also weit von ",[579,5893,5895,5908],{"className":5894},[582],[579,5896,5898],{"className":5897},[586],[588,5899,5900],{"xmlns":590},[592,5901,5902,5906],{},[595,5903,5904],{},[619,5905,621],{},[623,5907,621],{"encoding":625},[579,5909,5911],{"className":5910,"ariaHidden":631},[630],[579,5912,5914,5917],{"className":5913},[635],[579,5915],{"className":5916,"style":771},[639],[579,5918,621],{"className":5919},[644]," entfernt.",[576,5922,5923,6063,6064,6114,6115,6256],{},[579,5924,5926,5953],{"className":5925},[582],[579,5927,5929],{"className":5928},[586],[588,5930,5931],{"xmlns":590},[592,5932,5933,5951],{},[595,5934,5935,5947,5949],{},[598,5936,5937,5945],{},[595,5938,5939,5941,5943],{},[603,5940,605],{},[607,5942,609],{},[603,5944,612],{},[603,5946,612],{},[607,5948,617],{},[619,5950,621],{},[623,5952,626],{"encoding":625},[579,5954,5956,6054],{"className":5955,"ariaHidden":631},[630],[579,5957,5959,5962,6045,6048,6051],{"className":5958},[635],[579,5960],{"className":5961,"style":640},[639],[579,5963,5965,5968,6042],{"className":5964},[644],[579,5966],{"className":5967},[648,649],[579,5969,5971],{"className":5970},[598],[579,5972,5974,6034],{"className":5973},[656,657],[579,5975,5977,6031],{"className":5976},[661],[579,5978,5980,5994,6002],{"className":5979,"style":666},[665],[579,5981,5982,5985],{"style":669},[579,5983],{"className":5984,"style":674},[673],[579,5986,5988],{"className":5987},[678,679,680,681],[579,5989,5991],{"className":5990},[644,681],[579,5992,612],{"className":5993},[644,688,681],[579,5995,5996,5999],{"style":691},[579,5997],{"className":5998,"style":674},[673],[579,6000],{"className":6001,"style":699},[698],[579,6003,6004,6007],{"style":702},[579,6005],{"className":6006,"style":674},[673],[579,6008,6010],{"className":6009},[678,679,680,681],[579,6011,6013,6025,6028],{"className":6012},[644,681],[579,6014,6016,6019,6022],{"className":6015},[715,681],[579,6017,719],{"className":6018},[681],[579,6020,723],{"className":6021},[681],[579,6023,727],{"className":6024},[681],[579,6026],{"className":6027,"style":732},[731,681],[579,6029,612],{"className":6030},[644,688,681],[579,6032,740],{"className":6033},[739],[579,6035,6037],{"className":6036},[661],[579,6038,6040],{"className":6039,"style":747},[665],[579,6041],{},[579,6043],{"className":6044},[753,649],[579,6046],{"className":6047,"style":757},[731],[579,6049,617],{"className":6050},[761],[579,6052],{"className":6053,"style":757},[731],[579,6055,6057,6060],{"className":6056},[635],[579,6058],{"className":6059,"style":771},[639],[579,6061,621],{"className":6062},[644]," auch für ",[579,6065,6067,6084],{"className":6066},[582],[579,6068,6070],{"className":6069},[586],[588,6071,6072],{"xmlns":590},[592,6073,6074,6082],{},[595,6075,6076,6078,6080],{},[603,6077,612],{},[607,6079,617],{},[603,6081,1608],{"mathvariant":1607},[623,6083,2454],{"encoding":625},[579,6085,6087,6105],{"className":6086,"ariaHidden":631},[630],[579,6088,6090,6093,6096,6099,6102],{"className":6089},[635],[579,6091],{"className":6092,"style":807},[639],[579,6094,612],{"className":6095},[644,688],[579,6097],{"className":6098,"style":757},[731],[579,6100,617],{"className":6101},[761],[579,6103],{"className":6104,"style":757},[731],[579,6106,6108,6111],{"className":6107},[635],[579,6109],{"className":6110,"style":807},[639],[579,6112,1608],{"className":6113},[644]," annehmen. Dort gilt ",[579,6116,6118,6146],{"className":6117},[582],[579,6119,6121],{"className":6120},[586],[588,6122,6123],{"xmlns":590},[592,6124,6125,6143],{},[595,6126,6127,6139,6141],{},[598,6128,6129,6137],{},[595,6130,6131,6133,6135],{},[603,6132,605],{},[607,6134,609],{},[603,6136,612],{},[603,6138,612],{},[607,6140,617],{},[619,6142,794],{},[623,6144,6145],{"encoding":625},"\\frac{\\sin x}{x} \\to 0",[579,6147,6149,6247],{"className":6148,"ariaHidden":631},[630],[579,6150,6152,6155,6238,6241,6244],{"className":6151},[635],[579,6153],{"className":6154,"style":640},[639],[579,6156,6158,6161,6235],{"className":6157},[644],[579,6159],{"className":6160},[648,649],[579,6162,6164],{"className":6163},[598],[579,6165,6167,6227],{"className":6166},[656,657],[579,6168,6170,6224],{"className":6169},[661],[579,6171,6173,6187,6195],{"className":6172,"style":666},[665],[579,6174,6175,6178],{"style":669},[579,6176],{"className":6177,"style":674},[673],[579,6179,6181],{"className":6180},[678,679,680,681],[579,6182,6184],{"className":6183},[644,681],[579,6185,612],{"className":6186},[644,688,681],[579,6188,6189,6192],{"style":691},[579,6190],{"className":6191,"style":674},[673],[579,6193],{"className":6194,"style":699},[698],[579,6196,6197,6200],{"style":702},[579,6198],{"className":6199,"style":674},[673],[579,6201,6203],{"className":6202},[678,679,680,681],[579,6204,6206,6218,6221],{"className":6205},[644,681],[579,6207,6209,6212,6215],{"className":6208},[715,681],[579,6210,719],{"className":6211},[681],[579,6213,723],{"className":6214},[681],[579,6216,727],{"className":6217},[681],[579,6219],{"className":6220,"style":732},[731,681],[579,6222,612],{"className":6223},[644,688,681],[579,6225,740],{"className":6226},[739],[579,6228,6230],{"className":6229},[661],[579,6231,6233],{"className":6232,"style":747},[665],[579,6234],{},[579,6236],{"className":6237},[753,649],[579,6239],{"className":6240,"style":757},[731],[579,6242,617],{"className":6243},[761],[579,6245],{"className":6246,"style":757},[731],[579,6248,6250,6253],{"className":6249},[635],[579,6251],{"className":6252,"style":771},[639],[579,6254,794],{"className":6255},[644],", weil der Zähler beschränkt ist.",[576,6258,6259,6384,6385,6413,6414,6512,6513,6541,6542,6737,6738,927],{},[579,6260,6262,6284],{"className":6261},[582],[579,6263,6265],{"className":6264},[586],[588,6266,6267],{"xmlns":590},[592,6268,6269,6281],{},[595,6270,6271,6277,6279],{},[1455,6272,6273,6275],{},[603,6274,727],{},[603,6276,727],{},[607,6278,617],{},[603,6280,1608],{"mathvariant":1607},[623,6282,6283],{"encoding":625},"\\sqrt[n]{n} \\to \\infty",[579,6285,6287,6375],{"className":6286,"ariaHidden":631},[630],[579,6288,6290,6293,6366,6369,6372],{"className":6289},[635],[579,6291],{"className":6292,"style":1477},[639],[579,6294,6296,6322],{"className":6295},[644,1481],[579,6297,6299],{"className":6298},[1485],[579,6300,6302],{"className":6301},[656],[579,6303,6305],{"className":6304},[661],[579,6306,6308],{"className":6307,"style":1495},[665],[579,6309,6310,6313],{"style":1498},[579,6311],{"className":6312,"style":1056},[673],[579,6314,6316],{"className":6315},[678,679,1061,681],[579,6317,6319],{"className":6318},[644,681],[579,6320,727],{"className":6321},[644,688,681],[579,6323,6325,6358],{"className":6324},[656,657],[579,6326,6328,6355],{"className":6327},[661],[579,6329,6331,6343],{"className":6330,"style":1520},[665],[579,6332,6334,6337],{"className":6333,"style":1525},[1524],[579,6335],{"className":6336,"style":674},[673],[579,6338,6340],{"className":6339,"style":1532},[644],[579,6341,727],{"className":6342},[644,688],[579,6344,6345,6348],{"style":1538},[579,6346],{"className":6347,"style":674},[673],[579,6349,6351],{"className":6350,"style":1546},[1545],[1548,6352,6353],{"xmlns":1550,"width":1551,"height":1552,"viewBox":1553,"preserveAspectRatio":1554},[1556,6354],{"d":1558},[579,6356,740],{"className":6357},[739],[579,6359,6361],{"className":6360},[661],[579,6362,6364],{"className":6363,"style":1568},[665],[579,6365],{},[579,6367],{"className":6368,"style":757},[731],[579,6370,617],{"className":6371},[761],[579,6373],{"className":6374,"style":757},[731],[579,6376,6378,6381],{"className":6377},[635],[579,6379],{"className":6380,"style":807},[639],[579,6382,1608],{"className":6383},[644]," vermuten, weil ",[579,6386,6388,6401],{"className":6387},[582],[579,6389,6391],{"className":6390},[586],[588,6392,6393],{"xmlns":590},[592,6394,6395,6399],{},[595,6396,6397],{},[603,6398,727],{},[623,6400,727],{"encoding":625},[579,6402,6404],{"className":6403,"ariaHidden":631},[630],[579,6405,6407,6410],{"className":6406},[635],[579,6408],{"className":6409,"style":807},[639],[579,6411,727],{"className":6412},[644,688]," wächst. Der Exponent ",[579,6415,6417,6435],{"className":6416},[582],[579,6418,6420],{"className":6419},[586],[588,6421,6422],{"xmlns":590},[592,6423,6424,6432],{},[595,6425,6426],{},[598,6427,6428,6430],{},[619,6429,621],{},[603,6431,727],{},[623,6433,6434],{"encoding":625},"\\frac{1}{n}",[579,6436,6438],{"className":6437,"ariaHidden":631},[630],[579,6439,6441,6444],{"className":6440},[635],[579,6442],{"className":6443,"style":3683},[639],[579,6445,6447,6450,6509],{"className":6446},[644],[579,6448],{"className":6449},[648,649],[579,6451,6453],{"className":6452},[598],[579,6454,6456,6501],{"className":6455},[656,657],[579,6457,6459,6498],{"className":6458},[661],[579,6460,6462,6476,6484],{"className":6461,"style":1926},[665],[579,6463,6464,6467],{"style":669},[579,6465],{"className":6466,"style":674},[673],[579,6468,6470],{"className":6469},[678,679,680,681],[579,6471,6473],{"className":6472},[644,681],[579,6474,727],{"className":6475},[644,688,681],[579,6477,6478,6481],{"style":691},[579,6479],{"className":6480,"style":674},[673],[579,6482],{"className":6483,"style":699},[698],[579,6485,6486,6489],{"style":702},[579,6487],{"className":6488,"style":674},[673],[579,6490,6492],{"className":6491},[678,679,680,681],[579,6493,6495],{"className":6494},[644,681],[579,6496,621],{"className":6497},[644,681],[579,6499,740],{"className":6500},[739],[579,6502,6504],{"className":6503},[661],[579,6505,6507],{"className":6506,"style":747},[665],[579,6508],{},[579,6510],{"className":6511},[753,649]," geht schneller gegen ",[579,6514,6516,6529],{"className":6515},[582],[579,6517,6519],{"className":6518},[586],[588,6520,6521],{"xmlns":590},[592,6522,6523,6527],{},[595,6524,6525],{},[619,6526,794],{},[623,6528,794],{"encoding":625},[579,6530,6532],{"className":6531,"ariaHidden":631},[630],[579,6533,6535,6538],{"className":6534},[635],[579,6536],{"className":6537,"style":771},[639],[579,6539,794],{"className":6540},[644],": ",[579,6543,6545,6586],{"className":6544},[582],[579,6546,6548],{"className":6547},[586],[588,6549,6550],{"xmlns":590},[592,6551,6552,6583],{},[595,6553,6554,6560,6562],{},[1455,6555,6556,6558],{},[603,6557,727],{},[603,6559,727],{},[607,6561,3246],{},[947,6563,6564,6566],{},[603,6565,951],{},[595,6567,6568,6570,6572,6574,6576,6578,6581],{},[603,6569,1294],{},[607,6571,609],{},[607,6573,1300],{"stretchy":1299},[603,6575,727],{},[607,6577,1310],{"stretchy":1299},[603,6579,6580],{"mathvariant":1607},"\u002F",[603,6582,727],{},[623,6584,6585],{"encoding":625},"\\sqrt[n]{n} = e^{\\ln(n)\u002Fn}",[579,6587,6589,6677],{"className":6588,"ariaHidden":631},[630],[579,6590,6592,6595,6668,6671,6674],{"className":6591},[635],[579,6593],{"className":6594,"style":1477},[639],[579,6596,6598,6624],{"className":6597},[644,1481],[579,6599,6601],{"className":6600},[1485],[579,6602,6604],{"className":6603},[656],[579,6605,6607],{"className":6606},[661],[579,6608,6610],{"className":6609,"style":1495},[665],[579,6611,6612,6615],{"style":1498},[579,6613],{"className":6614,"style":1056},[673],[579,6616,6618],{"className":6617},[678,679,1061,681],[579,6619,6621],{"className":6620},[644,681],[579,6622,727],{"className":6623},[644,688,681],[579,6625,6627,6660],{"className":6626},[656,657],[579,6628,6630,6657],{"className":6629},[661],[579,6631,6633,6645],{"className":6632,"style":1520},[665],[579,6634,6636,6639],{"className":6635,"style":1525},[1524],[579,6637],{"className":6638,"style":674},[673],[579,6640,6642],{"className":6641,"style":1532},[644],[579,6643,727],{"className":6644},[644,688],[579,6646,6647,6650],{"style":1538},[579,6648],{"className":6649,"style":674},[673],[579,6651,6653],{"className":6652,"style":1546},[1545],[1548,6654,6655],{"xmlns":1550,"width":1551,"height":1552,"viewBox":1553,"preserveAspectRatio":1554},[1556,6656],{"d":1558},[579,6658,740],{"className":6659},[739],[579,6661,6663],{"className":6662},[661],[579,6664,6666],{"className":6665,"style":1568},[665],[579,6667],{},[579,6669],{"className":6670,"style":757},[731],[579,6672,3246],{"className":6673},[761],[579,6675],{"className":6676,"style":757},[731],[579,6678,6680,6684],{"className":6679},[635],[579,6681],{"className":6682,"style":6683},[639],"height:0.888em;",[579,6685,6687,6690],{"className":6686},[644],[579,6688,951],{"className":6689},[644,688],[579,6691,6693],{"className":6692},[1039],[579,6694,6696],{"className":6695},[656],[579,6697,6699],{"className":6698},[661],[579,6700,6702],{"className":6701,"style":6683},[665],[579,6703,6704,6707],{"style":1206},[579,6705],{"className":6706,"style":1210},[673],[579,6708,6710],{"className":6709},[678,679,680,681],[579,6711,6713,6722,6725,6728,6731,6734],{"className":6712},[644,681],[579,6714,6716,6719],{"className":6715},[715,681],[579,6717,1389],{"className":6718},[681],[579,6720,727],{"className":6721},[681],[579,6723,1300],{"className":6724},[648,681],[579,6726,727],{"className":6727},[644,688,681],[579,6729,1310],{"className":6730},[753,681],[579,6732,6580],{"className":6733},[644,681],[579,6735,727],{"className":6736},[644,688,681]," und ",[579,6739,6741,6769],{"className":6740},[582],[579,6742,6744],{"className":6743},[586],[588,6745,6746],{"xmlns":590},[592,6747,6748,6766],{},[595,6749,6750,6762,6764],{},[598,6751,6752,6760],{},[595,6753,6754,6756,6758],{},[603,6755,1294],{},[607,6757,609],{},[603,6759,727],{},[603,6761,727],{},[607,6763,617],{},[619,6765,794],{},[623,6767,6768],{"encoding":625},"\\frac{\\ln n}{n} \\to 0",[579,6770,6772,6867],{"className":6771,"ariaHidden":631},[630],[579,6773,6775,6778,6858,6861,6864],{"className":6774},[635],[579,6776],{"className":6777,"style":5807},[639],[579,6779,6781,6784,6855],{"className":6780},[644],[579,6782],{"className":6783},[648,649],[579,6785,6787],{"className":6786},[598],[579,6788,6790,6847],{"className":6789},[656,657],[579,6791,6793,6844],{"className":6792},[661],[579,6794,6796,6810,6818],{"className":6795,"style":2581},[665],[579,6797,6798,6801],{"style":669},[579,6799],{"className":6800,"style":674},[673],[579,6802,6804],{"className":6803},[678,679,680,681],[579,6805,6807],{"className":6806},[644,681],[579,6808,727],{"className":6809},[644,688,681],[579,6811,6812,6815],{"style":691},[579,6813],{"className":6814,"style":674},[673],[579,6816],{"className":6817,"style":699},[698],[579,6819,6820,6823],{"style":702},[579,6821],{"className":6822,"style":674},[673],[579,6824,6826],{"className":6825},[678,679,680,681],[579,6827,6829,6838,6841],{"className":6828},[644,681],[579,6830,6832,6835],{"className":6831},[715,681],[579,6833,1389],{"className":6834},[681],[579,6836,727],{"className":6837},[681],[579,6839],{"className":6840,"style":732},[731,681],[579,6842,727],{"className":6843},[644,688,681],[579,6845,740],{"className":6846},[739],[579,6848,6850],{"className":6849},[661],[579,6851,6853],{"className":6852,"style":747},[665],[579,6854],{},[579,6856],{"className":6857},[753,649],[579,6859],{"className":6860,"style":757},[731],[579,6862,617],{"className":6863},[761],[579,6865],{"className":6866,"style":757},[731],[579,6868,6870,6873],{"className":6869},[635],[579,6871],{"className":6872,"style":771},[639],[579,6874,794],{"className":6875},[644],[576,6877,6878,6879,7010,7011,7039,7040,7068],{},"Den Grenzwert ",[579,6880,6882,6912],{"className":6881},[582],[579,6883,6885],{"className":6884},[586],[588,6886,6887],{"xmlns":590},[592,6888,6889,6909],{},[595,6890,6891],{},[598,6892,6893,6907],{},[595,6894,6895,6897,6899,6901,6903,6905],{},[603,6896,605],{},[607,6898,609],{},[607,6900,1300],{"stretchy":1299},[619,6902,3036],{},[603,6904,612],{},[607,6906,1310],{"stretchy":1299},[603,6908,612],{},[623,6910,6911],{"encoding":625},"\\frac{\\sin(3x)}{x}",[579,6913,6915],{"className":6914,"ariaHidden":631},[630],[579,6916,6918,6921],{"className":6917},[635],[579,6919],{"className":6920,"style":1329},[639],[579,6922,6924,6927,7007],{"className":6923},[644],[579,6925],{"className":6926},[648,649],[579,6928,6930],{"className":6929},[598],[579,6931,6933,6999],{"className":6932},[656,657],[579,6934,6936,6996],{"className":6935},[661],[579,6937,6939,6953,6961],{"className":6938,"style":1348},[665],[579,6940,6941,6944],{"style":669},[579,6942],{"className":6943,"style":674},[673],[579,6945,6947],{"className":6946},[678,679,680,681],[579,6948,6950],{"className":6949},[644,681],[579,6951,612],{"className":6952},[644,688,681],[579,6954,6955,6958],{"style":691},[579,6956],{"className":6957,"style":674},[673],[579,6959],{"className":6960,"style":699},[698],[579,6962,6963,6966],{"style":1373},[579,6964],{"className":6965,"style":674},[673],[579,6967,6969],{"className":6968},[678,679,680,681],[579,6970,6972,6984,6987,6990,6993],{"className":6971},[644,681],[579,6973,6975,6978,6981],{"className":6974},[715,681],[579,6976,719],{"className":6977},[681],[579,6979,723],{"className":6980},[681],[579,6982,727],{"className":6983},[681],[579,6985,1300],{"className":6986},[648,681],[579,6988,3036],{"className":6989},[644,681],[579,6991,612],{"className":6992},[644,688,681],[579,6994,1310],{"className":6995},[753,681],[579,6997,740],{"className":6998},[739],[579,7000,7002],{"className":7001},[661],[579,7003,7005],{"className":7004,"style":747},[665],[579,7006],{},[579,7008],{"className":7009},[753,649]," mit ",[579,7012,7014,7027],{"className":7013},[582],[579,7015,7017],{"className":7016},[586],[588,7018,7019],{"xmlns":590},[592,7020,7021,7025],{},[595,7022,7023],{},[619,7024,621],{},[623,7026,621],{"encoding":625},[579,7028,7030],{"className":7029,"ariaHidden":631},[630],[579,7031,7033,7036],{"className":7032},[635],[579,7034],{"className":7035,"style":771},[639],[579,7037,621],{"className":7038},[644]," angeben, ohne den Faktor ",[579,7041,7043,7056],{"className":7042},[582],[579,7044,7046],{"className":7045},[586],[588,7047,7048],{"xmlns":590},[592,7049,7050,7054],{},[595,7051,7052],{},[619,7053,3036],{},[623,7055,3036],{"encoding":625},[579,7057,7059],{"className":7058,"ariaHidden":631},[630],[579,7060,7062,7065],{"className":7061},[635],[579,7063],{"className":7064,"style":771},[639],[579,7066,3036],{"className":7067},[644]," auszugleichen.",{"title":7070,"searchDepth":7071,"depth":7071,"links":7072},"",2,[7073,7074,7075],{"id":562,"depth":7071,"text":563},{"id":2990,"depth":7071,"text":2991},{"id":5505,"depth":7071,"text":5506},[7077,7079,7081,7083,7086,7089,7091,7094,7097,7099],{"lhs":7078,"rhs":621},"round(sin(1e-4)\u002F1e-4, 6)",{"lhs":7080,"rhs":621},"round((exp(1e-6) - 1)\u002F1e-6, 5)",{"lhs":7082,"rhs":621},"round(log(1 + 1e-6)\u002F1e-6, 5)",{"lhs":7084,"rhs":7085},"round(1000^(1\u002F1000), 4)","1.0069",{"lhs":7087,"rhs":7088},"3*sin(3*x)\u002F(3*x)","sin(3*x)\u002Fx",{"lhs":7090,"rhs":3036},"round(sin(3*1e-5)\u002F1e-5, 6)",{"lhs":7092,"rhs":7093},"(1 - cos(x))\u002Fx^2","2*sin(x\u002F2)^2\u002Fx^2",{"lhs":7095,"rhs":7096},"round((1 - cos(1e-3))\u002F1e-6, 4)","0.5",{"lhs":7098,"rhs":794},"round(100^3\u002Fexp(100), 9)",{"lhs":7100,"rhs":7101},"round(sin(pi\u002F180), 4)","0.0175",null,"md",{"caption":7105,"x":7106,"y":7109,"unit":7112,"unitY":7113,"ticks":7114,"axes":7116,"items":7117},"Graph von sin x \u002F x; bei x = 0 ist die Funktion nicht definiert, die Werte nähern sich aber 1",[7107,7108],-7.5,7.5,[7110,7111],-0.5,1.45,18,120,[7071,7115],0.5,true,[7118,7123,7128],{"type":7119,"expr":7120,"domain":7121},"function","sin(x)\u002Fx",[7107,7122],6.6,{"type":7124,"at":7125,"open":7116},"point",[7126,7127],0,1,{"type":7129,"at":7130,"text":7133,"upright":7116},"label",[7131,7132],3.6,0.95,"sin x \u002F x","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 270 234\" width=\"270\" height=\"234\" role=\"img\" aria-label=\"Graph von sin x \u002F x; bei x = 0 ist die Funktion nicht definiert, die Werte nähern sich aber 1\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-standard-limits-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-standard-limits-clip\">\u003Crect x=\"0\" y=\"0\" width=\"270\" height=\"234\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cline x1=\"0\" y1=\"174\" x2=\"270\" y2=\"174\" class=\"fig-axis\" marker-end=\"url(#fig-standard-limits-arrow)\"\u002F>\u003Cline x1=\"135\" y1=\"234\" x2=\"135\" y2=\"0\" class=\"fig-axis\" marker-end=\"url(#fig-standard-limits-arrow)\"\u002F>\u003Cline x1=\"27\" y1=\"171\" x2=\"27\" y2=\"177\" class=\"fig-axis\"\u002F>\u003Ctext x=\"30\" y=\"188\" text-anchor=\"start\" class=\"fig-tick\">−6\u003C\u002Ftext>\u003Cline x1=\"63\" y1=\"171\" x2=\"63\" y2=\"177\" class=\"fig-axis\"\u002F>\u003Ctext x=\"66\" y=\"188\" text-anchor=\"start\" class=\"fig-tick\">−4\u003C\u002Ftext>\u003Cline x1=\"99\" y1=\"171\" x2=\"99\" y2=\"177\" class=\"fig-axis\"\u002F>\u003Ctext x=\"102\" y=\"188\" text-anchor=\"start\" class=\"fig-tick\">−2\u003C\u002Ftext>\u003Cline x1=\"171\" y1=\"171\" x2=\"171\" y2=\"177\" class=\"fig-axis\"\u002F>\u003Ctext x=\"174\" y=\"188\" text-anchor=\"start\" class=\"fig-tick\">2\u003C\u002Ftext>\u003Cline x1=\"207\" y1=\"171\" x2=\"207\" y2=\"177\" class=\"fig-axis\"\u002F>\u003Ctext x=\"210\" y=\"188\" text-anchor=\"start\" class=\"fig-tick\">4\u003C\u002Ftext>\u003Cline x1=\"243\" y1=\"171\" x2=\"243\" y2=\"177\" class=\"fig-axis\"\u002F>\u003Ctext x=\"246\" y=\"188\" text-anchor=\"start\" class=\"fig-tick\">6\u003C\u002Ftext>\u003Cline x1=\"132\" y1=\"234\" x2=\"138\" y2=\"234\" class=\"fig-axis\"\u002F>\u003Ctext x=\"129\" y=\"227\" text-anchor=\"end\" dominant-baseline=\"middle\" class=\"fig-tick\">−0,5\u003C\u002Ftext>\u003Cline x1=\"132\" y1=\"114\" x2=\"138\" y2=\"114\" class=\"fig-axis\"\u002F>\u003Ctext x=\"129\" y=\"107\" text-anchor=\"end\" dominant-baseline=\"middle\" class=\"fig-tick\">0,5\u003C\u002Ftext>\u003Cline x1=\"132\" y1=\"54\" x2=\"138\" y2=\"54\" class=\"fig-axis\"\u002F>\u003Ctext x=\"129\" y=\"47\" text-anchor=\"end\" dominant-baseline=\"middle\" class=\"fig-tick\">1\u003C\u002Ftext>\u003Ctext x=\"264\" y=\"162\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">x\u003C\u002Ftext>\u003Ctext x=\"147\" y=\"8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">y\u003C\u002Ftext>\u003Cpath d=\"M 0 158.99 L 1.06 159.23 L 2.11 159.52 L 3.17 159.86 L 4.23 160.27 L 5.29 160.72 L 6.35 161.23 L 7.4 161.79 L 8.46 162.4 L 9.52 163.07 L 10.58 163.78 L 11.63 164.54 L 12.69 165.35 L 13.75 166.2 L 14.8 167.1 L 15.86 168.03 L 16.92 169 L 17.98 170.01 L 19.04 171.05 L 20.09 172.11 L 21.15 173.21 L 22.21 174.32 L 23.27 175.46 L 24.32 176.62 L 25.38 177.78 L 26.44 178.96 L 27.49 180.14 L 28.55 181.33 L 29.61 182.51 L 30.67 183.69 L 31.73 184.85 L 32.78 186.01 L 33.84 187.15 L 34.9 188.26 L 35.95 189.35 L 37.01 190.41 L 38.07 191.43 L 39.13 192.42 L 40.19 193.36 L 41.24 194.26 L 42.3 195.11 L 43.36 195.9 L 44.41 196.63 L 45.47 197.31 L 46.53 197.92 L 47.59 198.46 L 48.65 198.92 L 49.7 199.31 L 50.76 199.63 L 51.82 199.86 L 52.88 200.01 L 53.93 200.07 L 54.99 200.04 L 56.05 199.92 L 57.1 199.7 L 58.16 199.39 L 59.22 198.98 L 60.28 198.47 L 61.33 197.87 L 62.39 197.16 L 63.45 196.35 L 64.51 195.43 L 65.57 194.42 L 66.62 193.3 L 67.68 192.07 L 68.74 190.75 L 69.8 189.32 L 70.85 187.8 L 71.91 186.17 L 72.97 184.44 L 74.02 182.62 L 75.08 180.71 L 76.14 178.7 L 77.2 176.6 L 78.25 174.42 L 79.31 172.14 L 80.37 169.79 L 81.43 167.36 L 82.48 164.86 L 83.54 162.28 L 84.6 159.64 L 85.66 156.94 L 86.72 154.18 L 87.77 151.36 L 88.83 148.49 L 89.89 145.59 L 90.95 142.64 L 92 139.65 L 93.06 136.64 L 94.12 133.61 L 95.18 130.55 L 96.23 127.49 L 97.29 124.41 L 98.35 121.34 L 99.4 118.27 L 100.46 115.21 L 101.52 112.16 L 102.58 109.14 L 103.64 106.15 L 104.69 103.18 L 105.75 100.26 L 106.81 97.38 L 107.87 94.56 L 108.92 91.79 L 109.98 89.08 L 111.04 86.43 L 112.1 83.86 L 113.15 81.37 L 114.21 78.96 L 115.27 76.63 L 116.33 74.4 L 117.38 72.26 L 118.44 70.23 L 119.5 68.29 L 120.56 66.47 L 121.61 64.76 L 122.67 63.17 L 123.73 61.69 L 124.79 60.34 L 125.84 59.11 L 126.9 58.01 L 127.96 57.04 L 129.02 56.2 L 130.07 55.49 L 131.13 54.92 L 132.19 54.49 L 133.25 54.19 L 134.3 54.03 L 135.36 54.01 L 136.42 54.12 L 137.48 54.38 L 138.53 54.77 L 139.59 55.3 L 140.65 55.96 L 141.7 56.76 L 142.76 57.69 L 143.82 58.74 L 144.88 59.93 L 145.94 61.25 L 146.99 62.68 L 148.05 64.24 L 149.11 65.91 L 150.17 67.7 L 151.22 69.6 L 152.28 71.6 L 153.34 73.71 L 154.39 75.91 L 155.45 78.2 L 156.51 80.59 L 157.57 83.06 L 158.63 85.6 L 159.68 88.23 L 160.74 90.91 L 161.8 93.67 L 162.86 96.48 L 163.91 99.34 L 164.97 102.25 L 166.03 105.2 L 167.08 108.18 L 168.14 111.2 L 169.2 114.23 L 170.26 117.29 L 171.32 120.36 L 172.37 123.43 L 173.43 126.51 L 174.49 129.57 L 175.55 132.63 L 176.6 135.67 L 177.66 138.69 L 178.72 141.69 L 179.78 144.65 L 180.83 147.57 L 181.89 150.45 L 182.95 153.28 L 184.01 156.06 L 185.06 158.79 L 186.12 161.45 L 187.18 164.05 L 188.24 166.57 L 189.29 169.03 L 190.35 171.4 L 191.41 173.7 L 192.46 175.91 L 193.52 178.04 L 194.58 180.08 L 195.64 182.02 L 196.7 183.87 L 197.75 185.63 L 198.81 187.29 L 199.87 188.85 L 200.93 190.31 L 201.98 191.66 L 203.04 192.92 L 204.1 194.07 L 205.16 195.12 L 206.21 196.07 L 207.27 196.91 L 208.33 197.65 L 209.38 198.29 L 210.44 198.83 L 211.5 199.27 L 212.56 199.61 L 213.62 199.86 L 214.67 200.01 L 215.73 200.07 L 216.79 200.04 L 217.84 199.92 L 218.9 199.71 L 219.96 199.42 L 221.02 199.06 L 222.08 198.61 L 223.13 198.1 L 224.19 197.51 L 225.25 196.86 L 226.31 196.14 L 227.36 195.36 L 228.42 194.53 L 229.48 193.65 L 230.54 192.72 L 231.59 191.75 L 232.65 190.74 L 233.71 189.69 L 234.77 188.61 L 235.82 187.5 L 236.88 186.37 L 237.94 185.22 L 239 184.06 L 240.05 182.89 L 241.11 181.71 L 242.17 180.52 L 243.23 179.34 L 244.28 178.16 L 245.34 176.99 L 246.4 175.83 L 247.46 174.69 L 248.51 173.56 L 249.57 172.46 L 250.63 171.38 L 251.68 170.33 L 252.74 169.32 L 253.8 168.34\" class=\"fig-main fig-graph\" clip-path=\"url(#fig-standard-limits-clip)\"\u002F>\u003Ccircle cx=\"135\" cy=\"54\" r=\"3\" class=\"fig-open\"\u002F>\u003Ctext x=\"199.8\" y=\"60\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">sin x \u002F x\u003C\u002Ftext>\u003C\u002Fsvg>","standard-limits","\\lim_{x \\to 0} \\frac{\\sin x}{x} = 1,\\quad \\lim_{x \\to 0} \\frac{e^x - 1}{x} = 1,\\quad \\lim_{n \\to \\infty} \\sqrt[n]{n} = 1","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmunder>\u003Cmrow>\u003Cmi>lim\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>→\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmunder>\u003Cmfrac>\u003Cmrow>\u003Cmi>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"1em\"\u002F>\u003Cmunder>\u003Cmrow>\u003Cmi>lim\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>→\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmunder>\u003Cmfrac>\u003Cmrow>\u003Cmsup>\u003Cmi>e\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"1em\"\u002F>\u003Cmunder>\u003Cmrow>\u003Cmi>lim\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>→\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmunder>\u003Cmroot>\u003Cmi>n\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmroot>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\lim_{x \\to 0} \\frac{\\sin x}{x} = 1,\\quad \\lim_{x \\to 0} \\frac{e^x - 1}{x} = 1,\\quad \\lim_{n \\to \\infty} \\sqrt[n]{n} = 1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.062em;vertical-align:-0.7171em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6944em;\">\u003Cspan style=\"top:-2.3829em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">x\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">→\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop\">lim\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7171em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3449em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mop\">sin\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0585em;vertical-align:-0.7171em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:1em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6944em;\">\u003Cspan style=\"top:-2.3829em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">x\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">→\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop\">lim\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7171em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3414em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">e\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6644em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.5492em;vertical-align:-0.7em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:1em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6944em;\">\u003Cspan style=\"top:-2.4em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">→\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop\">lim\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord sqrt\">\u003Cspan class=\"katex-root\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6103em;\">\u003Cspan style=\"top:-2.895em;\">\u003Cspan class=\"pstrut\" style=\"height:2.5em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size1 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8492em;\">\u003Cspan class=\"svg-align\" style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\" style=\"padding-left:0.833em;\">\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.8092em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"hide-tail\" style=\"min-width:0.853em;height:1.08em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"400em\" height=\"1.08em\" viewBox=\"0 0 400000 1080\" preserveAspectRatio=\"xMinYMin slice\">\u003Cpath d=\"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1908em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fcalculus\u002Fwichtige-grenzwerte",[],[7143,7144,7145,7146],"limit-rules","euler-number-limit","lhopital","sine-series",{"title":548,"description":7070},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fwichtige-grenzwerte","sin x \u002F x und (eˣ − 1)\u002Fx gehen für x → 0 gegen 1, die n-te Wurzel aus n für n → ∞ ebenfalls.",[7151,7152,7153,7154],"grenzwert","standardgrenzwerte","sinus","exponentialfunktion",[7156,7159,7162],{"symbol":612,"meaning":7157,"symbolHtml":7158},"reelle Variable (bei sin im Bogenmaß)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":727,"meaning":7160,"symbolHtml":7161},"natürliche Zahl","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":951,"meaning":7163,"symbolHtml":7164},"Eulersche Zahl, etwa 2,71828","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>e\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">e\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">e\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","9mVOWIo_6dNchkKCDGyWHvjaQSClgWTqvrJoyhvINXs",[7167,7170,7173,7176],{"stem":7168,"title":7169,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fgrenzwertsaetze","Grenzwertsätze",{"stem":7171,"title":7172,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fregel-von-l-hospital","Regel von L’Hospital",{"stem":7174,"title":7175,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Feulersche-zahl-grenzwert","Eulersche Zahl als Grenzwert",{"stem":7177,"title":7178,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fsinusreihe","Potenzreihe des Sinus",1793824284251]