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Ist ",[575,774,776,803],{"className":775},[578],[575,777,779],{"className":778},[582],[584,780,781],{"xmlns":586},[588,782,783,800],{},[591,784,785,787,789,791,793,796],{},[599,786,670],{},[594,788,742],{"stretchy":596},[599,790,709],{},[594,792,747],{"stretchy":596},[594,794,795],{},"=",[797,798,799],"mn",{},"0",[613,801,802],{"encoding":615},"f(m) = 0",[575,804,806,835],{"className":805,"ariaHidden":604},[620],[575,807,809,812,815,818,821,824,828,832],{"className":808},[624],[575,810],{"className":811,"style":629},[628],[575,813,670],{"className":814,"style":686},[637,638],[575,816,742],{"className":817},[633],[575,819,709],{"className":820},[637,638],[575,822,747],{"className":823},[654],[575,825],{"className":826,"style":827},[646],"margin-right:0.2778em;",[575,829,795],{"className":830},[831],"mrel",[575,833],{"className":834,"style":827},[646],[575,836,838,842],{"className":837},[624],[575,839],{"className":840,"style":841},[628],"height:0.6444em;",[575,843,799],{"className":844},[637],", hat man die Nullstelle gefunden.",[563,847,848,849,852,853,882,883,1055,1056,1059,1060,1161,1162,1225],{},"Das Verfahren ist ",[567,850,851],{},"robust",": Es konvergiert immer, wenn die Voraussetzungen erfüllt sind, und braucht keine Ableitung. Dafür ist es langsam. Nach ",[575,854,856,870],{"className":855},[578],[575,857,859],{"className":858},[582],[584,860,861],{"xmlns":586},[588,862,863,868],{},[591,864,865],{},[599,866,867],{},"n",[613,869,867],{"encoding":615},[575,871,873],{"className":872,"ariaHidden":604},[620],[575,874,876,879],{"className":875},[624],[575,877],{"className":878,"style":721},[628],[575,880,867],{"className":881},[637,638]," Schritten ist das Intervall ",[575,884,886,918],{"className":885},[578],[575,887,889],{"className":888},[582],[584,890,891],{"xmlns":586},[588,892,893,915],{},[591,894,895],{},[896,897,898,907],"mfrac",{},[591,899,900,902,905],{},[599,901,608],{},[594,903,904],{},"−",[599,906,601],{},[908,909,910,913],"msup",{},[797,911,912],{},"2",[599,914,867],{},[613,916,917],{"encoding":615},"\\frac{b - a}{2^n}",[575,919,921],{"className":920,"ariaHidden":604},[620],[575,922,924,928],{"className":923},[624],[575,925],{"className":926,"style":927},[628],"height:1.2251em;vertical-align:-0.345em;",[575,929,931,935,1052],{"className":930},[637],[575,932],{"className":933},[633,934],"nulldelimiter",[575,936,938],{"className":937},[896],[575,939,943,1043],{"className":940},[941,942],"vlist-t","vlist-t2",[575,944,947,1038],{"className":945},[946],"vlist-r",[575,948,952,1005,1016],{"className":949,"style":951},[950],"vlist","height:0.8801em;",[575,953,955,960],{"style":954},"top:-2.655em;",[575,956],{"className":957,"style":959},[958],"pstrut","height:3em;",[575,961,967],{"className":962},[963,964,965,966],"sizing","reset-size6","size3","mtight",[575,968,970],{"className":969},[637,966],[575,971,973,976],{"className":972},[637,966],[575,974,912],{"className":975},[637,966],[575,977,980],{"className":978},[979],"msupsub",[575,981,983],{"className":982},[941],[575,984,986],{"className":985},[946],[575,987,990],{"className":988,"style":989},[950],"height:0.5935em;",[575,991,993,997],{"style":992},"top:-2.786em;margin-right:0.0714em;",[575,994],{"className":995,"style":996},[958],"height:2.5em;",[575,998,1002],{"className":999},[963,1000,1001,966],"reset-size3","size1",[575,1003,867],{"className":1004},[637,638,966],[575,1006,1008,1011],{"style":1007},"top:-3.23em;",[575,1009],{"className":1010,"style":959},[958],[575,1012],{"className":1013,"style":1015},[1014],"frac-line","border-bottom-width:0.04em;",[575,1017,1019,1022],{"style":1018},"top:-3.394em;",[575,1020],{"className":1021,"style":959},[958],[575,1023,1025],{"className":1024},[963,964,965,966],[575,1026,1028,1031,1035],{"className":1027},[637,966],[575,1029,608],{"className":1030},[637,638,966],[575,1032,904],{"className":1033},[1034,966],"mbin",[575,1036,601],{"className":1037},[637,638,966],[575,1039,1042],{"className":1040},[1041],"vlist-s","​",[575,1044,1046],{"className":1045},[946],[575,1047,1050],{"className":1048,"style":1049},[950],"height:0.345em;",[575,1051],{},[575,1053],{"className":1054},[654,934]," lang, pro Schritt gewinnt man also nur ein Bit an Genauigkeit (",[567,1057,1058],{},"lineare Konvergenz"," mit Faktor ",[575,1061,1063,1082],{"className":1062},[578],[575,1064,1066],{"className":1065},[582],[584,1067,1068],{"xmlns":586},[588,1069,1070,1079],{},[591,1071,1072],{},[896,1073,1074,1077],{},[797,1075,1076],{},"1",[797,1078,912],{},[613,1080,1081],{"encoding":615},"\\frac{1}{2}",[575,1083,1085],{"className":1084,"ariaHidden":604},[620],[575,1086,1088,1092],{"className":1087},[624],[575,1089],{"className":1090,"style":1091},[628],"height:1.1901em;vertical-align:-0.345em;",[575,1093,1095,1098,1158],{"className":1094},[637],[575,1096],{"className":1097},[633,934],[575,1099,1101],{"className":1100},[896],[575,1102,1104,1150],{"className":1103},[941,942],[575,1105,1107,1147],{"className":1106},[946],[575,1108,1111,1125,1133],{"className":1109,"style":1110},[950],"height:0.8451em;",[575,1112,1113,1116],{"style":954},[575,1114],{"className":1115,"style":959},[958],[575,1117,1119],{"className":1118},[963,964,965,966],[575,1120,1122],{"className":1121},[637,966],[575,1123,912],{"className":1124},[637,966],[575,1126,1127,1130],{"style":1007},[575,1128],{"className":1129,"style":959},[958],[575,1131],{"className":1132,"style":1015},[1014],[575,1134,1135,1138],{"style":1018},[575,1136],{"className":1137,"style":959},[958],[575,1139,1141],{"className":1140},[963,964,965,966],[575,1142,1144],{"className":1143},[637,966],[575,1145,1076],{"className":1146},[637,966],[575,1148,1042],{"className":1149},[1041],[575,1151,1153],{"className":1152},[946],[575,1154,1156],{"className":1155,"style":1049},[950],[575,1157],{},[575,1159],{"className":1160},[654,934],"). Liegen mehrere Nullstellen im Intervall, findet man eine davon. Nullstellen ohne Vorzeichenwechsel, z.B. bei ",[575,1163,1165,1184],{"className":1164},[578],[575,1166,1168],{"className":1167},[582],[584,1169,1170],{"xmlns":586},[588,1171,1172,1181],{},[591,1173,1174],{},[908,1175,1176,1179],{},[599,1177,1178],{},"x",[797,1180,912],{},[613,1182,1183],{"encoding":615},"x^2",[575,1185,1187],{"className":1186,"ariaHidden":604},[620],[575,1188,1190,1194],{"className":1189},[624],[575,1191],{"className":1192,"style":1193},[628],"height:0.8141em;",[575,1195,1197,1200],{"className":1196},[637],[575,1198,1178],{"className":1199},[637,638],[575,1201,1203],{"className":1202},[979],[575,1204,1206],{"className":1205},[941],[575,1207,1209],{"className":1208},[946],[575,1210,1212],{"className":1211,"style":1193},[950],[575,1213,1215,1219],{"style":1214},"top:-3.063em;margin-right:0.05em;",[575,1216],{"className":1217,"style":1218},[958],"height:2.7em;",[575,1220,1222],{"className":1221},[963,964,965,966],[575,1223,912],{"className":1224},[637,966],", findet das Verfahren nicht.",[558,1227,1229],{"id":1228},"beispiele","Beispiele",[563,1231,1232,1233,1353,1354,1406,1407,1502,1503,1593],{},"Nullstelle von ",[575,1234,1236,1268],{"className":1235},[578],[575,1237,1239],{"className":1238},[582],[584,1240,1241],{"xmlns":586},[588,1242,1243,1265],{},[591,1244,1245,1247,1249,1251,1253,1255,1261,1263],{},[599,1246,670],{},[594,1248,742],{"stretchy":596},[599,1250,1178],{},[594,1252,747],{"stretchy":596},[594,1254,795],{},[908,1256,1257,1259],{},[599,1258,1178],{},[797,1260,912],{},[594,1262,904],{},[797,1264,912],{},[613,1266,1267],{"encoding":615},"f(x) = x^2 - 2",[575,1269,1271,1298,1344],{"className":1270,"ariaHidden":604},[620],[575,1272,1274,1277,1280,1283,1286,1289,1292,1295],{"className":1273},[624],[575,1275],{"className":1276,"style":629},[628],[575,1278,670],{"className":1279,"style":686},[637,638],[575,1281,742],{"className":1282},[633],[575,1284,1178],{"className":1285},[637,638],[575,1287,747],{"className":1288},[654],[575,1290],{"className":1291,"style":827},[646],[575,1293,795],{"className":1294},[831],[575,1296],{"className":1297,"style":827},[646],[575,1299,1301,1305,1334,1338,1341],{"className":1300},[624],[575,1302],{"className":1303,"style":1304},[628],"height:0.8974em;vertical-align:-0.0833em;",[575,1306,1308,1311],{"className":1307},[637],[575,1309,1178],{"className":1310},[637,638],[575,1312,1314],{"className":1313},[979],[575,1315,1317],{"className":1316},[941],[575,1318,1320],{"className":1319},[946],[575,1321,1323],{"className":1322,"style":1193},[950],[575,1324,1325,1328],{"style":1214},[575,1326],{"className":1327,"style":1218},[958],[575,1329,1331],{"className":1330},[963,964,965,966],[575,1332,912],{"className":1333},[637,966],[575,1335],{"className":1336,"style":1337},[646],"margin-right:0.2222em;",[575,1339,904],{"className":1340},[1034],[575,1342],{"className":1343,"style":1337},[646],[575,1345,1347,1350],{"className":1346},[624],[575,1348],{"className":1349,"style":841},[628],[575,1351,912],{"className":1352},[637]," auf ",[575,1355,1357,1379],{"className":1356},[578],[575,1358,1360],{"className":1359},[582],[584,1361,1362],{"xmlns":586},[588,1363,1364,1376],{},[591,1365,1366,1368,1370,1372,1374],{},[594,1367,597],{"stretchy":596},[797,1369,1076],{},[594,1371,605],{"separator":604},[797,1373,912],{},[594,1375,611],{"stretchy":596},[613,1377,1378],{"encoding":615},"[1, 2]",[575,1380,1382],{"className":1381,"ariaHidden":604},[620],[575,1383,1385,1388,1391,1394,1397,1400,1403],{"className":1384},[624],[575,1386],{"className":1387,"style":629},[628],[575,1389,597],{"className":1390},[633],[575,1392,1076],{"className":1393},[637],[575,1395,605],{"className":1396},[642],[575,1398],{"className":1399,"style":647},[646],[575,1401,912],{"className":1402},[637],[575,1404,611],{"className":1405},[654],": Es ist ",[575,1408,1410,1441],{"className":1409},[578],[575,1411,1413],{"className":1412},[582],[584,1414,1415],{"xmlns":586},[588,1416,1417,1438],{},[591,1418,1419,1421,1423,1425,1427,1429,1431,1433,1436],{},[599,1420,670],{},[594,1422,742],{"stretchy":596},[797,1424,1076],{},[594,1426,747],{"stretchy":596},[594,1428,795],{},[594,1430,904],{},[797,1432,1076],{},[594,1434,1435],{},"\u003C",[797,1437,799],{},[613,1439,1440],{"encoding":615},"f(1) = -1 \u003C 0",[575,1442,1444,1471,1493],{"className":1443,"ariaHidden":604},[620],[575,1445,1447,1450,1453,1456,1459,1462,1465,1468],{"className":1446},[624],[575,1448],{"className":1449,"style":629},[628],[575,1451,670],{"className":1452,"style":686},[637,638],[575,1454,742],{"className":1455},[633],[575,1457,1076],{"className":1458},[637],[575,1460,747],{"className":1461},[654],[575,1463],{"className":1464,"style":827},[646],[575,1466,795],{"className":1467},[831],[575,1469],{"className":1470,"style":827},[646],[575,1472,1474,1478,1481,1484,1487,1490],{"className":1473},[624],[575,1475],{"className":1476,"style":1477},[628],"height:0.7278em;vertical-align:-0.0833em;",[575,1479,904],{"className":1480},[637],[575,1482,1076],{"className":1483},[637],[575,1485],{"className":1486,"style":827},[646],[575,1488,1435],{"className":1489},[831],[575,1491],{"className":1492,"style":827},[646],[575,1494,1496,1499],{"className":1495},[624],[575,1497],{"className":1498,"style":841},[628],[575,1500,799],{"className":1501},[637]," und ",[575,1504,1506,1535],{"className":1505},[578],[575,1507,1509],{"className":1508},[582],[584,1510,1511],{"xmlns":586},[588,1512,1513,1532],{},[591,1514,1515,1517,1519,1521,1523,1525,1527,1530],{},[599,1516,670],{},[594,1518,742],{"stretchy":596},[797,1520,912],{},[594,1522,747],{"stretchy":596},[594,1524,795],{},[797,1526,912],{},[594,1528,1529],{},">",[797,1531,799],{},[613,1533,1534],{"encoding":615},"f(2) = 2 > 0",[575,1536,1538,1565,1584],{"className":1537,"ariaHidden":604},[620],[575,1539,1541,1544,1547,1550,1553,1556,1559,1562],{"className":1540},[624],[575,1542],{"className":1543,"style":629},[628],[575,1545,670],{"className":1546,"style":686},[637,638],[575,1548,742],{"className":1549},[633],[575,1551,912],{"className":1552},[637],[575,1554,747],{"className":1555},[654],[575,1557],{"className":1558,"style":827},[646],[575,1560,795],{"className":1561},[831],[575,1563],{"className":1564,"style":827},[646],[575,1566,1568,1572,1575,1578,1581],{"className":1567},[624],[575,1569],{"className":1570,"style":1571},[628],"height:0.6835em;vertical-align:-0.0391em;",[575,1573,912],{"className":1574},[637],[575,1576],{"className":1577,"style":827},[646],[575,1579,1529],{"className":1580},[831],[575,1582],{"className":1583,"style":827},[646],[575,1585,1587,1590],{"className":1586},[624],[575,1588],{"className":1589,"style":841},[628],[575,1591,799],{"className":1592},[637],".",[575,1595,1598],{"className":1596},[1597],"katex-display",[575,1599,1601,1959],{"className":1600},[578],[575,1602,1604],{"className":1603},[582],[584,1605,1607],{"xmlns":586,"display":1606},"block",[588,1608,1609,1956],{},[1610,1611,1615,1705,1789,1873],"mtable",{"rowspacing":1612,"columnalign":1613,"columnspacing":1614},"0.25em","right left right left right left","0em 1em 0em 1em 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&= 1{,}5: & f(m) &= 0{,}25 > 0 & &\\Rightarrow [1;\\ 1{,}5] \\\\\nm &= 1{,}25: & f(m) &= -0{,}4375 \u003C 0 & &\\Rightarrow [1{,}25;\\ 1{,}5] \\\\\nm &= 1{,}375: & f(m) &= -0{,}109375 \u003C 0 & &\\Rightarrow [1{,}375;\\ 1{,}5] \\\\\nm &= 1{,}4375: & f(m) &\\approx 0{,}0664 > 0 & &\\Rightarrow [1{,}375;\\ 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Der Mittelpunkt ",[575,3026,3028,3043],{"className":3027},[578],[575,3029,3031],{"className":3030},[582],[584,3032,3033],{"xmlns":586},[588,3034,3035,3040],{},[591,3036,3037],{},[797,3038,3039],{},"1,40625",[613,3041,3042],{"encoding":615},"1{,}40625",[575,3044,3046],{"className":3045,"ariaHidden":604},[620],[575,3047,3049,3052,3055,3061],{"className":3048},[624],[575,3050],{"className":3051,"style":3010},[628],[575,3053,1076],{"className":3054},[637],[575,3056,3058],{"className":3057},[637],[575,3059,605],{"className":3060},[642],[575,3062,3064],{"className":3063},[637],"40625"," weicht höchstens ",[575,3067,3069,3084],{"className":3068},[578],[575,3070,3072],{"className":3071},[582],[584,3073,3074],{"xmlns":586},[588,3075,3076,3081],{},[591,3077,3078],{},[797,3079,3080],{},"0,03125",[613,3082,3083],{"encoding":615},"0{,}03125",[575,3085,3087],{"className":3086,"ariaHidden":604},[620],[575,3088,3090,3093,3096,3102],{"className":3089},[624],[575,3091],{"className":3092,"style":3010},[628],[575,3094,799],{"className":3095},[637],[575,3097,3099],{"className":3098},[637],[575,3100,605],{"className":3101},[642],[575,3103,3105],{"className":3104},[637],"03125"," von ",[575,3108,3110,3127],{"className":3109},[578],[575,3111,3113],{"className":3112},[582],[584,3114,3115],{"xmlns":586},[588,3116,3117,3124],{},[591,3118,3119],{},[3120,3121,3122],"msqrt",{},[797,3123,912],{},[613,3125,3126],{"encoding":615},"\\sqrt{2}",[575,3128,3130],{"className":3129,"ariaHidden":604},[620],[575,3131,3133,3137],{"className":3132},[624],[575,3134],{"className":3135,"style":3136},[628],"height:1.04em;vertical-align:-0.1328em;",[575,3138,3141],{"className":3139},[637,3140],"sqrt",[575,3142,3144,3192],{"className":3143},[941,942],[575,3145,3147,3189],{"className":3146},[946],[575,3148,3151,3166],{"className":3149,"style":3150},[950],"height:0.9072em;",[575,3152,3156,3159],{"className":3153,"style":3155},[3154],"svg-align","top:-3em;",[575,3157],{"className":3158,"style":959},[958],[575,3160,3163],{"className":3161,"style":3162},[637],"padding-left:0.833em;",[575,3164,912],{"className":3165},[637],[575,3167,3169,3172],{"style":3168},"top:-2.8672em;",[575,3170],{"className":3171,"style":959},[958],[575,3173,3177],{"className":3174,"style":3176},[3175],"hide-tail","min-width:0.853em;height:1.08em;",[3178,3179,3185],"svg",{"xmlns":3180,"width":3181,"height":3182,"viewBox":3183,"preserveAspectRatio":3184},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[3186,3187],"path",{"d":3188},"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",[575,3190,1042],{"className":3191},[1041],[575,3193,3195],{"className":3194},[946],[575,3196,3199],{"className":3197,"style":3198},[950],"height:0.1328em;",[575,3200],{}," ab.",[563,3203,3204,3205,3233,3234,3308,3309,3426,3427,3612,3613,3665,3666,3806,3807,1593],{},"Wie viele Schritte braucht man, um ein Intervall der Länge ",[575,3206,3208,3221],{"className":3207},[578],[575,3209,3211],{"className":3210},[582],[584,3212,3213],{"xmlns":586},[588,3214,3215,3219],{},[591,3216,3217],{},[797,3218,1076],{},[613,3220,1076],{"encoding":615},[575,3222,3224],{"className":3223,"ariaHidden":604},[620],[575,3225,3227,3230],{"className":3226},[624],[575,3228],{"className":3229,"style":841},[628],[575,3231,1076],{"className":3232},[637]," auf höchstens ",[575,3235,3237,3261],{"className":3236},[578],[575,3238,3240],{"className":3239},[582],[584,3241,3242],{"xmlns":586},[588,3243,3244,3258],{},[591,3245,3246],{},[908,3247,3248,3251],{},[797,3249,3250],{},"10",[591,3252,3253,3255],{},[594,3254,904],{},[797,3256,3257],{},"6",[613,3259,3260],{"encoding":615},"10^{-6}",[575,3262,3264],{"className":3263,"ariaHidden":604},[620],[575,3265,3267,3270,3273],{"className":3266},[624],[575,3268],{"className":3269,"style":1193},[628],[575,3271,1076],{"className":3272},[637],[575,3274,3276,3279],{"className":3275},[637],[575,3277,799],{"className":3278},[637],[575,3280,3282],{"className":3281},[979],[575,3283,3285],{"className":3284},[941],[575,3286,3288],{"className":3287},[946],[575,3289,3291],{"className":3290,"style":1193},[950],[575,3292,3293,3296],{"style":1214},[575,3294],{"className":3295,"style":1218},[958],[575,3297,3299],{"className":3298},[963,964,965,966],[575,3300,3302,3305],{"className":3301},[637,966],[575,3303,904],{"className":3304},[637,966],[575,3306,3257],{"className":3307},[637,966]," zu verkleinern? Aus ",[575,3310,3312,3339],{"className":3311},[578],[575,3313,3315],{"className":3314},[582],[584,3316,3317],{"xmlns":586},[588,3318,3319,3336],{},[591,3320,3321,3327,3330],{},[908,3322,3323,3325],{},[797,3324,912],{},[599,3326,867],{},[594,3328,3329],{},"≥",[908,3331,3332,3334],{},[797,3333,3250],{},[797,3335,3257],{},[613,3337,3338],{"encoding":615},"2^n \\geq 10^6",[575,3340,3342,3388],{"className":3341,"ariaHidden":604},[620],[575,3343,3345,3349,3379,3382,3385],{"className":3344},[624],[575,3346],{"className":3347,"style":3348},[628],"height:0.8004em;vertical-align:-0.136em;",[575,3350,3352,3355],{"className":3351},[637],[575,3353,912],{"className":3354},[637],[575,3356,3358],{"className":3357},[979],[575,3359,3361],{"className":3360},[941],[575,3362,3364],{"className":3363},[946],[575,3365,3368],{"className":3366,"style":3367},[950],"height:0.6644em;",[575,3369,3370,3373],{"style":1214},[575,3371],{"className":3372,"style":1218},[958],[575,3374,3376],{"className":3375},[963,964,965,966],[575,3377,867],{"className":3378},[637,638,966],[575,3380],{"className":3381,"style":827},[646],[575,3383,3329],{"className":3384},[831],[575,3386],{"className":3387,"style":827},[646],[575,3389,3391,3394,3397],{"className":3390},[624],[575,3392],{"className":3393,"style":1193},[628],[575,3395,1076],{"className":3396},[637],[575,3398,3400,3403],{"className":3399},[637],[575,3401,799],{"className":3402},[637],[575,3404,3406],{"className":3405},[979],[575,3407,3409],{"className":3408},[941],[575,3410,3412],{"className":3411},[946],[575,3413,3415],{"className":3414,"style":1193},[950],[575,3416,3417,3420],{"style":1214},[575,3418],{"className":3419,"style":1218},[958],[575,3421,3423],{"className":3422},[963,964,965,966],[575,3424,3257],{"className":3425},[637,966]," folgt ",[575,3428,3430,3470],{"className":3429},[578],[575,3431,3433],{"className":3432},[582],[584,3434,3435],{"xmlns":586},[588,3436,3437,3467],{},[591,3438,3439,3441,3443,3456,3462,3464],{},[599,3440,867],{},[594,3442,3329],{},[3444,3445,3446,3454],"msub",{},[591,3447,3448,3451],{},[599,3449,3450],{},"log",[594,3452,3453],{},"⁡",[797,3455,912],{},[908,3457,3458,3460],{},[797,3459,3250],{},[797,3461,3257],{},[594,3463,1920],{},[797,3465,3466],{},"19,93",[613,3468,3469],{"encoding":615},"n \\geq \\log_2 10^6 \\approx 19{,}93",[575,3471,3473,3492,3592],{"className":3472,"ariaHidden":604},[620],[575,3474,3476,3480,3483,3486,3489],{"className":3475},[624],[575,3477],{"className":3478,"style":3479},[628],"height:0.7719em;vertical-align:-0.136em;",[575,3481,867],{"className":3482},[637,638],[575,3484],{"className":3485,"style":827},[646],[575,3487,3329],{"className":3488},[831],[575,3490],{"className":3491,"style":827},[646],[575,3493,3495,3499,3548,3551,3554,3583,3586,3589],{"className":3494},[624],[575,3496],{"className":3497,"style":3498},[628],"height:1.0582em;vertical-align:-0.2441em;",[575,3500,3503,3511],{"className":3501},[3502],"mop",[575,3504,3506,3507],{"className":3505},[3502],"lo",[575,3508,3510],{"style":3509},"margin-right:0.0139em;","g",[575,3512,3514],{"className":3513},[979],[575,3515,3517,3539],{"className":3516},[941,942],[575,3518,3520,3536],{"className":3519},[946],[575,3521,3524],{"className":3522,"style":3523},[950],"height:0.207em;",[575,3525,3527,3530],{"style":3526},"top:-2.4559em;margin-right:0.05em;",[575,3528],{"className":3529,"style":1218},[958],[575,3531,3533],{"className":3532},[963,964,965,966],[575,3534,912],{"className":3535},[637,966],[575,3537,1042],{"className":3538},[1041],[575,3540,3542],{"className":3541},[946],[575,3543,3546],{"className":3544,"style":3545},[950],"height:0.2441em;",[575,3547],{},[575,3549],{"className":3550,"style":647},[646],[575,3552,1076],{"className":3553},[637],[575,3555,3557,3560],{"className":3556},[637],[575,3558,799],{"className":3559},[637],[575,3561,3563],{"className":3562},[979],[575,3564,3566],{"className":3565},[941],[575,3567,3569],{"className":3568},[946],[575,3570,3572],{"className":3571,"style":1193},[950],[575,3573,3574,3577],{"style":1214},[575,3575],{"className":3576,"style":1218},[958],[575,3578,3580],{"className":3579},[963,964,965,966],[575,3581,3257],{"className":3582},[637,966],[575,3584],{"className":3585,"style":827},[646],[575,3587,1920],{"className":3588},[831],[575,3590],{"className":3591,"style":827},[646],[575,3593,3595,3598,3602,3608],{"className":3594},[624],[575,3596],{"className":3597,"style":3010},[628],[575,3599,3601],{"className":3600},[637],"19",[575,3603,3605],{"className":3604},[637],[575,3606,605],{"className":3607},[642],[575,3609,3611],{"className":3610},[637],"93",", also ",[575,3614,3616,3635],{"className":3615},[578],[575,3617,3619],{"className":3618},[582],[584,3620,3621],{"xmlns":586},[588,3622,3623,3632],{},[591,3624,3625,3627,3629],{},[599,3626,867],{},[594,3628,795],{},[797,3630,3631],{},"20",[613,3633,3634],{"encoding":615},"n = 20",[575,3636,3638,3656],{"className":3637,"ariaHidden":604},[620],[575,3639,3641,3644,3647,3650,3653],{"className":3640},[624],[575,3642],{"className":3643,"style":721},[628],[575,3645,867],{"className":3646},[637,638],[575,3648],{"className":3649,"style":827},[646],[575,3651,795],{"className":3652},[831],[575,3654],{"className":3655,"style":827},[646],[575,3657,3659,3662],{"className":3658},[624],[575,3660],{"className":3661,"style":841},[628],[575,3663,3631],{"className":3664},[637],". Denn ",[575,3667,3669,3700],{"className":3668},[578],[575,3670,3672],{"className":3671},[582],[584,3673,3674],{"xmlns":586},[588,3675,3676,3697],{},[591,3677,3678,3684,3686,3689,3691],{},[908,3679,3680,3682],{},[797,3681,912],{},[797,3683,3601],{},[594,3685,795],{},[797,3687,3688],{},"524288",[594,3690,1435],{},[908,3692,3693,3695],{},[797,3694,3250],{},[797,3696,3257],{},[613,3698,3699],{"encoding":615},"2^{19} = 524288 \u003C 10^6",[575,3701,3703,3750,3768],{"className":3702,"ariaHidden":604},[620],[575,3704,3706,3709,3741,3744,3747],{"className":3705},[624],[575,3707],{"className":3708,"style":1193},[628],[575,3710,3712,3715],{"className":3711},[637],[575,3713,912],{"className":3714},[637],[575,3716,3718],{"className":3717},[979],[575,3719,3721],{"className":3720},[941],[575,3722,3724],{"className":3723},[946],[575,3725,3727],{"className":3726,"style":1193},[950],[575,3728,3729,3732],{"style":1214},[575,3730],{"className":3731,"style":1218},[958],[575,3733,3735],{"className":3734},[963,964,965,966],[575,3736,3738],{"className":3737},[637,966],[575,3739,3601],{"className":3740},[637,966],[575,3742],{"className":3743,"style":827},[646],[575,3745,795],{"className":3746},[831],[575,3748],{"className":3749,"style":827},[646],[575,3751,3753,3756,3759,3762,3765],{"className":3752},[624],[575,3754],{"className":3755,"style":1571},[628],[575,3757,3688],{"className":3758},[637],[575,3760],{"className":3761,"style":827},[646],[575,3763,1435],{"className":3764},[831],[575,3766],{"className":3767,"style":827},[646],[575,3769,3771,3774,3777],{"className":3770},[624],[575,3772],{"className":3773,"style":1193},[628],[575,3775,1076],{"className":3776},[637],[575,3778,3780,3783],{"className":3779},[637],[575,3781,799],{"className":3782},[637],[575,3784,3786],{"className":3785},[979],[575,3787,3789],{"className":3788},[941],[575,3790,3792],{"className":3791},[946],[575,3793,3795],{"className":3794,"style":1193},[950],[575,3796,3797,3800],{"style":1214},[575,3798],{"className":3799,"style":1218},[958],[575,3801,3803],{"className":3802},[963,964,965,966],[575,3804,3257],{"className":3805},[637,966],", aber ",[575,3808,3810,3841],{"className":3809},[578],[575,3811,3813],{"className":3812},[582],[584,3814,3815],{"xmlns":586},[588,3816,3817,3838],{},[591,3818,3819,3825,3827,3830,3832],{},[908,3820,3821,3823],{},[797,3822,912],{},[797,3824,3631],{},[594,3826,795],{},[797,3828,3829],{},"1048576",[594,3831,3329],{},[908,3833,3834,3836],{},[797,3835,3250],{},[797,3837,3257],{},[613,3839,3840],{"encoding":615},"2^{20} = 1048576 \\geq 10^6",[575,3842,3844,3891,3910],{"className":3843,"ariaHidden":604},[620],[575,3845,3847,3850,3882,3885,3888],{"className":3846},[624],[575,3848],{"className":3849,"style":1193},[628],[575,3851,3853,3856],{"className":3852},[637],[575,3854,912],{"className":3855},[637],[575,3857,3859],{"className":3858},[979],[575,3860,3862],{"className":3861},[941],[575,3863,3865],{"className":3864},[946],[575,3866,3868],{"className":3867,"style":1193},[950],[575,3869,3870,3873],{"style":1214},[575,3871],{"className":3872,"style":1218},[958],[575,3874,3876],{"className":3875},[963,964,965,966],[575,3877,3879],{"className":3878},[637,966],[575,3880,3631],{"className":3881},[637,966],[575,3883],{"className":3884,"style":827},[646],[575,3886,795],{"className":3887},[831],[575,3889],{"className":3890,"style":827},[646],[575,3892,3894,3898,3901,3904,3907],{"className":3893},[624],[575,3895],{"className":3896,"style":3897},[628],"height:0.7804em;vertical-align:-0.136em;",[575,3899,3829],{"className":3900},[637],[575,3902],{"className":3903,"style":827},[646],[575,3905,3329],{"className":3906},[831],[575,3908],{"className":3909,"style":827},[646],[575,3911,3913,3916,3919],{"className":3912},[624],[575,3914],{"className":3915,"style":1193},[628],[575,3917,1076],{"className":3918},[637],[575,3920,3922,3925],{"className":3921},[637],[575,3923,799],{"className":3924},[637],[575,3926,3928],{"className":3927},[979],[575,3929,3931],{"className":3930},[941],[575,3932,3934],{"className":3933},[946],[575,3935,3937],{"className":3936,"style":1193},[950],[575,3938,3939,3942],{"style":1214},[575,3940],{"className":3941,"style":1218},[958],[575,3943,3945],{"className":3944},[963,964,965,966],[575,3946,3257],{"className":3947},[637,966],[558,3949,3951],{"id":3950},"typische-fehler","Typische Fehler",[3953,3954,3955,3959,4067],"ul",{},[3956,3957,3958],"li",{},"Die falsche Hälfte behalten. Entscheidend ist, wo das Vorzeichen wechselt, nicht, welcher Funktionswert kleiner ist.",[3956,3960,3961,3962,4066],{},"Das Verfahren auf ein Intervall ohne Vorzeichenwechsel anwenden. Aus ",[575,3963,3965,4000],{"className":3964},[578],[575,3966,3968],{"className":3967},[582],[584,3969,3970],{"xmlns":586},[588,3971,3972,3997],{},[591,3973,3974,3976,3978,3980,3982,3985,3987,3989,3991,3993,3995],{},[599,3975,670],{},[594,3977,742],{"stretchy":596},[599,3979,601],{},[594,3981,747],{"stretchy":596},[594,3983,3984],{},"⋅",[599,3986,670],{},[594,3988,742],{"stretchy":596},[599,3990,608],{},[594,3992,747],{"stretchy":596},[594,3994,1529],{},[797,3996,799],{},[613,3998,3999],{"encoding":615},"f(a) \\cdot f(b) > 0",[575,4001,4003,4030,4057],{"className":4002,"ariaHidden":604},[620],[575,4004,4006,4009,4012,4015,4018,4021,4024,4027],{"className":4005},[624],[575,4007],{"className":4008,"style":629},[628],[575,4010,670],{"className":4011,"style":686},[637,638],[575,4013,742],{"className":4014},[633],[575,4016,601],{"className":4017},[637,638],[575,4019,747],{"className":4020},[654],[575,4022],{"className":4023,"style":1337},[646],[575,4025,3984],{"className":4026},[1034],[575,4028],{"className":4029,"style":1337},[646],[575,4031,4033,4036,4039,4042,4045,4048,4051,4054],{"className":4032},[624],[575,4034],{"className":4035,"style":629},[628],[575,4037,670],{"className":4038,"style":686},[637,638],[575,4040,742],{"className":4041},[633],[575,4043,608],{"className":4044},[637,638],[575,4046,747],{"className":4047},[654],[575,4049],{"className":4050,"style":827},[646],[575,4052,1529],{"className":4053},[831],[575,4055],{"className":4056,"style":827},[646],[575,4058,4060,4063],{"className":4059},[624],[575,4061],{"className":4062,"style":841},[628],[575,4064,799],{"className":4065},[637]," folgt nicht, dass keine Nullstelle existiert, aber das Verfahren garantiert dann nichts.",[3956,4068,4069,4070,4205,4206,4263],{},"Stetigkeit vergessen: ",[575,4071,4073,4101],{"className":4072},[578],[575,4074,4076],{"className":4075},[582],[584,4077,4078],{"xmlns":586},[588,4079,4080,4098],{},[591,4081,4082,4084,4086,4088,4090,4092],{},[599,4083,670],{},[594,4085,742],{"stretchy":596},[599,4087,1178],{},[594,4089,747],{"stretchy":596},[594,4091,795],{},[896,4093,4094,4096],{},[797,4095,1076],{},[599,4097,1178],{},[613,4099,4100],{"encoding":615},"f(x) = \\frac{1}{x}",[575,4102,4104,4131],{"className":4103,"ariaHidden":604},[620],[575,4105,4107,4110,4113,4116,4119,4122,4125,4128],{"className":4106},[624],[575,4108],{"className":4109,"style":629},[628],[575,4111,670],{"className":4112,"style":686},[637,638],[575,4114,742],{"className":4115},[633],[575,4117,1178],{"className":4118},[637,638],[575,4120,747],{"className":4121},[654],[575,4123],{"className":4124,"style":827},[646],[575,4126,795],{"className":4127},[831],[575,4129],{"className":4130,"style":827},[646],[575,4132,4134,4137],{"className":4133},[624],[575,4135],{"className":4136,"style":1091},[628],[575,4138,4140,4143,4202],{"className":4139},[637],[575,4141],{"className":4142},[633,934],[575,4144,4146],{"className":4145},[896],[575,4147,4149,4194],{"className":4148},[941,942],[575,4150,4152,4191],{"className":4151},[946],[575,4153,4155,4169,4177],{"className":4154,"style":1110},[950],[575,4156,4157,4160],{"style":954},[575,4158],{"className":4159,"style":959},[958],[575,4161,4163],{"className":4162},[963,964,965,966],[575,4164,4166],{"className":4165},[637,966],[575,4167,1178],{"className":4168},[637,638,966],[575,4170,4171,4174],{"style":1007},[575,4172],{"className":4173,"style":959},[958],[575,4175],{"className":4176,"style":1015},[1014],[575,4178,4179,4182],{"style":1018},[575,4180],{"className":4181,"style":959},[958],[575,4183,4185],{"className":4184},[963,964,965,966],[575,4186,4188],{"className":4187},[637,966],[575,4189,1076],{"className":4190},[637,966],[575,4192,1042],{"className":4193},[1041],[575,4195,4197],{"className":4196},[946],[575,4198,4200],{"className":4199,"style":1049},[950],[575,4201],{},[575,4203],{"className":4204},[654,934]," wechselt auf ",[575,4207,4209,4233],{"className":4208},[578],[575,4210,4212],{"className":4211},[582],[584,4213,4214],{"xmlns":586},[588,4215,4216,4230],{},[591,4217,4218,4220,4222,4224,4226,4228],{},[594,4219,597],{"stretchy":596},[594,4221,904],{},[797,4223,1076],{},[594,4225,605],{"separator":604},[797,4227,1076],{},[594,4229,611],{"stretchy":596},[613,4231,4232],{"encoding":615},"[-1, 1]",[575,4234,4236],{"className":4235,"ariaHidden":604},[620],[575,4237,4239,4242,4245,4248,4251,4254,4257,4260],{"className":4238},[624],[575,4240],{"className":4241,"style":629},[628],[575,4243,597],{"className":4244},[633],[575,4246,904],{"className":4247},[637],[575,4249,1076],{"className":4250},[637],[575,4252,605],{"className":4253},[642],[575,4255],{"className":4256,"style":647},[646],[575,4258,1076],{"className":4259},[637],[575,4261,611],{"className":4262},[654]," das Vorzeichen, hat aber keine Nullstelle.",{"title":4265,"searchDepth":4266,"depth":4266,"links":4267},"",2,[4268,4269,4270],{"id":560,"depth":4266,"text":561},{"id":1228,"depth":4266,"text":1229},{"id":3950,"depth":4266,"text":3951},[4272,4275,4278,4280,4283,4286,4289,4292,4295,4298,4300,4302],{"lhs":4273,"rhs":4274},"(b - a)\u002F2^n","(b - a)*0.5^n",{"lhs":4276,"rhs":4277},"1^2 - 2","-1",{"lhs":4279,"rhs":912},"2^2 - 2",{"lhs":4281,"rhs":4282},"1.5^2 - 2","0.25",{"lhs":4284,"rhs":4285},"1.25^2 - 2","-0.4375",{"lhs":4287,"rhs":4288},"1.375^2 - 2","-0.109375",{"lhs":4290,"rhs":4291},"1.4375^2 - 2","0.06640625",{"lhs":4293,"rhs":4294},"(1.375 + 1.4375)\u002F2","1.40625",{"lhs":4296,"rhs":4297},"(2 - 1)\u002F2^4","0.0625",{"lhs":4299,"rhs":3631},"ceil(log(10^6, 2))",{"lhs":4301,"rhs":3829},"2^20",{"lhs":4303,"rhs":3688},"2^19","f \\text{ stetig auf } [a, b],\\ f(a) \\cdot f(b) \u003C 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath 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xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo><\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f(a) \\cdot f(b) < 0\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","bisection-method","m = \\frac{a + b}{2}, \\qquad [a, b] \\to \\begin{cases} [a, m], & f(a) \\cdot f(m) \\leq 0 \\\\ [m, b], & \\text{sonst} \\end{cases}","\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>\u003Cmi>m\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmo stretchy=\"false\">[\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">]\u003C\u002Fmo>\u003Cmo>→\u003C\u002Fmo>\u003Cmrow>\u003Cmo fence=\"true\">{\u003C\u002Fmo>\u003Cmtable rowspacing=\"0.36em\" columnalign=\"left left\" columnspacing=\"1em\">\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\u003Cmo stretchy=\"false\">[\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>m\u003C\u002Fmi>\u003Cmo stretchy=\"false\">]\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>m\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>≤\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\u003Cmo stretchy=\"false\">[\u003C\u002Fmo>\u003Cmi>m\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">]\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmtext>sonst\u003C\u002Fmtext>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003C\u002Fmtable>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">m = \\frac{a + b}{2}, \\qquad [a, b] \\to \\begin{cases} [a, m], & f(a) \\cdot f(m) \\leq 0 \\\\ [m, b], & \\text{sonst} \\end{cases}\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\">m\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:2.0574em;vertical-align:-0.686em;\">\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:1.3714em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan 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