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Dann behält man das Teilintervall, in dem der Vorzeichenwechsel liegt.",[563,870,871,872,900,901,1162,1163,1166,1167,1195],{},"Die Formel für ",[571,873,875,888],{"className":874},[574],[571,876,878],{"className":877},[578],[580,879,880],{"xmlns":582},[584,881,882,886],{},[587,883,884],{},[595,885,852],{},[609,887,852],{"encoding":611},[571,889,891],{"className":890,"ariaHidden":600},[616],[571,892,894,897],{"className":893},[620],[571,895],{"className":896,"style":864},[624],[571,898,852],{"className":899},[633,634]," ist dieselbe wie beim Sekantenverfahren, nur in symmetrischer Form geschrieben: ",[571,902,904,968],{"className":903},[574],[571,905,907],{"className":906},[578],[580,908,909],{"xmlns":582},[584,910,911,965],{},[587,912,913,915,918,920,923,925,927,929,931,934],{},[595,914,852],{},[590,916,917],{},"=",[595,919,597],{},[590,921,922],{},"−",[595,924,666],{},[590,926,698],{"stretchy":592},[595,928,597],{},[590,930,712],{"stretchy":592},[590,932,933],{},"⋅",[935,936,937,945],"mfrac",{},[587,938,939,941,943],{},[595,940,604],{},[590,942,922],{},[595,944,597],{},[587,946,947,949,951,953,955,957,959,961,963],{},[595,948,666],{},[590,950,698],{"stretchy":592},[595,952,604],{},[590,954,712],{"stretchy":592},[590,956,922],{},[595,958,666],{},[590,960,698],{"stretchy":592},[595,962,597],{},[590,964,712],{"stretchy":592},[609,966,967],{"encoding":611},"c = a - f(a) \\cdot \\frac{b - a}{f(b) - f(a)}",[571,969,971,989,1010,1037],{"className":970,"ariaHidden":600},[616],[571,972,974,977,980,983,986],{"className":973},[620],[571,975],{"className":976,"style":864},[624],[571,978,852],{"className":979},[633,634],[571,981],{"className":982,"style":736},[642],[571,984,917],{"className":985},[740],[571,987],{"className":988,"style":736},[642],[571,990,992,996,999,1003,1007],{"className":991},[620],[571,993],{"className":994,"style":995},[624],"height:0.6667em;vertical-align:-0.0833em;",[571,997,597],{"className":998},[633,634],[571,1000],{"className":1001,"style":1002},[642],"margin-right:0.2222em;",[571,1004,922],{"className":1005},[1006],"mbin",[571,1008],{"className":1009,"style":1002},[642],[571,1011,1013,1016,1019,1022,1025,1028,1031,1034],{"className":1012},[620],[571,1014],{"className":1015,"style":625},[624],[571,1017,666],{"className":1018,"style":682},[633,634],[571,1020,698],{"className":1021},[629],[571,1023,597],{"className":1024},[633,634],[571,1026,712],{"className":1027},[650],[571,1029],{"className":1030,"style":1002},[642],[571,1032,933],{"className":1033},[1006],[571,1035],{"className":1036,"style":1002},[642],[571,1038,1040,1044],{"className":1039},[620],[571,1041],{"className":1042,"style":1043},[624],"height:1.4001em;vertical-align:-0.52em;",[571,1045,1047,1051,1159],{"className":1046},[633],[571,1048],{"className":1049},[629,1050],"nulldelimiter",[571,1052,1054],{"className":1053},[935],[571,1055,1059,1150],{"className":1056},[1057,1058],"vlist-t","vlist-t2",[571,1060,1063,1145],{"className":1061},[1062],"vlist-r",[571,1064,1068,1113,1124],{"className":1065,"style":1067},[1066],"vlist","height:0.8801em;",[571,1069,1071,1076],{"style":1070},"top:-2.655em;",[571,1072],{"className":1073,"style":1075},[1074],"pstrut","height:3em;",[571,1077,1083],{"className":1078},[1079,1080,1081,1082],"sizing","reset-size6","size3","mtight",[571,1084,1086,1089,1092,1095,1098,1101,1104,1107,1110],{"className":1085},[633,1082],[571,1087,666],{"className":1088,"style":682},[633,634,1082],[571,1090,698],{"className":1091},[629,1082],[571,1093,604],{"className":1094},[633,634,1082],[571,1096,712],{"className":1097},[650,1082],[571,1099,922],{"className":1100},[1006,1082],[571,1102,666],{"className":1103,"style":682},[633,634,1082],[571,1105,698],{"className":1106},[629,1082],[571,1108,597],{"className":1109},[633,634,1082],[571,1111,712],{"className":1112},[650,1082],[571,1114,1116,1119],{"style":1115},"top:-3.23em;",[571,1117],{"className":1118,"style":1075},[1074],[571,1120],{"className":1121,"style":1123},[1122],"frac-line","border-bottom-width:0.04em;",[571,1125,1127,1130],{"style":1126},"top:-3.394em;",[571,1128],{"className":1129,"style":1075},[1074],[571,1131,1133],{"className":1132},[1079,1080,1081,1082],[571,1134,1136,1139,1142],{"className":1135},[633,1082],[571,1137,604],{"className":1138},[633,634,1082],[571,1140,922],{"className":1141},[1006,1082],[571,1143,597],{"className":1144},[633,634,1082],[571,1146,1149],{"className":1147},[1148],"vlist-s","​",[571,1151,1153],{"className":1152},[1062],[571,1154,1157],{"className":1155,"style":1156},[1066],"height:0.52em;",[571,1158],{},[571,1160],{"className":1161},[650,1050],". Der Unterschied liegt in der Auswahl der Punkte. Die Nullstelle bleibt immer ",[567,1164,1165],{},"eingeschlossen",", deshalb konvergiert das Verfahren bei stetigem ",[571,1168,1170,1183],{"className":1169},[574],[571,1171,1173],{"className":1172},[578],[580,1174,1175],{"xmlns":582},[584,1176,1177,1181],{},[587,1178,1179],{},[595,1180,666],{},[609,1182,666],{"encoding":611},[571,1184,1186],{"className":1185,"ariaHidden":600},[616],[571,1187,1189,1192],{"className":1188},[620],[571,1190],{"className":1191,"style":678},[624],[571,1193,666],{"className":1194,"style":682},[633,634]," garantiert.",[563,1197,1198,1199,1227,1228,1259,1260,1263,1264,1267],{},"Der Nachteil: Ist ",[571,1200,1202,1215],{"className":1201},[574],[571,1203,1205],{"className":1204},[578],[580,1206,1207],{"xmlns":582},[584,1208,1209,1213],{},[587,1210,1211],{},[595,1212,666],{},[609,1214,666],{"encoding":611},[571,1216,1218],{"className":1217,"ariaHidden":600},[616],[571,1219,1221,1224],{"className":1220},[620],[571,1222],{"className":1223,"style":678},[624],[571,1225,666],{"className":1226,"style":682},[633,634]," im Intervall konvex oder konkav, bleibt ein Endpunkt oft dauerhaft liegen. Die Intervallbreite geht dann nicht gegen ",[571,1229,1231,1246],{"className":1230},[574],[571,1232,1234],{"className":1233},[578],[580,1235,1236],{"xmlns":582},[584,1237,1238,1244],{},[587,1239,1240],{},[1241,1242,1243],"mn",{},"0",[609,1245,1243],{"encoding":611},[571,1247,1249],{"className":1248,"ariaHidden":600},[616],[571,1250,1252,1256],{"className":1251},[620],[571,1253],{"className":1254,"style":1255},[624],"height:0.6444em;",[571,1257,1243],{"className":1258},[633],", und die Konvergenz ist nur ",[567,1261,1262],{},"linear",", teils langsamer als die Bisektion. Varianten wie das ",[567,1265,1266],{},"Illinois-Verfahren"," halbieren in diesem Fall den Funktionswert am festhängenden Ende und beschleunigen so die Konvergenz.",[558,1269,1271],{"id":1270},"beispiele","Beispiele",[563,1273,1274,1275,1401,1402,1455,1456,1528,1529,1595],{},"Nullstelle von ",[571,1276,1278,1313],{"className":1277},[574],[571,1279,1281],{"className":1280},[578],[580,1282,1283],{"xmlns":582},[584,1284,1285,1310],{},[587,1286,1287,1289,1291,1294,1296,1298,1306,1308],{},[595,1288,666],{},[590,1290,698],{"stretchy":592},[595,1292,1293],{},"x",[590,1295,712],{"stretchy":592},[590,1297,917],{},[1299,1300,1301,1303],"msup",{},[595,1302,1293],{},[1241,1304,1305],{},"2",[590,1307,922],{},[1241,1309,1305],{},[609,1311,1312],{"encoding":611},"f(x) = x^2 - 2",[571,1314,1316,1343,1392],{"className":1315,"ariaHidden":600},[616],[571,1317,1319,1322,1325,1328,1331,1334,1337,1340],{"className":1318},[620],[571,1320],{"className":1321,"style":625},[624],[571,1323,666],{"className":1324,"style":682},[633,634],[571,1326,698],{"className":1327},[629],[571,1329,1293],{"className":1330},[633,634],[571,1332,712],{"className":1333},[650],[571,1335],{"className":1336,"style":736},[642],[571,1338,917],{"className":1339},[740],[571,1341],{"className":1342,"style":736},[642],[571,1344,1346,1350,1383,1386,1389],{"className":1345},[620],[571,1347],{"className":1348,"style":1349},[624],"height:0.8974em;vertical-align:-0.0833em;",[571,1351,1353,1356],{"className":1352},[633],[571,1354,1293],{"className":1355},[633,634],[571,1357,1360],{"className":1358},[1359],"msupsub",[571,1361,1363],{"className":1362},[1057],[571,1364,1366],{"className":1365},[1062],[571,1367,1370],{"className":1368,"style":1369},[1066],"height:0.8141em;",[571,1371,1373,1377],{"style":1372},"top:-3.063em;margin-right:0.05em;",[571,1374],{"className":1375,"style":1376},[1074],"height:2.7em;",[571,1378,1380],{"className":1379},[1079,1080,1081,1082],[571,1381,1305],{"className":1382},[633,1082],[571,1384],{"className":1385,"style":1002},[642],[571,1387,922],{"className":1388},[1006],[571,1390],{"className":1391,"style":1002},[642],[571,1393,1395,1398],{"className":1394},[620],[571,1396],{"className":1397,"style":1255},[624],[571,1399,1305],{"className":1400},[633]," auf ",[571,1403,1405,1428],{"className":1404},[574],[571,1406,1408],{"className":1407},[578],[580,1409,1410],{"xmlns":582},[584,1411,1412,1425],{},[587,1413,1414,1416,1419,1421,1423],{},[590,1415,593],{"stretchy":592},[1241,1417,1418],{},"1",[590,1420,601],{"separator":600},[1241,1422,1305],{},[590,1424,607],{"stretchy":592},[609,1426,1427],{"encoding":611},"[1, 2]",[571,1429,1431],{"className":1430,"ariaHidden":600},[616],[571,1432,1434,1437,1440,1443,1446,1449,1452],{"className":1433},[620],[571,1435],{"className":1436,"style":625},[624],[571,1438,593],{"className":1439},[629],[571,1441,1418],{"className":1442},[633],[571,1444,601],{"className":1445},[638],[571,1447],{"className":1448,"style":643},[642],[571,1450,1305],{"className":1451},[633],[571,1453,607],{"className":1454},[650]," mit ",[571,1457,1459,1485],{"className":1458},[574],[571,1460,1462],{"className":1461},[578],[580,1463,1464],{"xmlns":582},[584,1465,1466,1482],{},[587,1467,1468,1470,1472,1474,1476,1478,1480],{},[595,1469,666],{},[590,1471,698],{"stretchy":592},[1241,1473,1418],{},[590,1475,712],{"stretchy":592},[590,1477,917],{},[590,1479,922],{},[1241,1481,1418],{},[609,1483,1484],{"encoding":611},"f(1) = -1",[571,1486,1488,1515],{"className":1487,"ariaHidden":600},[616],[571,1489,1491,1494,1497,1500,1503,1506,1509,1512],{"className":1490},[620],[571,1492],{"className":1493,"style":625},[624],[571,1495,666],{"className":1496,"style":682},[633,634],[571,1498,698],{"className":1499},[629],[571,1501,1418],{"className":1502},[633],[571,1504,712],{"className":1505},[650],[571,1507],{"className":1508,"style":736},[642],[571,1510,917],{"className":1511},[740],[571,1513],{"className":1514,"style":736},[642],[571,1516,1518,1522,1525],{"className":1517},[620],[571,1519],{"className":1520,"style":1521},[624],"height:0.7278em;vertical-align:-0.0833em;",[571,1523,922],{"className":1524},[633],[571,1526,1418],{"className":1527},[633],", ",[571,1530,1532,1556],{"className":1531},[574],[571,1533,1535],{"className":1534},[578],[580,1536,1537],{"xmlns":582},[584,1538,1539,1553],{},[587,1540,1541,1543,1545,1547,1549,1551],{},[595,1542,666],{},[590,1544,698],{"stretchy":592},[1241,1546,1305],{},[590,1548,712],{"stretchy":592},[590,1550,917],{},[1241,1552,1305],{},[609,1554,1555],{"encoding":611},"f(2) = 2",[571,1557,1559,1586],{"className":1558,"ariaHidden":600},[616],[571,1560,1562,1565,1568,1571,1574,1577,1580,1583],{"className":1561},[620],[571,1563],{"className":1564,"style":625},[624],[571,1566,666],{"className":1567,"style":682},[633,634],[571,1569,698],{"className":1570},[629],[571,1572,1305],{"className":1573},[633],[571,1575,712],{"className":1576},[650],[571,1578],{"className":1579,"style":736},[642],[571,1581,917],{"className":1582},[740],[571,1584],{"className":1585,"style":736},[642],[571,1587,1589,1592],{"className":1588},[620],[571,1590],{"className":1591,"style":1255},[624],[571,1593,1305],{"className":1594},[633],":",[571,1597,1600],{"className":1598},[1599],"katex-display",[571,1601,1603,1993],{"className":1602},[574],[571,1604,1606],{"className":1605},[578],[580,1607,1609],{"xmlns":582,"display":1608},"block",[584,1610,1611,1990],{},[1612,1613,1617,1773,1920],"mtable",{"rowspacing":1614,"columnalign":1615,"columnspacing":1616},"0.25em","right left right left right left","0em 1em 0em 1em 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&= \\frac{1 \\cdot 2 - 2 \\cdot (-1)}{2 - (-1)} = \\frac{4}{3}, & f(c_1) &= -\\frac{2}{9} \u003C 0 & &\\Rightarrow [\\tfrac{4}{3};\\ 2] \\\\\nc_2 &= \\frac{\\frac{4}{3} \\cdot 2 - 2 \\cdot \\left(-\\frac{2}{9}\\right)}{2 + \\frac{2}{9}} = \\frac{7}{5}, & f(c_2) &= -0{,}04 \u003C 0 & &\\Rightarrow [1{,}4;\\ 2] \\\\\nc_3 &= \\frac{1{,}4 \\cdot 2 - 2 \\cdot (-0{,}04)}{2 + 0{,}04} = \\frac{24}{17} \\approx 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ersten beiden Schritte stimmen mit dem Sekantenverfahren überein. Im dritten Schritt bleibt der rechte Endpunkt ",[571,3662,3664,3682],{"className":3663},[574],[571,3665,3667],{"className":3666},[578],[580,3668,3669],{"xmlns":582},[584,3670,3671,3679],{},[587,3672,3673,3675,3677],{},[595,3674,604],{},[590,3676,917],{},[1241,3678,1305],{},[609,3680,3681],{"encoding":611},"b = 2",[571,3683,3685,3704],{"className":3684,"ariaHidden":600},[616],[571,3686,3688,3692,3695,3698,3701],{"className":3687},[620],[571,3689],{"className":3690,"style":3691},[624],"height:0.6944em;",[571,3693,604],{"className":3694},[633,634],[571,3696],{"className":3697,"style":736},[642],[571,3699,917],{"className":3700},[740],[571,3702],{"className":3703,"style":736},[642],[571,3705,3707,3710],{"className":3706},[620],[571,3708],{"className":3709,"style":1255},[624],[571,3711,1305],{"className":3712},[633]," stehen, weil ",[571,3715,3717,3730],{"className":3716},[574],[571,3718,3720],{"className":3719},[578],[580,3721,3722],{"xmlns":582},[584,3723,3724,3728],{},[587,3725,3726],{},[595,3727,666],{},[609,3729,666],{"encoding":611},[571,3731,3733],{"className":3732,"ariaHidden":600},[616],[571,3734,3736,3739],{"className":3735},[620],[571,3737],{"className":3738,"style":678},[624],[571,3740,666],{"className":3741,"style":682},[633,634]," konvex ist. Das Sekantenverfahren liefert hier schon ",[571,3744,3746,3761],{"className":3745},[574],[571,3747,3749],{"className":3748},[578],[580,3750,3751],{"xmlns":582},[584,3752,3753,3758],{},[587,3754,3755],{},[1241,3756,3757],{},"1,414634",[609,3759,3760],{"encoding":611},"1{,}414634",[571,3762,3764],{"className":3763,"ariaHidden":600},[616],[571,3765,3767,3771,3774,3780],{"className":3766},[620],[571,3768],{"className":3769,"style":3770},[624],"height:0.8389em;vertical-align:-0.1944em;",[571,3772,1418],{"className":3773},[633],[571,3775,3777],{"className":3776},[633],[571,3778,601],{"className":3779},[638],[571,3781,3783],{"className":3782},[633],"414634",", die Regula falsi nur ",[571,3786,3788,3802],{"className":3787},[574],[571,3789,3791],{"className":3790},[578],[580,3792,3793],{"xmlns":582},[584,3794,3795,3799],{},[587,3796,3797],{},[1241,3798,1989],{},[609,3800,3801],{"encoding":611},"1{,}4118",[571,3803,3805],{"className":3804,"ariaHidden":600},[616],[571,3806,3808,3811,3814,3820],{"className":3807},[620],[571,3809],{"className":3810,"style":3770},[624],[571,3812,1418],{"className":3813},[633],[571,3815,3817],{"className":3816},[633],[571,3818,601],{"className":3819},[638],[571,3821,3115],{"className":3822},[633],", ist dafür aber abgesichert.",[558,3825,3827],{"id":3826},"typische-fehler","Typische Fehler",[3829,3830,3831,3835,4091],"ul",{},[3832,3833,3834],"li",{},"Die Regula falsi mit dem Sekantenverfahren gleichsetzen. Die Formel ist gleich, die Wahl der beiden Punkte nicht.",[3832,3836,3837,3838,3964,3965,4090],{},"Im Zähler ",[571,3839,3841,3879],{"className":3840},[574],[571,3842,3844],{"className":3843},[578],[580,3845,3846],{"xmlns":582},[584,3847,3848,3876],{},[587,3849,3850,3852,3854,3856,3858,3860,3862,3864,3866,3868,3870,3872,3874],{},[595,3851,597],{},[590,3853,933],{},[595,3855,666],{},[590,3857,698],{"stretchy":592},[595,3859,597],{},[590,3861,712],{"stretchy":592},[590,3863,922],{},[595,3865,604],{},[590,3867,933],{},[595,3869,666],{},[590,3871,698],{"stretchy":592},[595,3873,604],{},[590,3875,712],{"stretchy":592},[609,3877,3878],{"encoding":611},"a \\cdot f(a) - b \\cdot f(b)",[571,3880,3882,3901,3928,3946],{"className":3881,"ariaHidden":600},[616],[571,3883,3885,3889,3892,3895,3898],{"className":3884},[620],[571,3886],{"className":3887,"style":3888},[624],"height:0.4445em;",[571,3890,597],{"className":3891},[633,634],[571,3893],{"className":3894,"style":1002},[642],[571,3896,933],{"className":3897},[1006],[571,3899],{"className":3900,"style":1002},[642],[571,3902,3904,3907,3910,3913,3916,3919,3922,3925],{"className":3903},[620],[571,3905],{"className":3906,"style":625},[624],[571,3908,666],{"className":3909,"style":682},[633,634],[571,3911,698],{"className":3912},[629],[571,3914,597],{"className":3915},[633,634],[571,3917,712],{"className":3918},[650],[571,3920],{"className":3921,"style":1002},[642],[571,3923,922],{"className":3924},[1006],[571,3926],{"className":3927,"style":1002},[642],[571,3929,3931,3934,3937,3940,3943],{"className":3930},[620],[571,3932],{"className":3933,"style":3691},[624],[571,3935,604],{"className":3936},[633,634],[571,3938],{"className":3939,"style":1002},[642],[571,3941,933],{"className":3942},[1006],[571,3944],{"className":3945,"style":1002},[642],[571,3947,3949,3952,3955,3958,3961],{"className":3948},[620],[571,3950],{"className":3951,"style":625},[624],[571,3953,666],{"className":3954,"style":682},[633,634],[571,3956,698],{"className":3957},[629],[571,3959,604],{"className":3960},[633,634],[571,3962,712],{"className":3963},[650]," schreiben. Richtig sind die „über Kreuz“ genommenen Werte ",[571,3966,3968,4006],{"className":3967},[574],[571,3969,3971],{"className":3970},[578],[580,3972,3973],{"xmlns":582},[584,3974,3975,4003],{},[587,3976,3977,3979,3981,3983,3985,3987,3989,3991,3993,3995,3997,3999,4001],{},[595,3978,597],{},[590,3980,933],{},[595,3982,666],{},[590,3984,698],{"stretchy":592},[595,3986,604],{},[590,3988,712],{"stretchy":592},[590,3990,922],{},[595,3992,604],{},[590,3994,933],{},[595,3996,666],{},[590,3998,698],{"stretchy":592},[595,4000,597],{},[590,4002,712],{"stretchy":592},[609,4004,4005],{"encoding":611},"a \\cdot f(b) - b \\cdot f(a)",[571,4007,4009,4027,4054,4072],{"className":4008,"ariaHidden":600},[616],[571,4010,4012,4015,4018,4021,4024],{"className":4011},[620],[571,4013],{"className":4014,"style":3888},[624],[571,4016,597],{"className":4017},[633,634],[571,4019],{"className":4020,"style":1002},[642],[571,4022,933],{"className":4023},[1006],[571,4025],{"className":4026,"style":1002},[642],[571,4028,4030,4033,4036,4039,4042,4045,4048,4051],{"className":4029},[620],[571,4031],{"className":4032,"style":625},[624],[571,4034,666],{"className":4035,"style":682},[633,634],[571,4037,698],{"className":4038},[629],[571,4040,604],{"className":4041},[633,634],[571,4043,712],{"className":4044},[650],[571,4046],{"className":4047,"style":1002},[642],[571,4049,922],{"className":4050},[1006],[571,4052],{"className":4053,"style":1002},[642],[571,4055,4057,4060,4063,4066,4069],{"className":4056},[620],[571,4058],{"className":4059,"style":3691},[624],[571,4061,604],{"className":4062},[633,634],[571,4064],{"className":4065,"style":1002},[642],[571,4067,933],{"className":4068},[1006],[571,4070],{"className":4071,"style":1002},[642],[571,4073,4075,4078,4081,4084,4087],{"className":4074},[620],[571,4076],{"className":4077,"style":625},[624],[571,4079,666],{"className":4080,"style":682},[633,634],[571,4082,698],{"className":4083},[629],[571,4085,597],{"className":4086},[633,634],[571,4088,712],{"className":4089},[650],".",[3832,4092,4093,4094,4149,4150,4178],{},"Als Abbruchkriterium die Intervallbreite verwenden. Weil ein Endpunkt hängen bleiben kann, wird sie oft nicht klein. Besser ",[571,4095,4097,4122],{"className":4096},[574],[571,4098,4100],{"className":4099},[578],[580,4101,4102],{"xmlns":582},[584,4103,4104,4119],{},[587,4105,4106,4109,4111,4113,4115,4117],{},[595,4107,703],{"mathvariant":4108},"normal",[595,4110,666],{},[590,4112,698],{"stretchy":592},[595,4114,852],{},[590,4116,712],{"stretchy":592},[595,4118,703],{"mathvariant":4108},[609,4120,4121],{"encoding":611},"|f(c)|",[571,4123,4125],{"className":4124,"ariaHidden":600},[616],[571,4126,4128,4131,4134,4137,4140,4143,4146],{"className":4127},[620],[571,4129],{"className":4130,"style":625},[624],[571,4132,703],{"className":4133},[633],[571,4135,666],{"className":4136,"style":682},[633,634],[571,4138,698],{"className":4139},[629],[571,4141,852],{"className":4142},[633,634],[571,4144,712],{"className":4145},[650],[571,4147,703],{"className":4148},[633]," oder die Änderung von ",[571,4151,4153,4166],{"className":4152},[574],[571,4154,4156],{"className":4155},[578],[580,4157,4158],{"xmlns":582},[584,4159,4160,4164],{},[587,4161,4162],{},[595,4163,852],{},[609,4165,852],{"encoding":611},[571,4167,4169],{"className":4168,"ariaHidden":600},[616],[571,4170,4172,4175],{"className":4171},[620],[571,4173],{"className":4174,"style":864},[624],[571,4176,852],{"className":4177},[633,634]," prüfen.",{"title":4180,"searchDepth":4181,"depth":4181,"links":4182},"",2,[4183,4184,4185],{"id":560,"depth":4181,"text":561},{"id":1270,"depth":4181,"text":1271},{"id":3826,"depth":4181,"text":3827},[4187,4190,4193,4196,4199,4202,4205,4208],{"lhs":4188,"rhs":4189},"a - fa*(b - a)\u002F(fb - fa)","(a*fb - b*fa)\u002F(fb - fa)",{"lhs":4191,"rhs":4192},"(a*(m*b + k) - b*(m*a + k))\u002F((m*b + k) - (m*a + k))","-k\u002Fm",{"lhs":4194,"rhs":4195},"(1*2 - 2*(-1))\u002F(2 - (-1))","4\u002F3",{"lhs":4197,"rhs":4198},"(4\u002F3)^2 - 2","-2\u002F9",{"lhs":4200,"rhs":4201},"(4\u002F3*2 - 2*(-2\u002F9))\u002F(2 - (-2\u002F9))","7\u002F5",{"lhs":4203,"rhs":4204},"1.4^2 - 2","-0.04",{"lhs":4206,"rhs":4207},"(1.4*2 - 2*(-0.04))\u002F(2 - (-0.04))","24\u002F17",{"lhs":4209,"rhs":4210},"round(24\u002F17, 4)","1.4118","f \\text{ stetig auf } [a, b],\\ f(a) \\cdot f(b) \u003C 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f\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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">stetig auf\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo stretchy=\"false\">[\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">]\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">[a, b],\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=\"mopen\">[\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">]\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath 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","regula-falsi","c = \\frac{a \\cdot f(b) - b \\cdot f(a)}{f(b) - f(a)}, \\qquad [a, b] \\to \\begin{cases} [a, c], & f(a) \\cdot f(c) \\leq 0 \\\\ [c, 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>c\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\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>c\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>c\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>c\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\">c = \\frac{a \\cdot f(b) - b \\cdot f(a)}{f(b) - f(a)}, \\qquad [a, b] \\to \\begin{cases} [a, c], & f(a) \\cdot f(c) \\leq 0 \\\\ [c, 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\">c\u003C\u002Fspan>\u003Cspan 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