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x_{n-1}}",[575,1046,1048],{"className":1047,"ariaHidden":651},[650],[575,1049,1051,1055],{"className":1050},[655],[575,1052],{"className":1053,"style":1054},[659],"height:1.4968em;vertical-align:-0.4868em;",[575,1056,1058,1062,1333],{"className":1057},[668],[575,1059],{"className":1060},[664,1061],"nulldelimiter",[575,1063,1065],{"className":1064},[984],[575,1066,1068,1324],{"className":1067},[680,681],[575,1069,1071,1321],{"className":1070},[685],[575,1072,1075,1188,1199],{"className":1073,"style":1074},[689],"height:1.01em;",[575,1076,1078,1082],{"style":1077},"top:-2.655em;",[575,1079],{"className":1080,"style":1081},[697],"height:3em;",[575,1083,1085],{"className":1084},[702,703,704,705],[575,1086,1088,1134,1137],{"className":1087},[668,705],[575,1089,1091,1094],{"className":1090},[668,705],[575,1092,604],{"className":1093},[668,672,705],[575,1095,1097],{"className":1096},[676],[575,1098,1100,1125],{"className":1099},[680,681],[575,1101,1103,1122],{"className":1102},[685],[575,1104,1107],{"className":1105,"style":1106},[689],"height:0.1645em;",[575,1108,1110,1114],{"style":1109},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[575,1111],{"className":1112,"style":1113},[697],"height:2.5em;",[575,1115,1119],{"className":1116},[702,1117,1118,705],"reset-size3","size1",[575,1120,609],{"className":1121},[668,672,705],[575,1123,723],{"className":1124},[722],[575,1126,1128],{"className":1127},[685],[575,1129,1132],{"className":1130,"style":1131},[689],"height:0.143em;",[575,1133],{},[575,1135,612],{"className":1136},[715,705],[575,1138,1140,1143],{"className":1139},[668,705],[575,1141,604],{"className":1142},[668,672,705],[575,1144,1146],{"className":1145},[676],[575,1147,1149,1179],{"className":1148},[680,681],[575,1150,1152,1176],{"className":1151},[685],[575,1153,1156],{"className":1154,"style":1155},[689],"height:0.3173em;",[575,1157,1158,1161],{"style":1109},[575,1159],{"className":1160,"style":1113},[697],[575,1162,1164],{"className":1163},[702,1117,1118,705],[575,1165,1167,1170,1173],{"className":1166},[668,705],[575,1168,609],{"className":1169},[668,672,705],[575,1171,612],{"className":1172},[715,705],[575,1174,616],{"className":1175},[668,705],[575,1177,723],{"className":1178},[722],[575,1180,1182],{"className":1181},[685],[575,1183,1186],{"className":1184,"style":1185},[689],"height:0.2025em;",[575,1187],{},[575,1189,1191,1194],{"style":1190},"top:-3.23em;",[575,1192],{"className":1193,"style":1081},[697],[575,1195],{"className":1196,"style":1198},[1197],"frac-line","border-bottom-width:0.04em;",[575,1200,1202,1205],{"style":1201},"top:-3.485em;",[575,1203],{"className":1204,"style":1081},[697],[575,1206,1208],{"className":1207},[702,703,704,705],[575,1209,1211,1214,1217,1257,1260,1263,1266,1269,1318],{"className":1210},[668,705],[575,1212,622],{"className":1213,"style":754},[668,672,705],[575,1215,597],{"className":1216},[664,705],[575,1218,1220,1223],{"className":1219},[668,705],[575,1221,604],{"className":1222},[668,672,705],[575,1224,1226],{"className":1225},[676],[575,1227,1229,1249],{"className":1228},[680,681],[575,1230,1232,1246],{"className":1231},[685],[575,1233,1235],{"className":1234,"style":1106},[689],[575,1236,1237,1240],{"style":1109},[575,1238],{"className":1239,"style":1113},[697],[575,1241,1243],{"className":1242},[702,1117,1118,705],[575,1244,609],{"className":1245},[668,672,705],[575,1247,723],{"className":1248},[722],[575,1250,1252],{"className":1251},[685],[575,1253,1255],{"className":1254,"style":1131},[689],[575,1256],{},[575,1258,639],{"className":1259},[810,705],[575,1261,612],{"className":1262},[715,705],[575,1264,622],{"className":1265,"style":754},[668,672,705],[575,1267,597],{"className":1268},[664,705],[575,1270,1272,1275],{"className":1271},[668,705],[575,1273,604],{"className":1274},[668,672,705],[575,1276,1278],{"className":1277},[676],[575,1279,1281,1310],{"className":1280},[680,681],[575,1282,1284,1307],{"className":1283},[685],[575,1285,1287],{"className":1286,"style":1155},[689],[575,1288,1289,1292],{"style":1109},[575,1290],{"className":1291,"style":1113},[697],[575,1293,1295],{"className":1294},[702,1117,1118,705],[575,1296,1298,1301,1304],{"className":1297},[668,705],[575,1299,609],{"className":1300},[668,672,705],[575,1302,612],{"className":1303},[715,705],[575,1305,616],{"className":1306},[668,705],[575,1308,723],{"className":1309},[722],[575,1311,1313],{"className":1312},[685],[575,1314,1316],{"className":1315,"style":1185},[689],[575,1317],{},[575,1319,639],{"className":1320},[810,705],[575,1322,723],{"className":1323},[722],[575,1325,1327],{"className":1326},[685],[575,1328,1331],{"className":1329,"style":1330},[689],"height:0.4868em;",[575,1332],{},[575,1334],{"className":1335},[810,1061]," ist die Sekantensteigung, also ein Differenzenquotient als Ersatz für ",[575,1338,1340,1372],{"className":1339},[578],[575,1341,1343],{"className":1342},[582],[584,1344,1345],{"xmlns":586},[588,1346,1347,1369],{},[591,1348,1349,1359,1361,1367],{},[1350,1351,1352,1354],"msup",{},[602,1353,622],{},[594,1355,1358],{"mathvariant":1356,"lspace":1357,"rspace":1357},"normal","0em","′",[594,1360,597],{"stretchy":596},[599,1362,1363,1365],{},[602,1364,604],{},[602,1366,609],{},[594,1368,639],{"stretchy":596},[643,1370,1371],{"encoding":645},"f'(x_n)",[575,1373,1375],{"className":1374,"ariaHidden":651},[650],[575,1376,1378,1382,1416,1419,1459],{"className":1377},[655],[575,1379],{"className":1380,"style":1381},[659],"height:1.0019em;vertical-align:-0.25em;",[575,1383,1385,1388],{"className":1384},[668],[575,1386,622],{"className":1387,"style":754},[668,672],[575,1389,1391],{"className":1390},[676],[575,1392,1394],{"className":1393},[680],[575,1395,1397],{"className":1396},[685],[575,1398,1401],{"className":1399,"style":1400},[689],"height:0.7519em;",[575,1402,1404,1407],{"style":1403},"top:-3.063em;margin-right:0.05em;",[575,1405],{"className":1406,"style":698},[697],[575,1408,1410],{"className":1409},[702,703,704,705],[575,1411,1413],{"className":1412},[668,705],[575,1414,1358],{"className":1415},[668,705],[575,1417,597],{"className":1418},[664],[575,1420,1422,1425],{"className":1421},[668],[575,1423,604],{"className":1424},[668,672],[575,1426,1428],{"className":1427},[676],[575,1429,1431,1451],{"className":1430},[680,681],[575,1432,1434,1448],{"className":1433},[685],[575,1435,1437],{"className":1436,"style":882},[689],[575,1438,1439,1442],{"style":693},[575,1440],{"className":1441,"style":698},[697],[575,1443,1445],{"className":1444},[702,703,704,705],[575,1446,609],{"className":1447},[668,672,705],[575,1449,723],{"className":1450},[722],[575,1452,1454],{"className":1453},[685],[575,1455,1457],{"className":1456,"style":903},[689],[575,1458],{},[575,1460,639],{"className":1461},[810],".",[563,1464,1465,1466,1469,1470,812,1542,1612,1613,1616],{},"Man braucht ",[567,1467,1468],{},"zwei Startwerte"," 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Anders als bei der Regula falsi müssen sie die Nullstelle nicht einschließen, und es werden immer die beiden ",[567,1614,1615],{},"letzten"," Näherungen verwendet.",[563,1618,1619,1620,1623,1624,1842,1843,812,1928,2028],{},"Nahe einer einfachen Nullstelle konvergiert das Verfahren ",[567,1621,1622],{},"superlinear"," mit der Ordnung ",[575,1625,1627,1663],{"className":1626},[578],[575,1628,1630],{"className":1629},[582],[584,1631,1632],{"xmlns":586},[588,1633,1634,1660],{},[591,1635,1636,1654,1657],{},[984,1637,1638,1651],{},[591,1639,1640,1642,1645],{},[614,1641,616],{},[594,1643,1644],{},"+",[1646,1647,1648],"msqrt",{},[614,1649,1650],{},"5",[614,1652,1653],{},"2",[594,1655,1656],{},"≈",[614,1658,1659],{},"1,618",[643,1661,1662],{"encoding":645},"\\frac{1 + \\sqrt{5}}{2} \\approx 1{,}618",[575,1664,1666,1820],{"className":1665,"ariaHidden":651},[650],[575,1667,1669,1673,1811,1814,1817],{"className":1668},[655],[575,1670],{"className":1671,"style":1672},[659],"height:1.383em;vertical-align:-0.345em;",[575,1674,1676,1679,1808],{"className":1675},[668],[575,1677],{"className":1678},[664,1061],[575,1680,1682],{"className":1681},[984],[575,1683,1685,1799],{"className":1684},[680,681],[575,1686,1688,1796],{"className":1687},[685],[575,1689,1692,1706,1714],{"className":1690,"style":1691},[689],"height:1.038em;",[575,1693,1694,1697],{"style":1077},[575,1695],{"className":1696,"style":1081},[697],[575,1698,1700],{"className":1699},[702,703,704,705],[575,1701,1703],{"className":1702},[668,705],[575,1704,1653],{"className":1705},[668,705],[575,1707,1708,1711],{"style":1190},[575,1709],{"className":1710,"style":1081},[697],[575,1712],{"className":1713,"style":1198},[1197],[575,1715,1717,1720],{"style":1716},"top:-3.399em;",[575,1718],{"className":1719,"style":1081},[697],[575,1721,1723],{"className":1722},[702,703,704,705],[575,1724,1726,1729,1732],{"className":1725},[668,705],[575,1727,616],{"className":1728},[668,705],[575,1730,1644],{"className":1731},[715,705],[575,1733,1736],{"className":1734},[668,1735,705],"sqrt",[575,1737,1739,1787],{"className":1738},[680,681],[575,1740,1742,1784],{"className":1741},[685],[575,1743,1746,1761],{"className":1744,"style":1745},[689],"height:0.9128em;",[575,1747,1751,1754],{"className":1748,"style":1750},[1749],"svg-align","top:-3em;",[575,1752],{"className":1753,"style":1081},[697],[575,1755,1758],{"className":1756,"style":1757},[668,705],"padding-left:0.833em;",[575,1759,1650],{"className":1760},[668,705],[575,1762,1764,1767],{"style":1763},"top:-2.8728em;",[575,1765],{"className":1766,"style":1081},[697],[575,1768,1772],{"className":1769,"style":1771},[1770,705],"hide-tail","min-width:0.853em;height:1.08em;",[1773,1774,1780],"svg",{"xmlns":1775,"width":1776,"height":1777,"viewBox":1778,"preserveAspectRatio":1779},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[1781,1782],"path",{"d":1783},"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",[575,1785,723],{"className":1786},[722],[575,1788,1790],{"className":1789},[685],[575,1791,1794],{"className":1792,"style":1793},[689],"height:0.1272em;",[575,1795],{},[575,1797,723],{"className":1798},[722],[575,1800,1802],{"className":1801},[685],[575,1803,1806],{"className":1804,"style":1805},[689],"height:0.345em;",[575,1807],{},[575,1809],{"className":1810},[810,1061],[575,1812],{"className":1813,"style":737},[736],[575,1815,1656],{"className":1816},[741],[575,1818],{"className":1819,"style":737},[736],[575,1821,1823,1827,1830,1838],{"className":1822},[655],[575,1824],{"className":1825,"style":1826},[659],"height:0.8389em;vertical-align:-0.1944em;",[575,1828,616],{"className":1829},[668],[575,1831,1833],{"className":1832},[668],[575,1834,1837],{"className":1835},[1836],"mpunct",",",[575,1839,1841],{"className":1840},[668],"618",". Das ist langsamer als Newton pro Schritt, aber jeder Schritt braucht nur eine neue Funktionsauswertung. Ohne Einschließung kann das Verfahren bei schlechten Startwerten divergieren. Sind 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fast gleich, entsteht Auslöschung im Nenner.",[558,2030,2032],{"id":2031},"beispiele","Beispiele",[563,2034,2035,2036,2159,2160,2252,2253,2345,2346,2252,2459,2566],{},"Nullstelle von ",[575,2037,2039,2072],{"className":2038},[578],[575,2040,2042],{"className":2041},[582],[584,2043,2044],{"xmlns":586},[588,2045,2046,2069],{},[591,2047,2048,2050,2052,2054,2056,2059,2065,2067],{},[602,2049,622],{},[594,2051,597],{"stretchy":596},[602,2053,604],{},[594,2055,639],{"stretchy":596},[594,2057,2058],{},"=",[1350,2060,2061,2063],{},[602,2062,604],{},[614,2064,1653],{},[594,2066,612],{},[614,2068,1653],{},[643,2070,2071],{"encoding":645},"f(x) = x^2 - 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&= 2 - 2 \\cdot \\frac{2 - 1}{2 - (-1)} = \\frac{4}{3}, & f(x_2) &= -\\frac{2}{9} \\\\\nx_3 &= \\frac{4}{3} - \\left(-\\frac{2}{9}\\right) \\cdot \\frac{4\u002F3 - 2}{-2\u002F9 - 2} = \\frac{7}{5} = 1{,}4, & f(x_3) &= -0{,}04 \\\\\nx_4 &= 1{,}4 - (-0{,}04) \\cdot \\frac{1{,}4 - 4\u002F3}{-0{,}04 + 2\u002F9} = \\frac{58}{41} \\approx 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",[575,4381,4383,4396],{"className":4382},[578],[575,4384,4386],{"className":4385},[582],[584,4387,4388],{"xmlns":586},[588,4389,4390,4394],{},[591,4391,4392],{},[602,4393,622],{},[643,4395,622],{"encoding":645},[575,4397,4399],{"className":4398,"ariaHidden":651},[650],[575,4400,4402,4406],{"className":4401},[655],[575,4403],{"className":4404,"style":4405},[659],"height:0.8889em;vertical-align:-0.1944em;",[575,4407,622],{"className":4408,"style":754},[668,672]," linear, ist die Sekante der Graph selbst, und schon der erste Schritt liefert die exakte Nullstelle.",[558,4411,4413],{"id":4412},"typische-fehler","Typische Fehler",[4415,4416,4417,4751,4754],"ul",{},[4418,4419,4420,4421,4571,4572,4750],"li",{},"Die Startwerte für die Rechnung falsch zuordnen: Im Zähler steht ",[575,4422,4424,4456],{"className":4423},[578],[575,4425,4427],{"className":4426},[582],[584,4428,4429],{"xmlns":586},[588,4430,4431,4453],{},[591,4432,4433,4439,4441],{},[599,4434,4435,4437],{},[602,4436,604],{},[602,4438,609],{},[594,4440,612],{},[599,4442,4443,4445],{},[602,4444,604],{},[591,4446,4447,4449,4451],{},[602,4448,609],{},[594,4450,612],{},[614,4452,616],{},[643,4454,4455],{"encoding":645},"x_n - x_{n-1}",[575,4457,4459,4515],{"className":4458,"ariaHidden":651},[650],[575,4460,4462,4466,4506,4509,4512],{"className":4461},[655],[575,4463],{"className":4464,"style":4465},[659],"height:0.7333em;vertical-align:-0.15em;",[575,4467,4469,4472],{"className":4468},[668],[575,4470,604],{"className":4471},[668,672],[575,4473,4475],{"className":4474},[676],[575,4476,4478,4498],{"className":4477},[680,681],[575,4479,4481,4495],{"className":4480},[685],[575,4482,4484],{"className":4483,"style":882},[689],[575,4485,4486,4489],{"style":693},[575,4487],{"className":4488,"style":698},[697],[575,4490,4492],{"className":4491},[702,703,704,705],[575,4493,609],{"className":4494},[668,672,705],[575,4496,723],{"className":4497},[722],[575,4499,4501],{"className":4500},[685],[575,4502,4504],{"className":4503,"style":903},[689],[575,4505],{},[575,4507],{"className":4508,"style":2142},[736],[575,4510,612],{"className":4511},[715],[575,4513],{"className":4514,"style":2142},[736],[575,4516,4518,4522],{"className":4517},[655],[575,4519],{"className":4520,"style":4521},[659],"height:0.6389em;vertical-align:-0.2083em;",[575,4523,4525,4528],{"className":4524},[668],[575,4526,604],{"className":4527},[668,672],[575,4529,4531],{"className":4530},[676],[575,4532,4534,4563],{"className":4533},[680,681],[575,4535,4537,4560],{"className":4536},[685],[575,4538,4540],{"className":4539,"style":690},[689],[575,4541,4542,4545],{"style":693},[575,4543],{"className":4544,"style":698},[697],[575,4546,4548],{"className":4547},[702,703,704,705],[575,4549,4551,4554,4557],{"className":4550},[668,705],[575,4552,609],{"className":4553},[668,672,705],[575,4555,612],{"className":4556},[715,705],[575,4558,616],{"className":4559},[668,705],[575,4561,723],{"className":4562},[722],[575,4564,4566],{"className":4565},[685],[575,4567,4569],{"className":4568,"style":730},[689],[575,4570],{},", im Nenner ",[575,4573,4575,4619],{"className":4574},[578],[575,4576,4578],{"className":4577},[582],[584,4579,4580],{"xmlns":586},[588,4581,4582,4616],{},[591,4583,4584,4586,4588,4594,4596,4598,4600,4602,4614],{},[602,4585,622],{},[594,4587,597],{"stretchy":596},[599,4589,4590,4592],{},[602,4591,604],{},[602,4593,609],{},[594,4595,639],{"stretchy":596},[594,4597,612],{},[602,4599,622],{},[594,4601,597],{"stretchy":596},[599,4603,4604,4606],{},[602,4605,604],{},[591,4607,4608,4610,4612],{},[602,4609,609],{},[594,4611,612],{},[614,4613,616],{},[594,4615,639],{"stretchy":596},[643,4617,4618],{"encoding":645},"f(x_n) - f(x_{n-1})",[575,4620,4622,4686],{"className":4621,"ariaHidden":651},[650],[575,4623,4625,4628,4631,4634,4674,4677,4680,4683],{"className":4624},[655],[575,4626],{"className":4627,"style":660},[659],[575,4629,622],{"className":4630,"style":754},[668,672],[575,4632,597],{"className":4633},[664],[575,4635,4637,4640],{"className":4636},[668],[575,4638,604],{"className":4639},[668,672],[575,4641,4643],{"className":4642},[676],[575,4644,4646,4666],{"className":4645},[680,681],[575,4647,4649,4663],{"className":4648},[685],[575,4650,4652],{"className":4651,"style":882},[689],[575,4653,4654,4657],{"style":693},[575,4655],{"className":4656,"style":698},[697],[575,4658,4660],{"className":4659},[702,703,704,705],[575,4661,609],{"className":4662},[668,672,705],[575,4664,723],{"className":4665},[722],[575,4667,4669],{"className":4668},[685],[575,4670,4672],{"className":4671,"style":903},[689],[575,4673],{},[575,4675,639],{"className":4676},[810],[575,4678],{"className":4679,"style":2142},[736],[575,4681,612],{"className":4682},[715],[575,4684],{"className":4685,"style":2142},[736],[575,4687,4689,4692,4695,4698,4747],{"className":4688},[655],[575,4690],{"className":4691,"style":660},[659],[575,4693,622],{"className":4694,"style":754},[668,672],[575,4696,597],{"className":4697},[664],[575,4699,4701,4704],{"className":4700},[668],[575,4702,604],{"className":4703},[668,672],[575,4705,4707],{"className":4706},[676],[575,4708,4710,4739],{"className":4709},[680,681],[575,4711,4713,4736],{"className":4712},[685],[575,4714,4716],{"className":4715,"style":690},[689],[575,4717,4718,4721],{"style":693},[575,4719],{"className":4720,"style":698},[697],[575,4722,4724],{"className":4723},[702,703,704,705],[575,4725,4727,4730,4733],{"className":4726},[668,705],[575,4728,609],{"className":4729},[668,672,705],[575,4731,612],{"className":4732},[715,705],[575,4734,616],{"className":4735},[668,705],[575,4737,723],{"className":4738},[722],[575,4740,4742],{"className":4741},[685],[575,4743,4745],{"className":4744,"style":730},[689],[575,4746],{},[575,4748,639],{"className":4749},[810],", in derselben Reihenfolge.",[4418,4752,4753],{},"Wie bei der Regula falsi immer einen Punkt mit anderem Vorzeichen behalten. Beim Sekantenverfahren werden stur die zwei letzten Punkte verwendet.",[4418,4755,4756,4757,4935,4936,4964],{},"Das Verfahren fortsetzen, wenn ",[575,4758,4760,4804],{"className":4759},[578],[575,4761,4763],{"className":4762},[582],[584,4764,4765],{"xmlns":586},[588,4766,4767,4801],{},[591,4768,4769,4771,4773,4779,4781,4783,4785,4787,4799],{},[602,4770,622],{},[594,4772,597],{"stretchy":596},[599,4774,4775,4777],{},[602,4776,604],{},[602,4778,609],{},[594,4780,639],{"stretchy":596},[594,4782,1656],{},[602,4784,622],{},[594,4786,597],{"stretchy":596},[599,4788,4789,4791],{},[602,4790,604],{},[591,4792,4793,4795,4797],{},[602,4794,609],{},[594,4796,612],{},[614,4798,616],{},[594,4800,639],{"stretchy":596},[643,4802,4803],{"encoding":645},"f(x_n) \\approx f(x_{n-1})",[575,4805,4807,4871],{"className":4806,"ariaHidden":651},[650],[575,4808,4810,4813,4816,4819,4859,4862,4865,4868],{"className":4809},[655],[575,4811],{"className":4812,"style":660},[659],[575,4814,622],{"className":4815,"style":754},[668,672],[575,4817,597],{"className":4818},[664],[575,4820,4822,4825],{"className":4821},[668],[575,4823,604],{"className":4824},[668,672],[575,4826,4828],{"className":4827},[676],[575,4829,4831,4851],{"className":4830},[680,681],[575,4832,4834,4848],{"className":4833},[685],[575,4835,4837],{"className":4836,"style":882},[689],[575,4838,4839,4842],{"style":693},[575,4840],{"className":4841,"style":698},[697],[575,4843,4845],{"className":4844},[702,703,704,705],[575,4846,609],{"className":4847},[668,672,705],[575,4849,723],{"className":4850},[722],[575,4852,4854],{"className":4853},[685],[575,4855,4857],{"className":4856,"style":903},[689],[575,4858],{},[575,4860,639],{"className":4861},[810],[575,4863],{"className":4864,"style":737},[736],[575,4866,1656],{"className":4867},[741],[575,4869],{"className":4870,"style":737},[736],[575,4872,4874,4877,4880,4883,4932],{"className":4873},[655],[575,4875],{"className":4876,"style":660},[659],[575,4878,622],{"className":4879,"style":754},[668,672],[575,4881,597],{"className":4882},[664],[575,4884,4886,4889],{"className":4885},[668],[575,4887,604],{"className":4888},[668,672],[575,4890,4892],{"className":4891},[676],[575,4893,4895,4924],{"className":4894},[680,681],[575,4896,4898,4921],{"className":4897},[685],[575,4899,4901],{"className":4900,"style":690},[689],[575,4902,4903,4906],{"style":693},[575,4904],{"className":4905,"style":698},[697],[575,4907,4909],{"className":4908},[702,703,704,705],[575,4910,4912,4915,4918],{"className":4911},[668,705],[575,4913,609],{"className":4914},[668,672,705],[575,4916,612],{"className":4917},[715,705],[575,4919,616],{"className":4920},[668,705],[575,4922,723],{"className":4923},[722],[575,4925,4927],{"className":4926},[685],[575,4928,4930],{"className":4929,"style":730},[689],[575,4931],{},[575,4933,639],{"className":4934},[810]," ist. Dann wird der Schritt riesig oder durch ",[575,4937,4939,4952],{"className":4938},[578],[575,4940,4942],{"className":4941},[582],[584,4943,4944],{"xmlns":586},[588,4945,4946,4950],{},[591,4947,4948],{},[614,4949,1488],{},[643,4951,1488],{"encoding":645},[575,4953,4955],{"className":4954,"ariaHidden":651},[650],[575,4956,4958,4961],{"className":4957},[655],[575,4959],{"className":4960,"style":2155},[659],[575,4962,1488],{"className":4963},[668]," geteilt.",{"title":4966,"searchDepth":4967,"depth":4967,"links":4968},"",2,[4969,4970,4971],{"id":560,"depth":4967,"text":561},{"id":2031,"depth":4967,"text":2032},{"id":4412,"depth":4967,"text":4413},[4973,4976,4979,4981,4984,4987,4990,4993,4996],{"lhs":4974,"rhs":4975},"x1 - (m*x1 + c)*(x1 - x0)\u002F((m*x1 + c) - (m*x0 + c))","-c\u002Fm",{"lhs":4977,"rhs":4978},"x1 - f1*(x1 - x0)\u002F(f1 - f0)","(x0*f1 - x1*f0)\u002F(f1 - f0)",{"lhs":4980,"rhs":3571},"2 - 2*(2 - 1)\u002F(2 - (-1))",{"lhs":4982,"rhs":4983},"(4\u002F3)^2 - 2","-2\u002F9",{"lhs":4985,"rhs":4986},"4\u002F3 - (-2\u002F9)*(4\u002F3 - 2)\u002F(-2\u002F9 - 2)","7\u002F5",{"lhs":4988,"rhs":4989},"1.4^2 - 2","-0.04",{"lhs":4991,"rhs":4992},"1.4 - (-0.04)*(1.4 - 4\u002F3)\u002F(-0.04 - (-2\u002F9))","58\u002F41",{"lhs":4994,"rhs":4995},"round(58\u002F41, 6)","1.414634",{"lhs":4997,"rhs":4998},"round((1 + sqrt(5))\u002F2, 3)","1.618","f(x_n) \\neq f(x_{n-1})","\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>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f(x_n) \\neq f(x_{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: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\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;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\">n\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\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\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan 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