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Die ",[892,957,958],{},"Lagrange-Form"," schreibt es direkt hin.",[563,961,962,963,966,967,1039,1040,1109,1110,1179,1180,1208,1209,1238,1239,1267,1268,1338,1339,1367],{},"Der Trick sind die ",[892,964,965],{},"Basispolynome"," ",[567,968,970,989],{"className":969},[570],[567,971,973],{"className":972},[574],[576,974,975],{"xmlns":578},[580,976,977,986],{},[583,978,979],{},[661,980,981,984],{},[586,982,983],{},"L",[586,985,668],{},[598,987,988],{"encoding":600},"L_i",[567,990,992],{"className":991,"ariaHidden":606},[605],[567,993,995,999],{"className":994},[610],[567,996],{"className":997,"style":998},[614],"height:0.8333em;vertical-align:-0.15em;",[567,1000,1002,1005],{"className":1001},[619],[567,1003,983],{"className":1004},[619,620],[567,1006,1008],{"className":1007},[708],[567,1009,1011,1031],{"className":1010},[712,713],[567,1012,1014,1028],{"className":1013},[717],[567,1015,1017],{"className":1016,"style":722},[721],[567,1018,1019,1022],{"style":725},[567,1020],{"className":1021,"style":730},[729],[567,1023,1025],{"className":1024},[734,735,736,737],[567,1026,668],{"className":1027},[619,620,737],[567,1029,745],{"className":1030},[744],[567,1032,1034],{"className":1033},[717],[567,1035,1037],{"className":1036,"style":752},[721],[567,1038],{},": Jedes ",[567,1041,1043,1060],{"className":1042},[570],[567,1044,1046],{"className":1045},[574],[576,1047,1048],{"xmlns":578},[580,1049,1050,1058],{},[583,1051,1052],{},[661,1053,1054,1056],{},[586,1055,983],{},[586,1057,668],{},[598,1059,988],{"encoding":600},[567,1061,1063],{"className":1062,"ariaHidden":606},[605],[567,1064,1066,1069],{"className":1065},[610],[567,1067],{"className":1068,"style":998},[614],[567,1070,1072,1075],{"className":1071},[619],[567,1073,983],{"className":1074},[619,620],[567,1076,1078],{"className":1077},[708],[567,1079,1081,1101],{"className":1080},[712,713],[567,1082,1084,1098],{"className":1083},[717],[567,1085,1087],{"className":1086,"style":722},[721],[567,1088,1089,1092],{"style":725},[567,1090],{"className":1091,"style":730},[729],[567,1093,1095],{"className":1094},[734,735,736,737],[567,1096,668],{"className":1097},[619,620,737],[567,1099,745],{"className":1100},[744],[567,1102,1104],{"className":1103},[717],[567,1105,1107],{"className":1106,"style":752},[721],[567,1108],{}," hat an der Stelle ",[567,1111,1113,1130],{"className":1112},[570],[567,1114,1116],{"className":1115},[574],[576,1117,1118],{"xmlns":578},[580,1119,1120,1128],{},[583,1121,1122],{},[661,1123,1124,1126],{},[586,1125,665],{},[586,1127,668],{},[598,1129,839],{"encoding":600},[567,1131,1133],{"className":1132,"ariaHidden":606},[605],[567,1134,1136,1139],{"className":1135},[610],[567,1137],{"className":1138,"style":849},[614],[567,1140,1142,1145],{"className":1141},[619],[567,1143,665],{"className":1144},[619,620],[567,1146,1148],{"className":1147},[708],[567,1149,1151,1171],{"className":1150},[712,713],[567,1152,1154,1168],{"className":1153},[717],[567,1155,1157],{"className":1156,"style":722},[721],[567,1158,1159,1162],{"style":725},[567,1160],{"className":1161,"style":730},[729],[567,1163,1165],{"className":1164},[734,735,736,737],[567,1166,668],{"className":1167},[619,620,737],[567,1169,745],{"className":1170},[744],[567,1172,1174],{"className":1173},[717],[567,1175,1177],{"className":1176,"style":752},[721],[567,1178],{}," den Wert ",[567,1181,1183,1196],{"className":1182},[570],[567,1184,1186],{"className":1185},[574],[576,1187,1188],{"xmlns":578},[580,1189,1190,1194],{},[583,1191,1192],{},[594,1193,596],{},[598,1195,596],{"encoding":600},[567,1197,1199],{"className":1198,"ariaHidden":606},[605],[567,1200,1202,1205],{"className":1201},[610],[567,1203],{"className":1204,"style":639},[614],[567,1206,596],{"className":1207},[619]," und an allen anderen Stützstellen den Wert ",[567,1210,1212,1226],{"className":1211},[570],[567,1213,1215],{"className":1214},[574],[576,1216,1217],{"xmlns":578},[580,1218,1219,1224],{},[583,1220,1221],{},[594,1222,1223],{},"0",[598,1225,1223],{"encoding":600},[567,1227,1229],{"className":1228,"ariaHidden":606},[605],[567,1230,1232,1235],{"className":1231},[610],[567,1233],{"className":1234,"style":639},[614],[567,1236,1223],{"className":1237},[619],". Der Zähler sorgt für die Nullstellen, der Nenner normiert auf ",[567,1240,1242,1255],{"className":1241},[570],[567,1243,1245],{"className":1244},[574],[576,1246,1247],{"xmlns":578},[580,1248,1249,1253],{},[583,1250,1251],{},[594,1252,596],{},[598,1254,596],{"encoding":600},[567,1256,1258],{"className":1257,"ariaHidden":606},[605],[567,1259,1261,1264],{"className":1260},[610],[567,1262],{"className":1263,"style":639},[614],[567,1265,596],{"className":1266},[619],". Multipliziert man mit ",[567,1269,1271,1289],{"className":1270},[570],[567,1272,1274],{"className":1273},[574],[576,1275,1276],{"xmlns":578},[580,1277,1278,1286],{},[583,1279,1280],{},[661,1281,1282,1284],{},[586,1283,676],{},[586,1285,668],{},[598,1287,1288],{"encoding":600},"y_i",[567,1290,1292],{"className":1291,"ariaHidden":606},[605],[567,1293,1295,1298],{"className":1294},[610],[567,1296],{"className":1297,"style":921},[614],[567,1299,1301,1304],{"className":1300},[619],[567,1302,676],{"className":1303,"style":778},[619,620],[567,1305,1307],{"className":1306},[708],[567,1308,1310,1330],{"className":1309},[712,713],[567,1311,1313,1327],{"className":1312},[717],[567,1314,1316],{"className":1315,"style":722},[721],[567,1317,1318,1321],{"style":793},[567,1319],{"className":1320,"style":730},[729],[567,1322,1324],{"className":1323},[734,735,736,737],[567,1325,668],{"className":1326},[619,620,737],[567,1328,745],{"className":1329},[744],[567,1331,1333],{"className":1332},[717],[567,1334,1336],{"className":1335,"style":752},[721],[567,1337],{}," und addiert, trifft ",[567,1340,1342,1355],{"className":1341},[570],[567,1343,1345],{"className":1344},[574],[576,1346,1347],{"xmlns":578},[580,1348,1349,1353],{},[583,1350,1351],{},[586,1352,563],{},[598,1354,563],{"encoding":600},[567,1356,1358],{"className":1357,"ariaHidden":606},[605],[567,1359,1361,1364],{"className":1360},[610],[567,1362],{"className":1363,"style":921},[614],[567,1365,563],{"className":1366},[619,620]," jeden Punkt.",[563,1369,1370,1371,1432,1433,1464,1465,1614],{},"Für die Abweichung von einer ",[567,1372,1374,1396],{"className":1373},[570],[567,1375,1377],{"className":1376},[574],[576,1378,1379],{"xmlns":578},[580,1380,1381,1393],{},[583,1382,1383,1385,1387,1389,1391],{},[590,1384,659],{"stretchy":658},[586,1386,588],{},[590,1388,592],{},[594,1390,596],{},[590,1392,681],{"stretchy":658},[598,1394,1395],{"encoding":600},"(n + 1)",[567,1397,1399,1420],{"className":1398,"ariaHidden":606},[605],[567,1400,1402,1405,1408,1411,1414,1417],{"className":1401},[610],[567,1403],{"className":1404,"style":694},[614],[567,1406,659],{"className":1407},[698],[567,1409,588],{"className":1410},[619,620],[567,1412],{"className":1413,"style":625},[624],[567,1415,592],{"className":1416},[629],[567,1418],{"className":1419,"style":625},[624],[567,1421,1423,1426,1429],{"className":1422},[610],[567,1424],{"className":1425,"style":694},[614],[567,1427,596],{"className":1428},[619],[567,1430,681],{"className":1431},[817],"-mal stetig differenzierbaren Funktion ",[567,1434,1436,1450],{"className":1435},[570],[567,1437,1439],{"className":1438},[574],[576,1440,1441],{"xmlns":578},[580,1442,1443,1448],{},[583,1444,1445],{},[586,1446,1447],{},"f",[598,1449,1447],{"encoding":600},[567,1451,1453],{"className":1452,"ariaHidden":606},[605],[567,1454,1456,1460],{"className":1455},[610],[567,1457],{"className":1458,"style":1459},[614],"height:0.8889em;vertical-align:-0.1944em;",[567,1461,1447],{"className":1462,"style":1463},[619,620],"margin-right:0.1076em;"," mit ",[567,1466,1468,1501],{"className":1467},[570],[567,1469,1471],{"className":1470},[574],[576,1472,1473],{"xmlns":578},[580,1474,1475,1498],{},[583,1476,1477,1483,1486,1488,1490,1496],{},[661,1478,1479,1481],{},[586,1480,676],{},[586,1482,668],{},[590,1484,1485],{},"=",[586,1487,1447],{},[590,1489,659],{"stretchy":658},[661,1491,1492,1494],{},[586,1493,665],{},[586,1495,668],{},[590,1497,681],{"stretchy":658},[598,1499,1500],{"encoding":600},"y_i = f(x_i)",[567,1502,1504,1559],{"className":1503,"ariaHidden":606},[605],[567,1505,1507,1510,1550,1553,1556],{"className":1506},[610],[567,1508],{"className":1509,"style":921},[614],[567,1511,1513,1516],{"className":1512},[619],[567,1514,676],{"className":1515,"style":778},[619,620],[567,1517,1519],{"className":1518},[708],[567,1520,1522,1542],{"className":1521},[712,713],[567,1523,1525,1539],{"className":1524},[717],[567,1526,1528],{"className":1527,"style":722},[721],[567,1529,1530,1533],{"style":793},[567,1531],{"className":1532,"style":730},[729],[567,1534,1536],{"className":1535},[734,735,736,737],[567,1537,668],{"className":1538},[619,620,737],[567,1540,745],{"className":1541},[744],[567,1543,1545],{"className":1544},[717],[567,1546,1548],{"className":1547,"style":752},[721],[567,1549],{},[567,1551],{"className":1552,"style":758},[624],[567,1554,1485],{"className":1555},[762],[567,1557],{"className":1558,"style":758},[624],[567,1560,1562,1565,1568,1571,1611],{"className":1561},[610],[567,1563],{"className":1564,"style":694},[614],[567,1566,1447],{"className":1567,"style":1463},[619,620],[567,1569,659],{"className":1570},[698],[567,1572,1574,1577],{"className":1573},[619],[567,1575,665],{"className":1576},[619,620],[567,1578,1580],{"className":1579},[708],[567,1581,1583,1603],{"className":1582},[712,713],[567,1584,1586,1600],{"className":1585},[717],[567,1587,1589],{"className":1588,"style":722},[721],[567,1590,1591,1594],{"style":725},[567,1592],{"className":1593,"style":730},[729],[567,1595,1597],{"className":1596},[734,735,736,737],[567,1598,668],{"className":1599},[619,620,737],[567,1601,745],{"className":1602},[744],[567,1604,1606],{"className":1605},[717],[567,1607,1609],{"className":1608,"style":752},[721],[567,1610],{},[567,1612,681],{"className":1613},[817]," gilt",[567,1616,1619],{"className":1617},[1618],"katex-display",[567,1620,1622,1731],{"className":1621},[570],[567,1623,1625],{"className":1624},[574],[576,1626,1628],{"xmlns":578,"display":1627},"block",[580,1629,1630,1728],{},[583,1631,1632,1634,1636,1638,1640,1643,1645,1647,1649,1651,1653,1697,1714,1716,1718,1720,1726],{},[586,1633,1447],{},[590,1635,659],{"stretchy":658},[586,1637,665],{},[590,1639,681],{"stretchy":658},[590,1641,1642],{},"−",[586,1644,563],{},[590,1646,659],{"stretchy":658},[586,1648,665],{},[590,1650,681],{"stretchy":658},[590,1652,1485],{},[1654,1655,1656,1682],"mfrac",{},[583,1657,1658,1675,1677,1680],{},[1659,1660,1661,1663],"msup",{},[586,1662,1447],{},[583,1664,1665,1667,1669,1671,1673],{},[590,1666,659],{"stretchy":658},[586,1668,588],{},[590,1670,592],{},[594,1672,596],{},[590,1674,681],{"stretchy":658},[590,1676,659],{"stretchy":658},[586,1678,1679],{},"ξ",[590,1681,681],{"stretchy":658},[583,1683,1684,1686,1688,1690,1692,1694],{},[590,1685,659],{"stretchy":658},[586,1687,588],{},[590,1689,592],{},[594,1691,596],{},[590,1693,681],{"stretchy":658},[590,1695,1696],{"stretchy":658},"!",[1698,1699,1700,1703,1712],"munderover",{},[590,1701,1702],{},"∏",[583,1704,1705,1708,1710],{},[586,1706,1707],{},"j",[590,1709,1485],{},[594,1711,1223],{},[586,1713,588],{},[590,1715,659],{"stretchy":658},[586,1717,665],{},[590,1719,1642],{},[661,1721,1722,1724],{},[586,1723,665],{},[586,1725,1707],{},[590,1727,681],{"stretchy":658},[598,1729,1730],{"encoding":600},"f(x) - p(x) = \\frac{f^{(n+1)}(\\xi)}{(n + 1)!} \\prod_{j=0}^{n} (x - x_j)",[567,1732,1734,1761,1788,2035],{"className":1733,"ariaHidden":606},[605],[567,1735,1737,1740,1743,1746,1749,1752,1755,1758],{"className":1736},[610],[567,1738],{"className":1739,"style":694},[614],[567,1741,1447],{"className":1742,"style":1463},[619,620],[567,1744,659],{"className":1745},[698],[567,1747,665],{"className":1748},[619,620],[567,1750,681],{"className":1751},[817],[567,1753],{"className":1754,"style":625},[624],[567,1756,1642],{"className":1757},[629],[567,1759],{"className":1760,"style":625},[624],[567,1762,1764,1767,1770,1773,1776,1779,1782,1785],{"className":1763},[610],[567,1765],{"className":1766,"style":694},[614],[567,1768,563],{"className":1769},[619,620],[567,1771,659],{"className":1772},[698],[567,1774,665],{"className":1775},[619,620],[567,1777,681],{"className":1778},[817],[567,1780],{"className":1781,"style":758},[624],[567,1783,1485],{"className":1784},[762],[567,1786],{"className":1787,"style":758},[624],[567,1789,1791,1795,1938,1942,2020,2023,2026,2029,2032],{"className":1790},[610],[567,1792],{"className":1793,"style":1794},[614],"height:3.0652em;vertical-align:-1.4138em;",[567,1796,1798,1802,1935],{"className":1797},[619],[567,1799],{"className":1800},[698,1801],"nulldelimiter",[567,1803,1805],{"className":1804},[1654],[567,1806,1808,1926],{"className":1807},[712,713],[567,1809,1811,1923],{"className":1810},[717],[567,1812,1815,1847,1858],{"className":1813,"style":1814},[721],"height:1.565em;",[567,1816,1818,1822],{"style":1817},"top:-2.314em;",[567,1819],{"className":1820,"style":1821},[729],"height:3em;",[567,1823,1825,1828,1831,1834,1837,1840,1843],{"className":1824},[619],[567,1826,659],{"className":1827},[698],[567,1829,588],{"className":1830},[619,620],[567,1832],{"className":1833,"style":625},[624],[567,1835,592],{"className":1836},[629],[567,1838],{"className":1839,"style":625},[624],[567,1841,596],{"className":1842},[619],[567,1844,1846],{"className":1845},[817],")!",[567,1848,1850,1853],{"style":1849},"top:-3.23em;",[567,1851],{"className":1852,"style":1821},[729],[567,1854],{"className":1855,"style":1857},[1856],"frac-line","border-bottom-width:0.04em;",[567,1859,1861,1864],{"style":1860},"top:-3.677em;",[567,1862],{"className":1863,"style":1821},[729],[567,1865,1867,1913,1916,1920],{"className":1866},[619],[567,1868,1870,1873],{"className":1869},[619],[567,1871,1447],{"className":1872,"style":1463},[619,620],[567,1874,1876],{"className":1875},[708],[567,1877,1879],{"className":1878},[712],[567,1880,1882],{"className":1881},[717],[567,1883,1886],{"className":1884,"style":1885},[721],"height:0.888em;",[567,1887,1889,1892],{"style":1888},"top:-3.063em;margin-right:0.05em;",[567,1890],{"className":1891,"style":730},[729],[567,1893,1895],{"className":1894},[734,735,736,737],[567,1896,1898,1901,1904,1907,1910],{"className":1897},[619,737],[567,1899,659],{"className":1900},[698,737],[567,1902,588],{"className":1903},[619,620,737],[567,1905,592],{"className":1906},[629,737],[567,1908,596],{"className":1909},[619,737],[567,1911,681],{"className":1912},[817,737],[567,1914,659],{"className":1915},[698],[567,1917,1679],{"className":1918,"style":1919},[619,620],"margin-right:0.046em;",[567,1921,681],{"className":1922},[817],[567,1924,745],{"className":1925},[744],[567,1927,1929],{"className":1928},[717],[567,1930,1933],{"className":1931,"style":1932},[721],"height:0.936em;",[567,1934],{},[567,1936],{"className":1937},[817,1801],[567,1939],{"className":1940,"style":1941},[624],"margin-right:0.1667em;",[567,1943,1947],{"className":1944},[1945,1946],"mop","op-limits",[567,1948,1950,2011],{"className":1949},[712,713],[567,1951,1953,2008],{"className":1952},[717],[567,1954,1957,1980,1993],{"className":1955,"style":1956},[721],"height:1.6514em;",[567,1958,1960,1964],{"style":1959},"top:-1.8723em;margin-left:0em;",[567,1961],{"className":1962,"style":1963},[729],"height:3.05em;",[567,1965,1967],{"className":1966},[734,735,736,737],[567,1968,1970,1974,1977],{"className":1969},[619,737],[567,1971,1707],{"className":1972,"style":1973},[619,620,737],"margin-right:0.0572em;",[567,1975,1485],{"className":1976},[762,737],[567,1978,1223],{"className":1979},[619,737],[567,1981,1983,1986],{"style":1982},"top:-3.05em;",[567,1984],{"className":1985,"style":1963},[729],[567,1987,1988],{},[567,1989,1702],{"className":1990},[1945,1991,1992],"op-symbol","large-op",[567,1994,1996,1999],{"style":1995},"top:-4.3em;margin-left:0em;",[567,1997],{"className":1998,"style":1963},[729],[567,2000,2002],{"className":2001},[734,735,736,737],[567,2003,2005],{"className":2004},[619,737],[567,2006,588],{"className":2007},[619,620,737],[567,2009,745],{"className":2010},[744],[567,2012,2014],{"className":2013},[717],[567,2015,2018],{"className":2016,"style":2017},[721],"height:1.4138em;",[567,2019],{},[567,2021,659],{"className":2022},[698],[567,2024,665],{"className":2025},[619,620],[567,2027],{"className":2028,"style":625},[624],[567,2030,1642],{"className":2031},[629],[567,2033],{"className":2034,"style":625},[624],[567,2036,2038,2042,2083],{"className":2037},[610],[567,2039],{"className":2040,"style":2041},[614],"height:1.0361em;vertical-align:-0.2861em;",[567,2043,2045,2048],{"className":2044},[619],[567,2046,665],{"className":2047},[619,620],[567,2049,2051],{"className":2050},[708],[567,2052,2054,2074],{"className":2053},[712,713],[567,2055,2057,2071],{"className":2056},[717],[567,2058,2060],{"className":2059,"style":722},[721],[567,2061,2062,2065],{"style":725},[567,2063],{"className":2064,"style":730},[729],[567,2066,2068],{"className":2067},[734,735,736,737],[567,2069,1707],{"className":2070,"style":1973},[619,620,737],[567,2072,745],{"className":2073},[744],[567,2075,2077],{"className":2076},[717],[567,2078,2081],{"className":2079,"style":2080},[721],"height:0.2861em;",[567,2082],{},[567,2084,681],{"className":2085},[817],[563,2087,2088,2089,2118,2119,2147],{},"für ein ",[567,2090,2092,2106],{"className":2091},[570],[567,2093,2095],{"className":2094},[574],[576,2096,2097],{"xmlns":578},[580,2098,2099,2103],{},[583,2100,2101],{},[586,2102,1679],{},[598,2104,2105],{"encoding":600},"\\xi",[567,2107,2109],{"className":2108,"ariaHidden":606},[605],[567,2110,2112,2115],{"className":2111},[610],[567,2113],{"className":2114,"style":1459},[614],[567,2116,1679],{"className":2117,"style":1919},[619,620]," im kleinsten Intervall, das ",[567,2120,2122,2135],{"className":2121},[570],[567,2123,2125],{"className":2124},[574],[576,2126,2127],{"xmlns":578},[580,2128,2129,2133],{},[583,2130,2131],{},[586,2132,665],{},[598,2134,665],{"encoding":600},[567,2136,2138],{"className":2137,"ariaHidden":606},[605],[567,2139,2141,2144],{"className":2140},[610],[567,2142],{"className":2143,"style":951},[614],[567,2145,665],{"className":2146},[619,620]," und alle Stützstellen enthält.",[563,2149,2150,2151,2154],{},"Die Lagrange-Form eignet sich gut für Theorie und Herleitungen, z.B. von Quadraturformeln wie der Simpsonregel. Zum Rechnen mit vielen oder neu hinzukommenden Punkten ist die Newton-Form oder die baryzentrische Form günstiger. Bei vielen äquidistanten Stützstellen schwingt das Polynom am Rand stark (",[892,2152,2153],{},"Runge-Phänomen","); dann sind Tschebyschow-Stützstellen oder Splines besser.",[558,2156,2158],{"id":2157},"beispiele","Beispiele",[563,2160,2161,2162,2223,2224,2286,2287,2350],{},"Polynom durch ",[567,2163,2165,2187],{"className":2164},[570],[567,2166,2168],{"className":2167},[574],[576,2169,2170],{"xmlns":578},[580,2171,2172,2184],{},[583,2173,2174,2176,2178,2180,2182],{},[590,2175,659],{"stretchy":658},[594,2177,1223],{},[590,2179,671],{},[594,2181,596],{},[590,2183,681],{"stretchy":658},[598,2185,2186],{"encoding":600},"(0 \\mid 1)",[567,2188,2190,2211],{"className":2189,"ariaHidden":606},[605],[567,2191,2193,2196,2199,2202,2205,2208],{"className":2192},[610],[567,2194],{"className":2195,"style":694},[614],[567,2197,659],{"className":2198},[698],[567,2200,1223],{"className":2201},[619],[567,2203],{"className":2204,"style":758},[624],[567,2206,671],{"className":2207},[762],[567,2209],{"className":2210,"style":758},[624],[567,2212,2214,2217,2220],{"className":2213},[610],[567,2215],{"className":2216,"style":694},[614],[567,2218,596],{"className":2219},[619],[567,2221,681],{"className":2222},[817],", ",[567,2225,2227,2250],{"className":2226},[570],[567,2228,2230],{"className":2229},[574],[576,2231,2232],{"xmlns":578},[580,2233,2234,2247],{},[583,2235,2236,2238,2240,2242,2245],{},[590,2237,659],{"stretchy":658},[594,2239,596],{},[590,2241,671],{},[594,2243,2244],{},"3",[590,2246,681],{"stretchy":658},[598,2248,2249],{"encoding":600},"(1 \\mid 3)",[567,2251,2253,2274],{"className":2252,"ariaHidden":606},[605],[567,2254,2256,2259,2262,2265,2268,2271],{"className":2255},[610],[567,2257],{"className":2258,"style":694},[614],[567,2260,659],{"className":2261},[698],[567,2263,596],{"className":2264},[619],[567,2266],{"className":2267,"style":758},[624],[567,2269,671],{"className":2270},[762],[567,2272],{"className":2273,"style":758},[624],[567,2275,2277,2280,2283],{"className":2276},[610],[567,2278],{"className":2279,"style":694},[614],[567,2281,2244],{"className":2282},[619],[567,2284,681],{"className":2285},[817]," und ",[567,2288,2290,2314],{"className":2289},[570],[567,2291,2293],{"className":2292},[574],[576,2294,2295],{"xmlns":578},[580,2296,2297,2311],{},[583,2298,2299,2301,2304,2306,2309],{},[590,2300,659],{"stretchy":658},[594,2302,2303],{},"2",[590,2305,671],{},[594,2307,2308],{},"7",[590,2310,681],{"stretchy":658},[598,2312,2313],{"encoding":600},"(2 \\mid 7)",[567,2315,2317,2338],{"className":2316,"ariaHidden":606},[605],[567,2318,2320,2323,2326,2329,2332,2335],{"className":2319},[610],[567,2321],{"className":2322,"style":694},[614],[567,2324,659],{"className":2325},[698],[567,2327,2303],{"className":2328},[619],[567,2330],{"className":2331,"style":758},[624],[567,2333,671],{"className":2334},[762],[567,2336],{"className":2337,"style":758},[624],[567,2339,2341,2344,2347],{"className":2340},[610],[567,2342],{"className":2343,"style":694},[614],[567,2345,2308],{"className":2346},[619],[567,2348,681],{"className":2349},[817],":",[567,2352,2354],{"className":2353},[1618],[567,2355,2357,2668],{"className":2356},[570],[567,2358,2360],{"className":2359},[574],[576,2361,2362],{"xmlns":578,"display":1627},[580,2363,2364,2665],{},[2365,2366,2370,2477,2569],"mtable",{"rowspacing":2367,"columnalign":2368,"columnspacing":2369},"0.25em","right left","0em",[2371,2372,2373,2393],"mtr",{},[2374,2375,2376],"mtd",{},[2377,2378,2379],"mstyle",{"scriptlevel":1223,"displaystyle":606},[583,2380,2381,2387,2389,2391],{},[661,2382,2383,2385],{},[586,2384,983],{},[594,2386,1223],{},[590,2388,659],{"stretchy":658},[586,2390,665],{},[590,2392,681],{"stretchy":658},[2374,2394,2395],{},[2377,2396,2397],{"scriptlevel":1223,"displaystyle":606},[583,2398,2399,2401,2403,2449,2451],{},[583,2400],{},[590,2402,1485],{},[1654,2404,2405,2427],{},[583,2406,2407,2409,2411,2413,2415,2417,2419,2421,2423,2425],{},[590,2408,659],{"stretchy":658},[586,2410,665],{},[590,2412,1642],{},[594,2414,596],{},[590,2416,681],{"stretchy":658},[590,2418,659],{"stretchy":658},[586,2420,665],{},[590,2422,1642],{},[594,2424,2303],{},[590,2426,681],{"stretchy":658},[583,2428,2429,2431,2433,2435,2437,2439,2441,2443,2445,2447],{},[590,2430,659],{"stretchy":658},[594,2432,1223],{},[590,2434,1642],{},[594,2436,596],{},[590,2438,681],{"stretchy":658},[590,2440,659],{"stretchy":658},[594,2442,1223],{},[590,2444,1642],{},[594,2446,2303],{},[590,2448,681],{"stretchy":658},[590,2450,1485],{},[1654,2452,2453,2475],{},[583,2454,2455,2457,2459,2461,2463,2465,2467,2469,2471,2473],{},[590,2456,659],{"stretchy":658},[586,2458,665],{},[590,2460,1642],{},[594,2462,596],{},[590,2464,681],{"stretchy":658},[590,2466,659],{"stretchy":658},[586,2468,665],{},[590,2470,1642],{},[594,2472,2303],{},[590,2474,681],{"stretchy":658},[594,2476,2303],{},[2371,2478,2479,2497],{},[2374,2480,2481],{},[2377,2482,2483],{"scriptlevel":1223,"displaystyle":606},[583,2484,2485,2491,2493,2495],{},[661,2486,2487,2489],{},[586,2488,983],{},[594,2490,596],{},[590,2492,659],{"stretchy":658},[586,2494,665],{},[590,2496,681],{"stretchy":658},[2374,2498,2499],{},[2377,2500,2501],{"scriptlevel":1223,"displaystyle":606},[583,2502,2503,2505,2507,2553,2555,2557,2559,2561,2563,2565,2567],{},[583,2504],{},[590,2506,1485],{},[1654,2508,2509,2531],{},[583,2510,2511,2513,2515,2517,2519,2521,2523,2525,2527,2529],{},[590,2512,659],{"stretchy":658},[586,2514,665],{},[590,2516,1642],{},[594,2518,1223],{},[590,2520,681],{"stretchy":658},[590,2522,659],{"stretchy":658},[586,2524,665],{},[590,2526,1642],{},[594,2528,2303],{},[590,2530,681],{"stretchy":658},[583,2532,2533,2535,2537,2539,2541,2543,2545,2547,2549,2551],{},[590,2534,659],{"stretchy":658},[594,2536,596],{},[590,2538,1642],{},[594,2540,1223],{},[590,2542,681],{"stretchy":658},[590,2544,659],{"stretchy":658},[594,2546,596],{},[590,2548,1642],{},[594,2550,2303],{},[590,2552,681],{"stretchy":658},[590,2554,1485],{},[590,2556,1642],{},[586,2558,665],{},[590,2560,659],{"stretchy":658},[586,2562,665],{},[590,2564,1642],{},[594,2566,2303],{},[590,2568,681],{"stretchy":658},[2371,2570,2571,2589],{},[2374,2572,2573],{},[2377,2574,2575],{"scriptlevel":1223,"displaystyle":606},[583,2576,2577,2583,2585,2587],{},[661,2578,2579,2581],{},[586,2580,983],{},[594,2582,2303],{},[590,2584,659],{"stretchy":658},[586,2586,665],{},[590,2588,681],{"stretchy":658},[2374,2590,2591],{},[2377,2592,2593],{"scriptlevel":1223,"displaystyle":606},[583,2594,2595,2597,2599,2645,2647],{},[583,2596],{},[590,2598,1485],{},[1654,2600,2601,2623],{},[583,2602,2603,2605,2607,2609,2611,2613,2615,2617,2619,2621],{},[590,2604,659],{"stretchy":658},[586,2606,665],{},[590,2608,1642],{},[594,2610,1223],{},[590,2612,681],{"stretchy":658},[590,2614,659],{"stretchy":658},[586,2616,665],{},[590,2618,1642],{},[594,2620,596],{},[590,2622,681],{"stretchy":658},[583,2624,2625,2627,2629,2631,2633,2635,2637,2639,2641,2643],{},[590,2626,659],{"stretchy":658},[594,2628,2303],{},[590,2630,1642],{},[594,2632,1223],{},[590,2634,681],{"stretchy":658},[590,2636,659],{"stretchy":658},[594,2638,2303],{},[590,2640,1642],{},[594,2642,596],{},[590,2644,681],{"stretchy":658},[590,2646,1485],{},[1654,2648,2649,2663],{},[583,2650,2651,2653,2655,2657,2659,2661],{},[586,2652,665],{},[590,2654,659],{"stretchy":658},[586,2656,665],{},[590,2658,1642],{},[594,2660,596],{},[590,2662,681],{"stretchy":658},[594,2664,2303],{},[598,2666,2667],{"encoding":600},"\\begin{aligned}\nL_0(x) &= \\frac{(x - 1)(x - 2)}{(0 - 1)(0 - 2)} = \\frac{(x - 1)(x - 2)}{2} \\\\\nL_1(x) &= \\frac{(x - 0)(x - 2)}{(1 - 0)(1 - 2)} = -x(x - 2) \\\\\nL_2(x) &= \\frac{(x - 0)(x - 1)}{(2 - 0)(2 - 1)} = \\frac{x(x - 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= 1 \\cdot L_0(x) + 3 \\cdot L_1(x) + 7 \\cdot L_2(x) = x^2 + x + 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0 400000 1080","xMinYMin slice",[4254,4255],"path",{"d":4256},"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",[567,4258,745],{"className":4259},[744],[567,4261,4263],{"className":4262},[717],[567,4264,4267],{"className":4265,"style":4266},[721],"height:0.1328em;",[567,4268],{}," aus den Werten ",[567,4271,4273,4293],{"className":4272},[570],[567,4274,4276],{"className":4275},[574],[576,4277,4278],{"xmlns":578},[580,4279,4280,4290],{},[583,4281,4282,4286,4288],{},[4188,4283,4284],{},[594,4285,4161],{},[590,4287,1485],{},[594,4289,2303],{},[598,4291,4292],{"encoding":600},"\\sqrt{4} = 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= 3",[567,4392,4394,4456],{"className":4393,"ariaHidden":606},[605],[567,4395,4397,4400,4447,4450,4453],{"className":4396},[610],[567,4398],{"className":4399,"style":4204},[614],[567,4401,4403],{"className":4402},[619,4208],[567,4404,4406,4439],{"className":4405},[712,713],[567,4407,4409,4436],{"className":4408},[717],[567,4410,4412,4424],{"className":4411,"style":4218},[721],[567,4413,4415,4418],{"className":4414,"style":4223},[4222],[567,4416],{"className":4417,"style":1821},[729],[567,4419,4421],{"className":4420,"style":4230},[619],[567,4422,4383],{"className":4423},[619],[567,4425,4426,4429],{"style":4236},[567,4427],{"className":4428,"style":1821},[729],[567,4430,4432],{"className":4431,"style":4244},[4243],[4246,4433,4434],{"xmlns":4248,"width":4249,"height":4250,"viewBox":4251,"preserveAspectRatio":4252},[4254,4435],{"d":4256},[567,4437,745],{"className":4438},[744],[567,4440,4442],{"className":4441},[717],[567,4443,4445],{"className":4444,"style":4266},[721],[567,4446],{},[567,4448],{"className":4449,"style":758},[624],[567,4451,1485],{"className":4452},[762],[567,4454],{"className":4455,"style":758},[624],[567,4457,4459,4462],{"className":4458},[610],[567,4460],{"className":4461,"style":639},[614],[567,4463,2244],{"className":4464},[619],[567,4466,4468,4489],{"className":4467},[570],[567,4469,4471],{"className":4470},[574],[576,4472,4473],{"xmlns":578},[580,4474,4475,4486],{},[583,4476,4477,4482,4484],{},[4188,4478,4479],{},[594,4480,4481],{},"16",[590,4483,1485],{},[594,4485,4161],{},[598,4487,4488],{"encoding":600},"\\sqrt{16} = 4",[567,4490,4492,4554],{"className":4491,"ariaHidden":606},[605],[567,4493,4495,4498,4545,4548,4551],{"className":4494},[610],[567,4496],{"className":4497,"style":4204},[614],[567,4499,4501],{"className":4500},[619,4208],[567,4502,4504,4537],{"className":4503},[712,713],[567,4505,4507,4534],{"className":4506},[717],[567,4508,4510,4522],{"className":4509,"style":4218},[721],[567,4511,4513,4516],{"className":4512,"style":4223},[4222],[567,4514],{"className":4515,"style":1821},[729],[567,4517,4519],{"className":4518,"style":4230},[619],[567,4520,4481],{"className":4521},[619],[567,4523,4524,4527],{"style":4236},[567,4525],{"className":4526,"style":1821},[729],[567,4528,4530],{"className":4529,"style":4244},[4243],[4246,4531,4532],{"xmlns":4248,"width":4249,"height":4250,"viewBox":4251,"preserveAspectRatio":4252},[4254,4533],{"d":4256},[567,4535,745],{"className":4536},[744],[567,4538,4540],{"className":4539},[717],[567,4541,4543],{"className":4542,"style":4266},[721],[567,4544],{},[567,4546],{"className":4547,"style":758},[624],[567,4549,1485],{"className":4550},[762],[567,4552],{"className":4553,"style":758},[624],[567,4555,4557,4560],{"className":4556},[610],[567,4558],{"className":4559,"style":639},[614],[567,4561,4161],{"className":4562},[619],[567,4564,4566],{"className":4565},[1618],[567,4567,4569,4751],{"className":4568},[570],[567,4570,4572],{"className":4571},[574],[576,4573,4574],{"xmlns":578,"display":1627},[580,4575,4576,4748],{},[583,4577,4578,4580,4582,4584,4586,4588,4590,4592,4638,4640,4642,4644,4690,4692,4694,4696,4742,4745],{},[586,4579,563],{},[590,4581,659],{"stretchy":658},[594,4583,4138],{},[590,4585,681],{"stretchy":658},[590,4587,1485],{},[594,4589,2303],{},[590,4591,3659],{},[1654,4593,4594,4616],{},[583,4595,4596,4598,4600,4602,4604,4606,4608,4610,4612,4614],{},[590,4597,659],{"stretchy":658},[594,4599,4138],{},[590,4601,1642],{},[594,4603,4383],{},[590,4605,681],{"stretchy":658},[590,4607,659],{"stretchy":658},[594,4609,4138],{},[590,4611,1642],{},[594,4613,4481],{},[590,4615,681],{"stretchy":658},[583,4617,4618,4620,4622,4624,4626,4628,4630,4632,4634,4636],{},[590,4619,659],{"stretchy":658},[594,4621,4161],{},[590,4623,1642],{},[594,4625,4383],{},[590,4627,681],{"stretchy":658},[590,4629,659],{"stretchy":658},[594,4631,4161],{},[590,4633,1642],{},[594,4635,4481],{},[590,4637,681],{"stretchy":658},[590,4639,592],{},[594,4641,2244],{},[590,4643,3659],{},[1654,4645,4646,4668],{},[583,4647,4648,4650,4652,4654,4656,4658,4660,4662,4664,4666],{},[590,4649,659],{"stretchy":658},[594,4651,4138],{},[590,4653,1642],{},[594,4655,4161],{},[590,4657,681],{"stretchy":658},[590,4659,659],{"stretchy":658},[594,4661,4138],{},[590,4663,1642],{},[594,4665,4481],{},[590,4667,681],{"stretchy":658},[583,4669,4670,4672,4674,4676,4678,4680,4682,4684,4686,4688],{},[590,4671,659],{"stretchy":658},[594,4673,4383],{},[590,4675,1642],{},[594,4677,4161],{},[590,4679,681],{"stretchy":658},[590,4681,659],{"stretchy":658},[594,4683,4383],{},[590,4685,1642],{},[594,4687,4481],{},[590,4689,681],{"stretchy":658},[590,4691,592],{},[594,4693,4161],{},[590,4695,3659],{},[1654,4697,4698,4720],{},[583,4699,4700,4702,4704,4706,4708,4710,4712,4714,4716,4718],{},[590,4701,659],{"stretchy":658},[594,4703,4138],{},[590,4705,1642],{},[594,4707,4161],{},[590,4709,681],{"stretchy":658},[590,4711,659],{"stretchy":658},[594,4713,4138],{},[590,4715,1642],{},[594,4717,4383],{},[590,4719,681],{"stretchy":658},[583,4721,4722,4724,4726,4728,4730,4732,4734,4736,4738,4740],{},[590,4723,659],{"stretchy":658},[594,4725,4481],{},[590,4727,1642],{},[594,4729,4161],{},[590,4731,681],{"stretchy":658},[590,4733,659],{"stretchy":658},[594,4735,4481],{},[590,4737,1642],{},[594,4739,4383],{},[590,4741,681],{"stretchy":658},[590,4743,4744],{},"≈",[594,4746,4747],{},"2,2190",[598,4749,4750],{"encoding":600},"p(5) = 2 \\cdot \\frac{(5 - 9)(5 - 16)}{(4 - 9)(4 - 16)} + 3 \\cdot \\frac{(5 - 4)(5 - 16)}{(9 - 4)(9 - 16)} + 4 \\cdot \\frac{(5 - 4)(5 - 9)}{(16 - 4)(16 - 9)} \\approx 2{,}2190",[567,4752,4754,4781,4799,4955,4973,5128,5146,5301],{"className":4753,"ariaHidden":606},[605],[567,4755,4757,4760,4763,4766,4769,4772,4775,4778],{"className":4756},[610],[567,4758],{"className":4759,"style":694},[614],[567,4761,563],{"className":4762},[619,620],[567,4764,659],{"className":4765},[698],[567,4767,4138],{"className":4768},[619],[567,4770,681],{"className":4771},[817],[567,4773],{"className":4774,"style":758},[624],[567,4776,1485],{"className":4777},[762],[567,4779],{"className":4780,"style":758},[624],[567,4782,4784,4787,4790,4793,4796],{"className":4783},[610],[567,4785],{"className":4786,"style":639},[614],[567,4788,2303],{"className":4789},[619],[567,4791],{"className":4792,"style":625},[624],[567,4794,3659],{"className":4795},[629],[567,4797],{"className":4798,"style":625},[624],[567,4800,4802,4806,4946,4949,4952],{"className":4801},[610],[567,4803],{"className":4804,"style":4805},[614],"height:2.363em;vertical-align:-0.936em;",[567,4807,4809,4812,4943],{"className":4808},[619],[567,4810],{"className":4811},[698,1801],[567,4813,4815],{"className":4814},[1654],[567,4816,4818,4935],{"className":4817},[712,713],[567,4819,4821,4932],{"className":4820},[717],[567,4822,4824,4874,4882],{"className":4823,"style":2937},[721],[567,4825,4826,4829],{"style":1817},[567,4827],{"className":4828,"style":1821},[729],[567,4830,4832,4835,4838,4841,4844,4847,4850,4853,4856,4859,4862,4865,4868,4871],{"className":4831},[619],[567,4833,659],{"className":4834},[698],[567,4836,4161],{"className":4837},[619],[567,4839],{"className":4840,"style":625},[624],[567,4842,1642],{"className":4843},[629],[567,4845],{"className":4846,"style":625},[624],[567,4848,4383],{"className":4849},[619],[567,4851,681],{"className":4852},[817],[567,4854,659],{"className":4855},[698],[567,4857,4161],{"className":4858},[619],[567,4860],{"className":4861,"style":625},[624],[567,4863,1642],{"className":4864},[629],[567,4866],{"className":4867,"style":625},[624],[567,4869,4481],{"className":4870},[619],[567,4872,681],{"className":4873},[817],[567,4875,4876,4879],{"style":1849},[567,4877],{"className":4878,"style":1821},[729],[567,4880],{"className":4881,"style":1857},[1856],[567,4883,4884,4887],{"style":1860},[567,4885],{"className":4886,"style":1821},[729],[567,4888,4890,4893,4896,4899,4902,4905,4908,4911,4914,4917,4920,4923,4926,4929],{"className":4889},[619],[567,4891,659],{"className":4892},[698],[567,4894,4138],{"className":4895},[619],[567,4897],{"className":4898,"style":625},[624],[567,4900,1642],{"className":4901},[629],[567,4903],{"className":4904,"style":625},[624],[567,4906,4383],{"className":4907},[619],[567,4909,681],{"className":4910},[817],[567,4912,659],{"className":4913},[698],[567,4915,4138],{"className":4916},[619],[567,4918],{"className":4919,"style":625},[624],[567,4921,1642],{"className":4922},[629],[567,4924],{"className":4925,"style":625},[624],[567,4927,4481],{"className":4928},[619],[567,4930,681],{"className":4931},[817],[567,4933,745],{"className":4934},[744],[567,4936,4938],{"className":4937},[717],[567,4939,4941],{"className":4940,"style":1932},[721],[567,4942],{},[567,4944],{"className":4945},[817,1801],[567,4947],{"className":4948,"style":625},[624],[567,4950,592],{"className":4951},[629],[567,4953],{"className":4954,"style":625},[624],[567,4956,4958,4961,4964,4967,4970],{"className":4957},[610],[567,4959],{"className":4960,"style":639},[614],[567,4962,2244],{"className":4963},[619],[567,4965],{"className":4966,"style":625},[624],[567,4968,3659],{"className":4969},[629],[567,4971],{"className":4972,"style":625},[624],[567,4974,4976,4979,5119,5122,5125],{"className":4975},[610],[567,4977],{"className":4978,"style":4805},[614],[567,4980,4982,4985,5116],{"className":4981},[619],[567,4983],{"className":4984},[698,1801],[567,4986,4988],{"className":4987},[1654],[567,4989,4991,5108],{"className":4990},[712,713],[567,4992,4994,5105],{"className":4993},[717],[567,4995,4997,5047,5055],{"className":4996,"style":2937},[721],[567,4998,4999,5002],{"style":1817},[567,5000],{"className":5001,"style":1821},[729],[567,5003,5005,5008,5011,5014,5017,5020,5023,5026,5029,5032,5035,5038,5041,5044],{"className":5004},[619],[567,5006,659],{"className":5007},[698],[567,5009,4383],{"className":5010},[619],[567,5012],{"className":5013,"style":625},[624],[567,5015,1642],{"className":5016},[629],[567,5018],{"className":5019,"style":625},[624],[567,5021,4161],{"className":5022},[619],[567,5024,681],{"className":5025},[817],[567,5027,659],{"className":5028},[698],[567,5030,4383],{"className":5031},[619],[567,5033],{"className":5034,"style":625},[624],[567,5036,1642],{"className":5037},[629],[567,5039],{"className":5040,"style":625},[624],[567,5042,4481],{"className":5043},[619],[567,5045,681],{"className":5046},[817],[567,5048,5049,5052],{"style":1849},[567,5050],{"className":5051,"style":1821},[729],[567,5053],{"className":5054,"style":1857},[1856],[567,5056,5057,5060],{"style":1860},[567,5058],{"className":5059,"style":1821},[729],[567,5061,5063,5066,5069,5072,5075,5078,5081,5084,5087,5090,5093,5096,5099,5102],{"className":5062},[619],[567,5064,659],{"className":5065},[698],[567,5067,4138],{"className":5068},[619],[567,5070],{"className":5071,"style":625},[624],[567,5073,1642],{"className":5074},[629],[567,5076],{"className":5077,"style":625},[624],[567,5079,4161],{"className":5080},[619],[567,5082,681],{"className":5083},[817],[567,5085,659],{"className":5086},[698],[567,5088,4138],{"className":5089},[619],[567,5091],{"className":5092,"style":625},[624],[567,5094,1642],{"className":5095},[629],[567,5097],{"className":5098,"style":625},[624],[567,5100,4481],{"className":5101},[619],[567,5103,681],{"className":5104},[817],[567,5106,745],{"className":5107},[744],[567,5109,5111],{"className":5110},[717],[567,5112,5114],{"className":5113,"style":1932},[721],[567,5115],{},[567,5117],{"className":5118},[817,1801],[567,5120],{"className":5121,"style":625},[624],[567,5123,592],{"className":5124},[629],[567,5126],{"className":5127,"style":625},[624],[567,5129,5131,5134,5137,5140,5143],{"className":5130},[610],[567,5132],{"className":5133,"style":639},[614],[567,5135,4161],{"className":5136},[619],[567,5138],{"className":5139,"style":625},[624],[567,5141,3659],{"className":5142},[629],[567,5144],{"className":5145,"style":625},[624],[567,5147,5149,5152,5292,5295,5298],{"className":5148},[610],[567,5150],{"className":5151,"style":4805},[614],[567,5153,5155,5158,5289],{"className":5154},[619],[567,5156],{"className":5157},[698,1801],[567,5159,5161],{"className":5160},[1654],[567,5162,5164,5281],{"className":5163},[712,713],[567,5165,5167,5278],{"className":5166},[717],[567,5168,5170,5220,5228],{"className":5169,"style":2937},[721],[567,5171,5172,5175],{"style":1817},[567,5173],{"className":5174,"style":1821},[729],[567,5176,5178,5181,5184,5187,5190,5193,5196,5199,5202,5205,5208,5211,5214,5217],{"className":5177},[619],[567,5179,659],{"className":5180},[698],[567,5182,4481],{"className":5183},[619],[567,5185],{"className":5186,"style":625},[624],[567,5188,1642],{"className":5189},[629],[567,5191],{"className":5192,"style":625},[624],[567,5194,4161],{"className":5195},[619],[567,5197,681],{"className":5198},[817],[567,5200,659],{"className":5201},[698],[567,5203,4481],{"className":5204},[619],[567,5206],{"className":5207,"style":625},[624],[567,5209,1642],{"className":5210},[629],[567,5212],{"className":5213,"style":625},[624],[567,5215,4383],{"className":5216},[619],[567,5218,681],{"className":5219},[817],[567,5221,5222,5225],{"style":1849},[567,5223],{"className":5224,"style":1821},[729],[567,5226],{"className":5227,"style":1857},[1856],[567,5229,5230,5233],{"style":1860},[567,5231],{"className":5232,"style":1821},[729],[567,5234,5236,5239,5242,5245,5248,5251,5254,5257,5260,5263,5266,5269,5272,5275],{"className":5235},[619],[567,5237,659],{"className":5238},[698],[567,5240,4138],{"className":5241},[619],[567,5243],{"className":5244,"style":625},[624],[567,5246,1642],{"className":5247},[629],[567,5249],{"className":5250,"style":625},[624],[567,5252,4161],{"className":5253},[619],[567,5255,681],{"className":5256},[817],[567,5258,659],{"className":5259},[698],[567,5261,4138],{"className":5262},[619],[567,5264],{"className":5265,"style":625},[624],[567,5267,1642],{"className":5268},[629],[567,5270],{"className":5271,"style":625},[624],[567,5273,4383],{"className":5274},[619],[567,5276,681],{"className":5277},[817],[567,5279,745],{"className":5280},[744],[567,5282,5284],{"className":5283},[717],[567,5285,5287],{"className":5286,"style":1932},[721],[567,5288],{},[567,5290],{"className":5291},[817,1801],[567,5293],{"className":5294,"style":758},[624],[567,5296,4744],{"className":5297},[762],[567,5299],{"className":5300,"style":758},[624],[567,5302,5304,5307,5310,5316],{"className":5303},[610],[567,5305],{"className":5306,"style":4157},[614],[567,5308,2303],{"className":5309},[619],[567,5311,5313],{"className":5312},[619],[567,5314,4134],{"className":5315},[4133],[567,5317,5319],{"className":5318},[619],"2190",[563,5321,5322,5323,5431],{},"Der genaue Wert ist ",[567,5324,5326,5347],{"className":5325},[570],[567,5327,5329],{"className":5328},[574],[576,5330,5331],{"xmlns":578},[580,5332,5333,5344],{},[583,5334,5335,5339,5341],{},[4188,5336,5337],{},[594,5338,4138],{},[590,5340,4744],{},[594,5342,5343],{},"2,2361",[598,5345,5346],{"encoding":600},"\\sqrt{5} \\approx 2{,}2361",[567,5348,5350,5412],{"className":5349,"ariaHidden":606},[605],[567,5351,5353,5356,5403,5406,5409],{"className":5352},[610],[567,5354],{"className":5355,"style":4204},[614],[567,5357,5359],{"className":5358},[619,4208],[567,5360,5362,5395],{"className":5361},[712,713],[567,5363,5365,5392],{"className":5364},[717],[567,5366,5368,5380],{"className":5367,"style":4218},[721],[567,5369,5371,5374],{"className":5370,"style":4223},[4222],[567,5372],{"className":5373,"style":1821},[729],[567,5375,5377],{"className":5376,"style":4230},[619],[567,5378,4138],{"className":5379},[619],[567,5381,5382,5385],{"style":4236},[567,5383],{"className":5384,"style":1821},[729],[567,5386,5388],{"className":5387,"style":4244},[4243],[4246,5389,5390],{"xmlns":4248,"width":4249,"height":4250,"viewBox":4251,"preserveAspectRatio":4252},[4254,5391],{"d":4256},[567,5393,745],{"className":5394},[744],[567,5396,5398],{"className":5397},[717],[567,5399,5401],{"className":5400,"style":4266},[721],[567,5402],{},[567,5404],{"className":5405,"style":758},[624],[567,5407,4744],{"className":5408},[762],[567,5410],{"className":5411,"style":758},[624],[567,5413,5415,5418,5421,5427],{"className":5414},[610],[567,5416],{"className":5417,"style":4157},[614],[567,5419,2303],{"className":5420},[619],[567,5422,5424],{"className":5423},[619],[567,5425,4134],{"className":5426},[4133],[567,5428,5430],{"className":5429},[619],"2361",". Die Stützstellen liegen weit auseinander, deshalb ist die Näherung grob.",[558,5433,5435],{"id":5434},"typische-fehler","Typische Fehler",[5437,5438,5439,5782,6014,6017],"ul",{},[5440,5441,5442,5443,5496,5497,5753,5754,4172],"li",{},"Im Produkt den Faktor mit ",[567,5444,5446,5464],{"className":5445},[570],[567,5447,5449],{"className":5448},[574],[576,5450,5451],{"xmlns":578},[580,5452,5453,5461],{},[583,5454,5455,5457,5459],{},[586,5456,1707],{},[590,5458,1485],{},[586,5460,668],{},[598,5462,5463],{"encoding":600},"j = i",[567,5465,5467,5486],{"className":5466,"ariaHidden":606},[605],[567,5468,5470,5474,5477,5480,5483],{"className":5469},[610],[567,5471],{"className":5472,"style":5473},[614],"height:0.854em;vertical-align:-0.1944em;",[567,5475,1707],{"className":5476,"style":1973},[619,620],[567,5478],{"className":5479,"style":758},[624],[567,5481,1485],{"className":5482},[762],[567,5484],{"className":5485,"style":758},[624],[567,5487,5489,5493],{"className":5488},[610],[567,5490],{"className":5491,"style":5492},[614],"height:0.6595em;",[567,5494,668],{"className":5495},[619,620]," nicht weglassen. Er wäre ",[567,5498,5500,5542],{"className":5499},[570],[567,5501,5503],{"className":5502},[574],[576,5504,5505],{"xmlns":578},[580,5506,5507,5539],{},[583,5508,5509],{},[1654,5510,5511,5523],{},[583,5512,5513,5515,5517],{},[586,5514,665],{},[590,5516,1642],{},[661,5518,5519,5521],{},[586,5520,665],{},[586,5522,668],{},[583,5524,5525,5531,5533],{},[661,5526,5527,5529],{},[586,5528,665],{},[586,5530,668],{},[590,5532,1642],{},[661,5534,5535,5537],{},[586,5536,665],{},[586,5538,668],{},[598,5540,5541],{"encoding":600},"\\frac{x - x_i}{x_i - x_i}",[567,5543,5545],{"className":5544,"ariaHidden":606},[605],[567,5546,5548,5552],{"className":5547},[610],[567,5549],{"className":5550,"style":5551},[614],"height:1.2635em;vertical-align:-0.4451em;",[567,5553,5555,5558,5750],{"className":5554},[619],[567,5556],{"className":5557},[698,1801],[567,5559,5561],{"className":5560},[1654],[567,5562,5564,5741],{"className":5563},[712,713],[567,5565,5567,5738],{"className":5566},[717],[567,5568,5571,5672,5680],{"className":5569,"style":5570},[721],"height:0.8184em;",[567,5572,5574,5577],{"style":5573},"top:-2.655em;",[567,5575],{"className":5576,"style":1821},[729],[567,5578,5580],{"className":5579},[734,735,736,737],[567,5581,5583,5629,5632],{"className":5582},[619,737],[567,5584,5586,5589],{"className":5585},[619,737],[567,5587,665],{"className":5588},[619,620,737],[567,5590,5592],{"className":5591},[708],[567,5593,5595,5620],{"className":5594},[712,713],[567,5596,5598,5617],{"className":5597},[717],[567,5599,5602],{"className":5600,"style":5601},[721],"height:0.3281em;",[567,5603,5605,5609],{"style":5604},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[567,5606],{"className":5607,"style":5608},[729],"height:2.5em;",[567,5610,5614],{"className":5611},[734,5612,5613,737],"reset-size3","size1",[567,5615,668],{"className":5616},[619,620,737],[567,5618,745],{"className":5619},[744],[567,5621,5623],{"className":5622},[717],[567,5624,5627],{"className":5625,"style":5626},[721],"height:0.143em;",[567,5628],{},[567,5630,1642],{"className":5631},[629,737],[567,5633,5635,5638],{"className":5634},[619,737],[567,5636,665],{"className":5637},[619,620,737],[567,5639,5641],{"className":5640},[708],[567,5642,5644,5664],{"className":5643},[712,713],[567,5645,5647,5661],{"className":5646},[717],[567,5648,5650],{"className":5649,"style":5601},[721],[567,5651,5652,5655],{"style":5604},[567,5653],{"className":5654,"style":5608},[729],[567,5656,5658],{"className":5657},[734,5612,5613,737],[567,5659,668],{"className":5660},[619,620,737],[567,5662,745],{"className":5663},[744],[567,5665,5667],{"className":5666},[717],[567,5668,5670],{"className":5669,"style":5626},[721],[567,5671],{},[567,5673,5674,5677],{"style":1849},[567,5675],{"className":5676,"style":1821},[729],[567,5678],{"className":5679,"style":1857},[1856],[567,5681,5683,5686],{"style":5682},"top:-3.4101em;",[567,5684],{"className":5685,"style":1821},[729],[567,5687,5689],{"className":5688},[734,735,736,737],[567,5690,5692,5695,5698],{"className":5691},[619,737],[567,5693,665],{"className":5694},[619,620,737],[567,5696,1642],{"className":5697},[629,737],[567,5699,5701,5704],{"className":5700},[619,737],[567,5702,665],{"className":5703},[619,620,737],[567,5705,5707],{"className":5706},[708],[567,5708,5710,5730],{"className":5709},[712,713],[567,5711,5713,5727],{"className":5712},[717],[567,5714,5716],{"className":5715,"style":5601},[721],[567,5717,5718,5721],{"style":5604},[567,5719],{"className":5720,"style":5608},[729],[567,5722,5724],{"className":5723},[734,5612,5613,737],[567,5725,668],{"className":5726},[619,620,737],[567,5728,745],{"className":5729},[744],[567,5731,5733],{"className":5732},[717],[567,5734,5736],{"className":5735,"style":5626},[721],[567,5737],{},[567,5739,745],{"className":5740},[744],[567,5742,5744],{"className":5743},[717],[567,5745,5748],{"className":5746,"style":5747},[721],"height:0.4451em;",[567,5749],{},[567,5751],{"className":5752},[817,1801]," und damit eine Division durch ",[567,5755,5757,5770],{"className":5756},[570],[567,5758,5760],{"className":5759},[574],[576,5761,5762],{"xmlns":578},[580,5763,5764,5768],{},[583,5765,5766],{},[594,5767,1223],{},[598,5769,1223],{"encoding":600},[567,5771,5773],{"className":5772,"ariaHidden":606},[605],[567,5774,5776,5779],{"className":5775},[610],[567,5777],{"className":5778,"style":639},[614],[567,5780,1223],{"className":5781},[619],[5440,5783,5784,5785,5878,5879,6013],{},"Im Nenner ",[567,5786,5788,5810],{"className":5787},[570],[567,5789,5791],{"className":5790},[574],[576,5792,5793],{"xmlns":578},[580,5794,5795,5807],{},[583,5796,5797,5799,5801],{},[586,5798,665],{},[590,5800,1642],{},[661,5802,5803,5805],{},[586,5804,665],{},[586,5806,1707],{},[598,5808,5809],{"encoding":600},"x - x_j",[567,5811,5813,5831],{"className":5812,"ariaHidden":606},[605],[567,5814,5816,5819,5822,5825,5828],{"className":5815},[610],[567,5817],{"className":5818,"style":615},[614],[567,5820,665],{"className":5821},[619,620],[567,5823],{"className":5824,"style":625},[624],[567,5826,1642],{"className":5827},[629],[567,5829],{"className":5830,"style":625},[624],[567,5832,5834,5838],{"className":5833},[610],[567,5835],{"className":5836,"style":5837},[614],"height:0.7167em;vertical-align:-0.2861em;",[567,5839,5841,5844],{"className":5840},[619],[567,5842,665],{"className":5843},[619,620],[567,5845,5847],{"className":5846},[708],[567,5848,5850,5870],{"className":5849},[712,713],[567,5851,5853,5867],{"className":5852},[717],[567,5854,5856],{"className":5855,"style":722},[721],[567,5857,5858,5861],{"style":725},[567,5859],{"className":5860,"style":730},[729],[567,5862,5864],{"className":5863},[734,735,736,737],[567,5865,1707],{"className":5866,"style":1973},[619,620,737],[567,5868,745],{"className":5869},[744],[567,5871,5873],{"className":5872},[717],[567,5874,5876],{"className":5875,"style":2080},[721],[567,5877],{}," statt ",[567,5880,5882,5908],{"className":5881},[570],[567,5883,5885],{"className":5884},[574],[576,5886,5887],{"xmlns":578},[580,5888,5889,5905],{},[583,5890,5891,5897,5899],{},[661,5892,5893,5895],{},[586,5894,665],{},[586,5896,668],{},[590,5898,1642],{},[661,5900,5901,5903],{},[586,5902,665],{},[586,5904,1707],{},[598,5906,5907],{"encoding":600},"x_i - x_j",[567,5909,5911,5967],{"className":5910,"ariaHidden":606},[605],[567,5912,5914,5918,5958,5961,5964],{"className":5913},[610],[567,5915],{"className":5916,"style":5917},[614],"height:0.7333em;vertical-align:-0.15em;",[567,5919,5921,5924],{"className":5920},[619],[567,5922,665],{"className":5923},[619,620],[567,5925,5927],{"className":5926},[708],[567,5928,5930,5950],{"className":5929},[712,713],[567,5931,5933,5947],{"className":5932},[717],[567,5934,5936],{"className":5935,"style":722},[721],[567,5937,5938,5941],{"style":725},[567,5939],{"className":5940,"style":730},[729],[567,5942,5944],{"className":5943},[734,735,736,737],[567,5945,668],{"className":5946},[619,620,737],[567,5948,745],{"className":5949},[744],[567,5951,5953],{"className":5952},[717],[567,5954,5956],{"className":5955,"style":752},[721],[567,5957],{},[567,5959],{"className":5960,"style":625},[624],[567,5962,1642],{"className":5963},[629],[567,5965],{"className":5966,"style":625},[624],[567,5968,5970,5973],{"className":5969},[610],[567,5971],{"className":5972,"style":5837},[614],[567,5974,5976,5979],{"className":5975},[619],[567,5977,665],{"className":5978},[619,620],[567,5980,5982],{"className":5981},[708],[567,5983,5985,6005],{"className":5984},[712,713],[567,5986,5988,6002],{"className":5987},[717],[567,5989,5991],{"className":5990,"style":722},[721],[567,5992,5993,5996],{"style":725},[567,5994],{"className":5995,"style":730},[729],[567,5997,5999],{"className":5998},[734,735,736,737],[567,6000,1707],{"className":6001,"style":1973},[619,620,737],[567,6003,745],{"className":6004},[744],[567,6006,6008],{"className":6007},[717],[567,6009,6011],{"className":6010,"style":2080},[721],[567,6012],{}," schreiben.",[5440,6015,6016],{},"Annehmen, mehr Stützstellen verbesserten die Näherung immer. Bei äquidistanten Stützstellen kann der Fehler am Rand wachsen.",[5440,6018,6019],{},"Das Polynom außerhalb der Stützstellen (Extrapolation) für zuverlässig halten.",{"title":6021,"searchDepth":6022,"depth":6022,"links":6023},"",2,[6024,6025,6026],{"id":560,"depth":6022,"text":561},{"id":2157,"depth":6022,"text":2158},{"id":5434,"depth":6022,"text":5435},[6028,6031,6035,6037,6040,6043,6046],{"lhs":6029,"rhs":6030},"1*(x - 1)*(x - 2)\u002F((0 - 1)*(0 - 2)) + 3*(x - 0)*(x - 2)\u002F((1 - 0)*(1 - 2)) + 7*(x - 0)*(x - 1)\u002F((2 - 0)*(2 - 1))","x^2 + x + 1",{"lhs":6030,"rhs":6032,"where":6033},"4.75",{"x":6034},1.5,{"lhs":6036,"rhs":596},"(x - 1)*(x - 2)\u002F2 - x*(x - 2) + x*(x - 1)\u002F2",{"lhs":6038,"rhs":6039},"y0*(x - x1)\u002F(x0 - x1) + y1*(x - x0)\u002F(x1 - x0)","y0 + (y1 - y0)\u002F(x1 - x0)*(x - x0)",{"lhs":6041,"rhs":6042},"2*(5 - 9)*(5 - 16)\u002F((4 - 9)*(4 - 16)) + 3*(5 - 4)*(5 - 16)\u002F((9 - 4)*(9 - 16)) + 4*(5 - 4)*(5 - 9)\u002F((16 - 4)*(16 - 9))","88\u002F60 + 33\u002F35 - 16\u002F84",{"lhs":6044,"rhs":6045},"round(88\u002F60 + 33\u002F35 - 16\u002F84, 4)","2.2190",{"lhs":6047,"rhs":6048},"round(sqrt(5), 4)","2.2361","x_0, \\ldots, x_n \\text{ paarweise verschieden}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_0, \\ldots, x_n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\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 class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">0\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=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">paarweise verschieden\u003C\u002Fspan>",null,"md","lagrange-interpolation","p(x) = \\sum_{i=0}^{n} y_i \\, L_i(x), \\qquad L_i(x) = \\prod_{\\substack{j=0 \\\\ j \\neq i}}^{n} \\frac{x - x_j}{x_i - x_j}","\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>p\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmunderover>\u003Cmo>∑\u003C\u002Fmo>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmunderover>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmtext> \u003C\u002Fmtext>\u003Cmsub>\u003Cmi>L\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmsub>\u003Cmi>L\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmunderover>\u003Cmo>∏\u003C\u002Fmo>\u003Cmstyle scriptlevel=\"1\">\u003Cmtable rowspacing=\"0.1em\" columnalign=\"center\" columnspacing=\"1em\">\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"1\" displaystyle=\"false\">\u003Cmrow>\u003Cmi>j\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"1\" displaystyle=\"false\">\u003Cmrow>\u003Cmi>j\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003C\u002Fmtable>\u003C\u002Fmstyle>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmunderover>\u003Cmfrac>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p(x) = \\sum_{i=0}^{n} y_i \\, L_i(x), \\qquad L_i(x) = \\prod_{\\substack{j=0 \\\\ j \\neq i}}^{n} \\frac{x - x_j}{x_i - x_j}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan 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style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">L\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\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\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" 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style=\"top:-1.549em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mtable\">\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1214em;\">\u003Cspan style=\"top:-3.1619em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">=\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.273em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">\u003Cspan class=\"mrel mtight\">\u003Cspan class=\"mord katex-vbox mtight\">\u003Cspan class=\"katex-thinbox mtight\">\u003Cspan class=\"rlap mtight\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mrel mtight\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak mtight\">\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">i\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:0.6214em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.05em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop op-symbol large-op\">∏\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-4.3em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" 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class=\"mord mathnormal mtight\">i\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=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\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:0.3117em;\">\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 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style=\"margin-right:0.2222em;\">\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:0.3117em;\">\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\" style=\"margin-right:0.0572em;\">j\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:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:0.9721em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fnumerics\u002Flagrange-interpolation",[],[6062,6063,6064],"quadratic-function","linear-function","simpson-rule",{"title":548,"description":6021},"de\u002Fformulas\u002Fmath\u002Fnumerics\u002Flagrange-interpolation","Die Lagrange-Formel liefert das eindeutige Polynom vom Grad höchstens n durch n + 1 Punkte mit verschiedenen x-Werten.",[6069,6070,6071,6072],"interpolation","polynom","stützstellen","lagrange-polynome",[6074,6078,6082,6086],{"symbol":6075,"meaning":6076,"symbolHtml":6077},"p(x)","Interpolationspolynom vom Grad höchstens n","\u003Cspan 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