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a)\\,h^2}{12}\\,f''(\\xi)",[568,1106,1108,1207,1262],{"className":1107,"ariaHidden":605},[604],[568,1109,1111,1115,1172,1175,1178,1181,1184,1187,1190,1193,1196,1200,1204],{"className":1110},[609],[568,1112],{"className":1113,"style":1114},[613],"height:2.511em;vertical-align:-0.9119em;",[568,1116,1118,1123],{"className":1117},[738],[568,1119,693],{"className":1120,"style":1122},[738,742,1121],"large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[568,1124,1126],{"className":1125},[627],[568,1127,1129,1163],{"className":1128},[631,632],[568,1130,1132,1160],{"className":1131},[636],[568,1133,1136,1148],{"className":1134,"style":1135},[640],"height:1.599em;",[568,1137,1139,1142],{"style":1138},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[568,1140],{"className":1141,"style":649},[648],[568,1143,1145],{"className":1144},[653,654,655,656],[568,1146,696],{"className":1147},[618,622,656],[568,1149,1151,1154],{"style":1150},"top:-3.8129em;margin-right:0.05em;",[568,1152],{"className":1153,"style":649},[648],[568,1155,1157],{"className":1156},[653,654,655,656],[568,1158,699],{"className":1159},[618,622,656],[568,1161,664],{"className":1162},[663],[568,1164,1166],{"className":1165},[636],[568,1167,1170],{"className":1168,"style":1169},[640],"height:0.9119em;",[568,1171],{},[568,1173],{"className":1174,"style":798},[797],[568,1176,702],{"className":1177,"style":802},[618,622],[568,1179,706],{"className":1180},[806],[568,1182,709],{"className":1183},[618,622],[568,1185,712],{"className":1186},[813],[568,1188],{"className":1189,"style":798},[797],[568,1191,719],{"className":1192},[618,622],[568,1194,709],{"className":1195},[618,622],[568,1197],{"className":1198,"style":1199},[797],"margin-right:0.2222em;",[568,1201,1041],{"className":1202},[1203],"mbin",[568,1205],{"className":1206,"style":1199},[797],[568,1208,1210,1213,1253,1256,1259],{"className":1209},[609],[568,1211],{"className":1212,"style":614},[613],[568,1214,1216,1219],{"className":1215},[618],[568,1217,592],{"className":1218,"style":623},[618,622],[568,1220,1222],{"className":1221},[627],[568,1223,1225,1245],{"className":1224},[631,632],[568,1226,1228,1242],{"className":1227},[636],[568,1229,1231],{"className":1230,"style":641},[640],[568,1232,1233,1236],{"style":644},[568,1234],{"className":1235,"style":649},[648],[568,1237,1239],{"className":1238},[653,654,655,656],[568,1240,595],{"className":1241},[618,622,656],[568,1243,664],{"className":1244},[663],[568,1246,1248],{"className":1247},[636],[568,1249,1251],{"className":1250,"style":671},[640],[568,1252],{},[568,1254],{"className":1255,"style":965},[797],[568,1257,1050],{"className":1258},[969],[568,1260],{"className":1261,"style":965},[797],[568,1263,1265,1269,1272,1395,1398,1433,1436,1439],{"className":1264},[609],[568,1266],{"className":1267,"style":1268},[613],"height:2.1771em;vertical-align:-0.686em;",[568,1270,1041],{"className":1271},[618],[568,1273,1275,1279,1392],{"className":1274},[618],[568,1276],{"className":1277},[806,1278],"nulldelimiter",[568,1280,1282],{"className":1281},[1054],[568,1283,1285,1383],{"className":1284},[631,632],[568,1286,1288,1380],{"className":1287},[636],[568,1289,1292,1305,1316],{"className":1290,"style":1291},[640],"height:1.4911em;",[568,1293,1295,1299],{"style":1294},"top:-2.314em;",[568,1296],{"className":1297,"style":1298},[648],"height:3em;",[568,1300,1302],{"className":1301},[618],[568,1303,1081],{"className":1304},[618],[568,1306,1308,1311],{"style":1307},"top:-3.23em;",[568,1309],{"className":1310,"style":1298},[648],[568,1312],{"className":1313,"style":1315},[1314],"frac-line","border-bottom-width:0.04em;",[568,1317,1319,1322],{"style":1318},"top:-3.677em;",[568,1320],{"className":1321,"style":1298},[648],[568,1323,1325,1328,1331,1334,1337,1340,1343,1346,1349],{"className":1324},[618],[568,1326,706],{"className":1327},[806],[568,1329,699],{"className":1330},[618,622],[568,1332],{"className":1333,"style":1199},[797],[568,1335,1041],{"className":1336},[1203],[568,1338],{"className":1339,"style":1199},[797],[568,1341,696],{"className":1342},[618,622],[568,1344,712],{"className":1345},[813],[568,1347],{"className":1348,"style":798},[797],[568,1350,1352,1355],{"className":1351},[618],[568,1353,868],{"className":1354},[618,622],[568,1356,1358],{"className":1357},[627],[568,1359,1361],{"className":1360},[631],[568,1362,1364],{"className":1363},[636],[568,1365,1368],{"className":1366,"style":1367},[640],"height:0.8141em;",[568,1369,1371,1374],{"style":1370},"top:-3.063em;margin-right:0.05em;",[568,1372],{"className":1373,"style":649},[648],[568,1375,1377],{"className":1376},[653,654,655,656],[568,1378,1078],{"className":1379},[618,656],[568,1381,664],{"className":1382},[663],[568,1384,1386],{"className":1385},[636],[568,1387,1390],{"className":1388,"style":1389},[640],"height:0.686em;",[568,1391],{},[568,1393],{"className":1394},[813,1278],[568,1396],{"className":1397,"style":798},[797],[568,1399,1401,1404],{"className":1400},[618],[568,1402,702],{"className":1403,"style":802},[618,622],[568,1405,1407],{"className":1406},[627],[568,1408,1410],{"className":1409},[631],[568,1411,1413],{"className":1412},[636],[568,1414,1417],{"className":1415,"style":1416},[640],"height:0.8019em;",[568,1418,1420,1423],{"style":1419},"top:-3.113em;margin-right:0.05em;",[568,1421],{"className":1422,"style":649},[648],[568,1424,1426],{"className":1425},[653,654,655,656],[568,1427,1429],{"className":1428},[618,656],[568,1430,1432],{"className":1431},[618,656],"′′",[568,1434,706],{"className":1435},[806],[568,1437,929],{"className":1438,"style":961},[618,622],[568,1440,712],{"className":1441},[813],[564,1443,1444,1445,1474,1475,1569,1570,1646,1647,1699],{},"Weil man ",[568,1446,1448,1462],{"className":1447},[571],[568,1449,1451],{"className":1450},[575],[577,1452,1453],{"xmlns":579},[581,1454,1455,1459],{},[584,1456,1457],{},[590,1458,929],{},[597,1460,1461],{"encoding":599},"\\xi",[568,1463,1465],{"className":1464,"ariaHidden":605},[604],[568,1466,1468,1471],{"className":1467},[609],[568,1469],{"className":1470,"style":910},[613],[568,1472,929],{"className":1473,"style":961},[618,622]," nicht kennt, schätzt man ",[568,1476,1478,1511],{"className":1477},[571],[568,1479,1481],{"className":1480},[575],[577,1482,1483],{"xmlns":579},[581,1484,1485,1508],{},[584,1486,1487,1490,1500,1502,1504,1506],{},[590,1488,1489],{"mathvariant":1092},"∣",[1071,1491,1492,1494],{},[590,1493,702],{},[584,1495,1496,1498],{},[691,1497,1093],{"mathvariant":1092},[691,1499,1093],{"mathvariant":1092},[691,1501,706],{"stretchy":705},[590,1503,929],{},[691,1505,712],{"stretchy":705},[590,1507,1489],{"mathvariant":1092},[597,1509,1510],{"encoding":599},"|f''(\\xi)|",[568,1512,1514],{"className":1513,"ariaHidden":605},[604],[568,1515,1517,1521,1524,1557,1560,1563,1566],{"className":1516},[609],[568,1518],{"className":1519,"style":1520},[613],"height:1.0019em;vertical-align:-0.25em;",[568,1522,1489],{"className":1523},[618],[568,1525,1527,1530],{"className":1526},[618],[568,1528,702],{"className":1529,"style":802},[618,622],[568,1531,1533],{"className":1532},[627],[568,1534,1536],{"className":1535},[631],[568,1537,1539],{"className":1538},[636],[568,1540,1543],{"className":1541,"style":1542},[640],"height:0.7519em;",[568,1544,1545,1548],{"style":1370},[568,1546],{"className":1547,"style":649},[648],[568,1549,1551],{"className":1550},[653,654,655,656],[568,1552,1554],{"className":1553},[618,656],[568,1555,1432],{"className":1556},[618,656],[568,1558,706],{"className":1559},[806],[568,1561,929],{"className":1562,"style":961},[618,622],[568,1564,712],{"className":1565},[813],[568,1567,1489],{"className":1568},[618]," durch das Maximum von ",[568,1571,1573,1599],{"className":1572},[571],[568,1574,1576],{"className":1575},[575],[577,1577,1578],{"xmlns":579},[581,1579,1580,1596],{},[584,1581,1582,1584,1594],{},[590,1583,1489],{"mathvariant":1092},[1071,1585,1586,1588],{},[590,1587,702],{},[584,1589,1590,1592],{},[691,1591,1093],{"mathvariant":1092},[691,1593,1093],{"mathvariant":1092},[590,1595,1489],{"mathvariant":1092},[597,1597,1598],{"encoding":599},"|f''|",[568,1600,1602],{"className":1601,"ariaHidden":605},[604],[568,1603,1605,1608,1611,1643],{"className":1604},[609],[568,1606],{"className":1607,"style":1520},[613],[568,1609,1489],{"className":1610},[618],[568,1612,1614,1617],{"className":1613},[618],[568,1615,702],{"className":1616,"style":802},[618,622],[568,1618,1620],{"className":1619},[627],[568,1621,1623],{"className":1622},[631],[568,1624,1626],{"className":1625},[636],[568,1627,1629],{"className":1628,"style":1542},[640],[568,1630,1631,1634],{"style":1370},[568,1632],{"className":1633,"style":649},[648],[568,1635,1637],{"className":1636},[653,654,655,656],[568,1638,1640],{"className":1639},[618,656],[568,1641,1432],{"className":1642},[618,656],[568,1644,1489],{"className":1645},[618]," auf ",[568,1648,1650,1672],{"className":1649},[571],[568,1651,1653],{"className":1652},[575],[577,1654,1655],{"xmlns":579},[581,1656,1657,1669],{},[584,1658,1659,1661,1663,1665,1667],{},[691,1660,935],{"stretchy":705},[590,1662,696],{},[691,1664,940],{"separator":605},[590,1666,699],{},[691,1668,945],{"stretchy":705},[597,1670,1671],{"encoding":599},"[a, b]",[568,1673,1675],{"className":1674,"ariaHidden":605},[604],[568,1676,1678,1681,1684,1687,1690,1693,1696],{"className":1677},[609],[568,1679],{"className":1680,"style":979},[613],[568,1682,935],{"className":1683},[806],[568,1685,696],{"className":1686},[618,622],[568,1688,940],{"className":1689},[989],[568,1691],{"className":1692,"style":798},[797],[568,1694,699],{"className":1695},[618,622],[568,1697,945],{"className":1698},[813]," ab. Daraus folgt die Schranke oben.",[564,1701,1702],{},"Folgerungen:",[1704,1705,1706,1743,1838,2182],"ul",{},[1707,1708,1709,1713,1714,1742],"li",{},[1710,1711,1712],"strong",{},"Ordnung 2",": Halbiert man ",[568,1715,1717,1730],{"className":1716},[571],[568,1718,1720],{"className":1719},[575],[577,1721,1722],{"xmlns":579},[581,1723,1724,1728],{},[584,1725,1726],{},[590,1727,868],{},[597,1729,868],{"encoding":599},[568,1731,1733],{"className":1732,"ariaHidden":605},[604],[568,1734,1736,1739],{"className":1735},[609],[568,1737],{"className":1738,"style":880},[613],[568,1740,868],{"className":1741},[618,622],", wird der Fehler etwa viermal kleiner.",[1707,1744,1745,1746,1837],{},"Für lineare Funktionen ist ",[568,1747,1749,1776],{"className":1748},[571],[568,1750,1752],{"className":1751},[575],[577,1753,1754],{"xmlns":579},[581,1755,1756,1773],{},[584,1757,1758,1768,1770],{},[1071,1759,1760,1762],{},[590,1761,702],{},[584,1763,1764,1766],{},[691,1765,1093],{"mathvariant":1092},[691,1767,1093],{"mathvariant":1092},[691,1769,1050],{},[1076,1771,1772],{},"0",[597,1774,1775],{"encoding":599},"f'' = 0",[568,1777,1779,1827],{"className":1778,"ariaHidden":605},[604],[568,1780,1782,1786,1818,1821,1824],{"className":1781},[609],[568,1783],{"className":1784,"style":1785},[613],"height:0.9463em;vertical-align:-0.1944em;",[568,1787,1789,1792],{"className":1788},[618],[568,1790,702],{"className":1791,"style":802},[618,622],[568,1793,1795],{"className":1794},[627],[568,1796,1798],{"className":1797},[631],[568,1799,1801],{"className":1800},[636],[568,1802,1804],{"className":1803,"style":1542},[640],[568,1805,1806,1809],{"style":1370},[568,1807],{"className":1808,"style":649},[648],[568,1810,1812],{"className":1811},[653,654,655,656],[568,1813,1815],{"className":1814},[618,656],[568,1816,1432],{"className":1817},[618,656],[568,1819],{"className":1820,"style":965},[797],[568,1822,1050],{"className":1823},[969],[568,1825],{"className":1826,"style":965},[797],[568,1828,1830,1834],{"className":1829},[609],[568,1831],{"className":1832,"style":1833},[613],"height:0.6444em;",[568,1835,1772],{"className":1836},[618],", die Trapezregel ist dann exakt.",[1707,1839,1840,1841,1871,1872,2181],{},"Aus der Schranke bestimmt man, wie viele Teilintervalle für eine gewünschte Genauigkeit ",[568,1842,1844,1859],{"className":1843},[571],[568,1845,1847],{"className":1846},[575],[577,1848,1849],{"xmlns":579},[581,1850,1851,1856],{},[584,1852,1853],{},[590,1854,1855],{},"ε",[597,1857,1858],{"encoding":599},"\\varepsilon",[568,1860,1862],{"className":1861,"ariaHidden":605},[604],[568,1863,1865,1868],{"className":1864},[609],[568,1866],{"className":1867,"style":849},[613],[568,1869,1855],{"className":1870},[618,622]," reichen: ",[568,1873,1875,1937],{"className":1874},[571],[568,1876,1878],{"className":1877},[575],[577,1879,1880],{"xmlns":579},[581,1881,1882,1934],{},[584,1883,1884,1886,1889],{},[590,1885,868],{},[691,1887,1888],{},"≤",[1890,1891,1892],"msqrt",{},[1054,1893,1894,1902],{},[584,1895,1896,1898,1900],{},[1076,1897,1081],{},[714,1899,716],{},[590,1901,1855],{},[584,1903,1904,1906,1908,1910,1912,1914,1917,1920,1922,1932],{},[691,1905,706],{"stretchy":705},[590,1907,699],{},[691,1909,1041],{},[590,1911,696],{},[691,1913,712],{"stretchy":705},[590,1915,1916],{},"max",[691,1918,1919],{},"⁡",[590,1921,1489],{"mathvariant":1092},[1071,1923,1924,1926],{},[590,1925,702],{},[584,1927,1928,1930],{},[691,1929,1093],{"mathvariant":1092},[691,1931,1093],{"mathvariant":1092},[590,1933,1489],{"mathvariant":1092},[597,1935,1936],{"encoding":599},"h \\leq \\sqrt{\\frac{12\\,\\varepsilon}{(b - a) \\max |f''|}}",[568,1938,1940,1959],{"className":1939,"ariaHidden":605},[604],[568,1941,1943,1947,1950,1953,1956],{"className":1942},[609],[568,1944],{"className":1945,"style":1946},[613],"height:0.8304em;vertical-align:-0.136em;",[568,1948,868],{"className":1949},[618,622],[568,1951],{"className":1952,"style":965},[797],[568,1954,1888],{"className":1955},[969],[568,1957],{"className":1958,"style":965},[797],[568,1960,1962,1966],{"className":1961},[609],[568,1963],{"className":1964,"style":1965},[613],"height:1.84em;vertical-align:-0.6924em;",[568,1967,1970],{"className":1968},[618,1969],"sqrt",[568,1971,1973,2172],{"className":1972},[631,632],[568,1974,1976,2169],{"className":1975},[636],[568,1977,1980,2146],{"className":1978,"style":1979},[640],"height:1.1476em;",[568,1981,1985,1989],{"className":1982,"style":1984},[1983],"svg-align","top:-3.8em;",[568,1986],{"className":1987,"style":1988},[648],"height:3.8em;",[568,1990,1993],{"className":1991,"style":1992},[618],"padding-left:1em;",[568,1994,1996,1999,2143],{"className":1995},[618],[568,1997],{"className":1998},[806,1278],[568,2000,2002],{"className":2001},[1054],[568,2003,2005,2134],{"className":2004},[631,632],[568,2006,2008,2131],{"className":2007},[636],[568,2009,2012,2102,2110],{"className":2010,"style":2011},[640],"height:0.8451em;",[568,2013,2015,2018],{"style":2014},"top:-2.655em;",[568,2016],{"className":2017,"style":1298},[648],[568,2019,2021],{"className":2020},[653,654,655,656],[568,2022,2024,2027,2030,2033,2036,2039,2043,2056,2059,2062,2099],{"className":2023},[618,656],[568,2025,706],{"className":2026},[806,656],[568,2028,699],{"className":2029},[618,622,656],[568,2031,1041],{"className":2032},[1203,656],[568,2034,696],{"className":2035},[618,622,656],[568,2037,712],{"className":2038},[813,656],[568,2040],{"className":2041,"style":2042},[797,656],"margin-right:0.1952em;",[568,2044,2046,2050,2053],{"className":2045},[738,656],[568,2047,2049],{"className":2048},[656],"m",[568,2051,696],{"className":2052},[656],[568,2054,709],{"className":2055},[656],[568,2057],{"className":2058,"style":2042},[797,656],[568,2060,1489],{"className":2061},[618,656],[568,2063,2065,2068],{"className":2064},[618,656],[568,2066,702],{"className":2067,"style":802},[618,622,656],[568,2069,2071],{"className":2070},[627],[568,2072,2074],{"className":2073},[631],[568,2075,2077],{"className":2076},[636],[568,2078,2081],{"className":2079,"style":2080},[640],"height:0.6828em;",[568,2082,2084,2088],{"style":2083},"top:-2.786em;margin-right:0.0714em;",[568,2085],{"className":2086,"style":2087},[648],"height:2.5em;",[568,2089,2093],{"className":2090},[653,2091,2092,656],"reset-size3","size1",[568,2094,2096],{"className":2095},[618,656],[568,2097,1432],{"className":2098},[618,656],[568,2100,1489],{"className":2101},[618,656],[568,2103,2104,2107],{"style":1307},[568,2105],{"className":2106,"style":1298},[648],[568,2108],{"className":2109,"style":1315},[1314],[568,2111,2113,2116],{"style":2112},"top:-3.394em;",[568,2114],{"className":2115,"style":1298},[648],[568,2117,2119],{"className":2118},[653,654,655,656],[568,2120,2122,2125,2128],{"className":2121},[618,656],[568,2123,1081],{"className":2124},[618,656],[568,2126],{"className":2127,"style":2042},[797,656],[568,2129,1855],{"className":2130},[618,622,656],[568,2132,664],{"className":2133},[663],[568,2135,2137],{"className":2136},[636],[568,2138,2141],{"className":2139,"style":2140},[640],"height:0.52em;",[568,2142],{},[568,2144],{"className":2145},[813,1278],[568,2147,2149,2152],{"style":2148},"top:-3.1076em;",[568,2150],{"className":2151,"style":1988},[648],[568,2153,2157],{"className":2154,"style":2156},[2155],"hide-tail","min-width:1.02em;height:1.88em;",[2158,2159,2165],"svg",{"xmlns":2160,"width":2161,"height":2162,"viewBox":2163,"preserveAspectRatio":2164},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.88em","0 0 400000 1944","xMinYMin slice",[2166,2167],"path",{"d":2168},"M983 90\nl0 -0\nc4,-6.7,10,-10,18,-10 H400000v40\nH1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7\ns-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744\nc-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30\nc26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722\nc56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5\nc53.7,-170.3,84.5,-266.8,92.5,-289.5z\nM1001 80h400000v40h-400000z",[568,2170,664],{"className":2171},[663],[568,2173,2175],{"className":2174},[636],[568,2176,2179],{"className":2177,"style":2178},[640],"height:0.6924em;",[568,2180],{},".",[1707,2183,2184,2185,2213,2214,2658],{},"Für glatte ",[568,2186,2188,2201],{"className":2187},[571],[568,2189,2191],{"className":2190},[575],[577,2192,2193],{"xmlns":579},[581,2194,2195,2199],{},[584,2196,2197],{},[590,2198,702],{},[597,2200,702],{"encoding":599},[568,2202,2204],{"className":2203,"ariaHidden":605},[604],[568,2205,2207,2210],{"className":2206},[609],[568,2208],{"className":2209,"style":910},[613],[568,2211,702],{"className":2212,"style":802},[618,622]," gilt genauer ",[568,2215,2217,2300],{"className":2216},[571],[568,2218,2220],{"className":2219},[575],[577,2221,2222],{"xmlns":579},[581,2223,2224,2297],{},[584,2225,2226,2234,2236,2238,2240,2242,2244,2250,2253,2255,2265,2268,2275,2277,2279,2281,2283,2289,2291,2293,2295],{},[688,2227,2228,2230,2232],{},[691,2229,693],{},[590,2231,696],{},[590,2233,699],{},[590,2235,702],{},[714,2237,716],{},[590,2239,719],{},[590,2241,709],{},[691,2243,1041],{},[587,2245,2246,2248],{},[590,2247,592],{},[590,2249,595],{},[691,2251,2252],{},"≈",[691,2254,1041],{},[1054,2256,2257,2263],{},[1071,2258,2259,2261],{},[590,2260,868],{},[1076,2262,1078],{},[1076,2264,1081],{},[691,2266,706],{"fence":605,"stretchy":605,"minsize":2267,"maxsize":2267},"1.2em",[1071,2269,2270,2272],{},[590,2271,702],{},[691,2273,1093],{"mathvariant":1092,"lspace":2274,"rspace":2274},"0em",[691,2276,706],{"stretchy":705},[590,2278,699],{},[691,2280,712],{"stretchy":705},[691,2282,1041],{},[1071,2284,2285,2287],{},[590,2286,702],{},[691,2288,1093],{"mathvariant":1092,"lspace":2274,"rspace":2274},[691,2290,706],{"stretchy":705},[590,2292,696],{},[691,2294,712],{"stretchy":705},[691,2296,712],{"fence":605,"stretchy":605,"minsize":2267,"maxsize":2267},[597,2298,2299],{"encoding":599},"\\int_a^b f\\,dx - T_n \\approx -\\frac{h^2}{12}\\bigl(f'(b) - f'(a)\\bigr)",[568,2301,2303,2384,2439,2604],{"className":2302,"ariaHidden":605},[604],[568,2304,2306,2309,2360,2363,2366,2369,2372,2375,2378,2381],{"className":2305},[609],[568,2307],{"className":2308,"style":734},[613],[568,2310,2312,2315],{"className":2311},[738],[568,2313,693],{"className":2314,"style":744},[738,742,743],[568,2316,2318],{"className":2317},[627],[568,2319,2321,2352],{"className":2320},[631,632],[568,2322,2324,2349],{"className":2323},[636],[568,2325,2327,2338],{"className":2326,"style":757},[640],[568,2328,2329,2332],{"style":760},[568,2330],{"className":2331,"style":649},[648],[568,2333,2335],{"className":2334},[653,654,655,656],[568,2336,696],{"className":2337},[618,622,656],[568,2339,2340,2343],{"style":772},[568,2341],{"className":2342,"style":649},[648],[568,2344,2346],{"className":2345},[653,654,655,656],[568,2347,699],{"className":2348},[618,622,656],[568,2350,664],{"className":2351},[663],[568,2353,2355],{"className":2354},[636],[568,2356,2358],{"className":2357,"style":791},[640],[568,2359],{},[568,2361],{"className":2362,"style":798},[797],[568,2364,702],{"className":2365,"style":802},[618,622],[568,2367],{"className":2368,"style":798},[797],[568,2370,719],{"className":2371},[618,622],[568,2373,709],{"className":2374},[618,622],[568,2376],{"className":2377,"style":1199},[797],[568,2379,1041],{"className":2380},[1203],[568,2382],{"className":2383,"style":1199},[797],[568,2385,2387,2390,2430,2433,2436],{"className":2386},[609],[568,2388],{"className":2389,"style":614},[613],[568,2391,2393,2396],{"className":2392},[618],[568,2394,592],{"className":2395,"style":623},[618,622],[568,2397,2399],{"className":2398},[627],[568,2400,2402,2422],{"className":2401},[631,632],[568,2403,2405,2419],{"className":2404},[636],[568,2406,2408],{"className":2407,"style":641},[640],[568,2409,2410,2413],{"style":644},[568,2411],{"className":2412,"style":649},[648],[568,2414,2416],{"className":2415},[653,654,655,656],[568,2417,595],{"className":2418},[618,622,656],[568,2420,664],{"className":2421},[663],[568,2423,2425],{"className":2424},[636],[568,2426,2428],{"className":2427,"style":671},[640],[568,2429],{},[568,2431],{"className":2432,"style":965},[797],[568,2434,2252],{"className":2435},[969],[568,2437],{"className":2438,"style":965},[797],[568,2440,2442,2446,2449,2547,2554,2586,2589,2592,2595,2598,2601],{"className":2441},[609],[568,2443],{"className":2444,"style":2445},[613],"height:1.3679em;vertical-align:-0.35em;",[568,2447,1041],{"className":2448},[618],[568,2450,2452,2455,2544],{"className":2451},[618],[568,2453],{"className":2454},[806,1278],[568,2456,2458],{"className":2457},[1054],[568,2459,2461,2535],{"className":2460},[631,632],[568,2462,2464,2532],{"className":2463},[636],[568,2465,2468,2482,2490],{"className":2466,"style":2467},[640],"height:1.0179em;",[568,2469,2470,2473],{"style":2014},[568,2471],{"className":2472,"style":1298},[648],[568,2474,2476],{"className":2475},[653,654,655,656],[568,2477,2479],{"className":2478},[618,656],[568,2480,1081],{"className":2481},[618,656],[568,2483,2484,2487],{"style":1307},[568,2485],{"className":2486,"style":1298},[648],[568,2488],{"className":2489,"style":1315},[1314],[568,2491,2492,2495],{"style":2112},[568,2493],{"className":2494,"style":1298},[648],[568,2496,2498],{"className":2497},[653,654,655,656],[568,2499,2501],{"className":2500},[618,656],[568,2502,2504,2507],{"className":2503},[618,656],[568,2505,868],{"className":2506},[618,622,656],[568,2508,2510],{"className":2509},[627],[568,2511,2513],{"className":2512},[631],[568,2514,2516],{"className":2515},[636],[568,2517,2520],{"className":2518,"style":2519},[640],"height:0.8913em;",[568,2521,2523,2526],{"style":2522},"top:-2.931em;margin-right:0.0714em;",[568,2524],{"className":2525,"style":2087},[648],[568,2527,2529],{"className":2528},[653,2091,2092,656],[568,2530,1078],{"className":2531},[618,656],[568,2533,664],{"className":2534},[663],[568,2536,2538],{"className":2537},[636],[568,2539,2542],{"className":2540,"style":2541},[640],"height:0.345em;",[568,2543],{},[568,2545],{"className":2546},[813,1278],[568,2548,2550],{"className":2549},[806],[568,2551,706],{"className":2552},[2553,2092],"delimsizing",[568,2555,2557,2560],{"className":2556},[618],[568,2558,702],{"className":2559,"style":802},[618,622],[568,2561,2563],{"className":2562},[627],[568,2564,2566],{"className":2565},[631],[568,2567,2569],{"className":2568},[636],[568,2570,2572],{"className":2571,"style":1542},[640],[568,2573,2574,2577],{"style":1370},[568,2575],{"className":2576,"style":649},[648],[568,2578,2580],{"className":2579},[653,654,655,656],[568,2581,2583],{"className":2582},[618,656],[568,2584,1093],{"className":2585},[618,656],[568,2587,706],{"className":2588},[806],[568,2590,699],{"className":2591},[618,622],[568,2593,712],{"className":2594},[813],[568,2596],{"className":2597,"style":1199},[797],[568,2599,1041],{"className":2600},[1203],[568,2602],{"className":2603,"style":1199},[797],[568,2605,2607,2611,2643,2646,2649,2652],{"className":2606},[609],[568,2608],{"className":2609,"style":2610},[613],"height:1.2em;vertical-align:-0.35em;",[568,2612,2614,2617],{"className":2613},[618],[568,2615,702],{"className":2616,"style":802},[618,622],[568,2618,2620],{"className":2619},[627],[568,2621,2623],{"className":2622},[631],[568,2624,2626],{"className":2625},[636],[568,2627,2629],{"className":2628,"style":1542},[640],[568,2630,2631,2634],{"style":1370},[568,2632],{"className":2633,"style":649},[648],[568,2635,2637],{"className":2636},[653,654,655,656],[568,2638,2640],{"className":2639},[618,656],[568,2641,1093],{"className":2642},[618,656],[568,2644,706],{"className":2645},[806],[568,2647,696],{"className":2648},[618,622],[568,2650,712],{"className":2651},[813],[568,2653,2655],{"className":2654},[813],[568,2656,712],{"className":2657},[2553,2092],". Diese Näherung ist oft viel schärfer als die Schranke.",[559,2660,2662],{"id":2661},"beispiele","Beispiele",[564,2664,2665,2806,2807,2881,2882,1646,3023,3075],{},[568,2666,2668,2702],{"className":2667},[571],[568,2669,2671],{"className":2670},[575],[577,2672,2673],{"xmlns":579},[581,2674,2675,2699],{},[584,2676,2677,2686,2693,2695,2697],{},[688,2678,2679,2681,2683],{},[691,2680,693],{},[1076,2682,1772],{},[1076,2684,2685],{},"1",[1071,2687,2688,2691],{},[590,2689,2690],{},"e",[590,2692,709],{},[714,2694,716],{},[590,2696,719],{},[590,2698,709],{},[597,2700,2701],{"encoding":599},"\\int_0^1 e^x\\,dx",[568,2703,2705],{"className":2704,"ariaHidden":605},[604],[568,2706,2708,2712,2764,2767,2797,2800,2803],{"className":2707},[609],[568,2709],{"className":2710,"style":2711},[613],"height:1.3648em;vertical-align:-0.3558em;",[568,2713,2715,2718],{"className":2714},[738],[568,2716,693],{"className":2717,"style":744},[738,742,743],[568,2719,2721],{"className":2720},[627],[568,2722,2724,2756],{"className":2723},[631,632],[568,2725,2727,2753],{"className":2726},[636],[568,2728,2731,2742],{"className":2729,"style":2730},[640],"height:1.009em;",[568,2732,2733,2736],{"style":760},[568,2734],{"className":2735,"style":649},[648],[568,2737,2739],{"className":2738},[653,654,655,656],[568,2740,1772],{"className":2741},[618,656],[568,2743,2744,2747],{"style":772},[568,2745],{"className":2746,"style":649},[648],[568,2748,2750],{"className":2749},[653,654,655,656],[568,2751,2685],{"className":2752},[618,656],[568,2754,664],{"className":2755},[663],[568,2757,2759],{"className":2758},[636],[568,2760,2762],{"className":2761,"style":791},[640],[568,2763],{},[568,2765],{"className":2766,"style":798},[797],[568,2768,2770,2773],{"className":2769},[618],[568,2771,2690],{"className":2772},[618,622],[568,2774,2776],{"className":2775},[627],[568,2777,2779],{"className":2778},[631],[568,2780,2782],{"className":2781},[636],[568,2783,2786],{"className":2784,"style":2785},[640],"height:0.6644em;",[568,2787,2788,2791],{"style":1370},[568,2789],{"className":2790,"style":649},[648],[568,2792,2794],{"className":2793},[653,654,655,656],[568,2795,709],{"className":2796},[618,622,656],[568,2798],{"className":2799,"style":798},[797],[568,2801,719],{"className":2802},[618,622],[568,2804,709],{"className":2805},[618,622]," soll mit einem Fehler von höchstens ",[568,2808,2810,2834],{"className":2809},[571],[568,2811,2813],{"className":2812},[575],[577,2814,2815],{"xmlns":579},[581,2816,2817,2831],{},[584,2818,2819],{},[1071,2820,2821,2824],{},[1076,2822,2823],{},"10",[584,2825,2826,2828],{},[691,2827,1041],{},[1076,2829,2830],{},"4",[597,2832,2833],{"encoding":599},"10^{-4}",[568,2835,2837],{"className":2836,"ariaHidden":605},[604],[568,2838,2840,2843,2846],{"className":2839},[609],[568,2841],{"className":2842,"style":1367},[613],[568,2844,2685],{"className":2845},[618],[568,2847,2849,2852],{"className":2848},[618],[568,2850,1772],{"className":2851},[618],[568,2853,2855],{"className":2854},[627],[568,2856,2858],{"className":2857},[631],[568,2859,2861],{"className":2860},[636],[568,2862,2864],{"className":2863,"style":1367},[640],[568,2865,2866,2869],{"style":1370},[568,2867],{"className":2868,"style":649},[648],[568,2870,2872],{"className":2871},[653,654,655,656],[568,2873,2875,2878],{"className":2874},[618,656],[568,2876,1041],{"className":2877},[618,656],[568,2879,2830],{"className":2880},[618,656]," berechnet werden. Es ist ",[568,2883,2885,2919],{"className":2884},[571],[568,2886,2888],{"className":2887},[575],[577,2889,2890],{"xmlns":579},[581,2891,2892,2916],{},[584,2893,2894,2904,2906,2912,2914],{},[1071,2895,2896,2898],{},[590,2897,702],{},[584,2899,2900,2902],{},[691,2901,1093],{"mathvariant":1092},[691,2903,1093],{"mathvariant":1092},[691,2905,1050],{},[1071,2907,2908,2910],{},[590,2909,2690],{},[590,2911,709],{},[691,2913,1888],{},[590,2915,2690],{},[597,2917,2918],{"encoding":599},"f'' = e^x \\leq e",[568,2920,2922,2969,3014],{"className":2921,"ariaHidden":605},[604],[568,2923,2925,2928,2960,2963,2966],{"className":2924},[609],[568,2926],{"className":2927,"style":1785},[613],[568,2929,2931,2934],{"className":2930},[618],[568,2932,702],{"className":2933,"style":802},[618,622],[568,2935,2937],{"className":2936},[627],[568,2938,2940],{"className":2939},[631],[568,2941,2943],{"className":2942},[636],[568,2944,2946],{"className":2945,"style":1542},[640],[568,2947,2948,2951],{"style":1370},[568,2949],{"className":2950,"style":649},[648],[568,2952,2954],{"className":2953},[653,654,655,656],[568,2955,2957],{"className":2956},[618,656],[568,2958,1432],{"className":2959},[618,656],[568,2961],{"className":2962,"style":965},[797],[568,2964,1050],{"className":2965},[969],[568,2967],{"className":2968,"style":965},[797],[568,2970,2972,2976,3005,3008,3011],{"className":2971},[609],[568,2973],{"className":2974,"style":2975},[613],"height:0.8004em;vertical-align:-0.136em;",[568,2977,2979,2982],{"className":2978},[618],[568,2980,2690],{"className":2981},[618,622],[568,2983,2985],{"className":2984},[627],[568,2986,2988],{"className":2987},[631],[568,2989,2991],{"className":2990},[636],[568,2992,2994],{"className":2993,"style":2785},[640],[568,2995,2996,2999],{"style":1370},[568,2997],{"className":2998,"style":649},[648],[568,3000,3002],{"className":3001},[653,654,655,656],[568,3003,709],{"className":3004},[618,622,656],[568,3006],{"className":3007,"style":965},[797],[568,3009,1888],{"className":3010},[969],[568,3012],{"className":3013,"style":965},[797],[568,3015,3017,3020],{"className":3016},[609],[568,3018],{"className":3019,"style":849},[613],[568,3021,2690],{"className":3022},[618,622],[568,3024,3026,3048],{"className":3025},[571],[568,3027,3029],{"className":3028},[575],[577,3030,3031],{"xmlns":579},[581,3032,3033,3045],{},[584,3034,3035,3037,3039,3041,3043],{},[691,3036,935],{"stretchy":705},[1076,3038,1772],{},[691,3040,940],{"separator":605},[1076,3042,2685],{},[691,3044,945],{"stretchy":705},[597,3046,3047],{"encoding":599},"[0, 1]",[568,3049,3051],{"className":3050,"ariaHidden":605},[604],[568,3052,3054,3057,3060,3063,3066,3069,3072],{"className":3053},[609],[568,3055],{"className":3056,"style":979},[613],[568,3058,935],{"className":3059},[806],[568,3061,1772],{"className":3062},[618],[568,3064,940],{"className":3065},[989],[568,3067],{"className":3068,"style":798},[797],[568,3070,2685],{"className":3071},[618],[568,3073,945],{"className":3074},[813],", also muss gelten",[568,3077,3079],{"className":3078},[1003],[568,3080,3082,3166],{"className":3081},[571],[568,3083,3085],{"className":3084},[575],[577,3086,3087],{"xmlns":579,"display":1012},[581,3088,3089,3163],{},[584,3090,3091,3108,3110,3112,3114,3124,3127,3130,3132,3134,3136,3158,3160],{},[1054,3092,3093,3106],{},[584,3094,3095,3097,3100],{},[1076,3096,2685],{},[691,3098,3099],{},"⋅",[1071,3101,3102,3104],{},[590,3103,868],{},[1076,3105,1078],{},[1076,3107,1081],{},[691,3109,3099],{},[590,3111,2690],{},[691,3113,1888],{},[1071,3115,3116,3118],{},[1076,3117,2823],{},[584,3119,3120,3122],{},[691,3121,1041],{},[1076,3123,2830],{},[797,3125],{"width":3126},"1em",[691,3128,3129],{},"⇒",[797,3131],{"width":3126},[590,3133,868],{},[691,3135,1888],{},[1890,3137,3138],{},[1054,3139,3140,3156],{},[584,3141,3142,3144,3146],{},[1076,3143,1081],{},[691,3145,3099],{},[1071,3147,3148,3150],{},[1076,3149,2823],{},[584,3151,3152,3154],{},[691,3153,1041],{},[1076,3155,2830],{},[590,3157,2690],{},[691,3159,2252],{},[1076,3161,3162],{},"0,021",[597,3164,3165],{"encoding":599},"\\frac{1 \\cdot h^2}{12} \\cdot e \\leq 10^{-4} \\quad\\Rightarrow\\quad h \\leq \\sqrt{\\frac{12 \\cdot 10^{-4}}{e}} \\approx 0{,}021",[568,3167,3169,3284,3303,3364,3382,3563],{"className":3168,"ariaHidden":605},[604],[568,3170,3172,3175,3275,3278,3281],{"className":3171},[609],[568,3173],{"className":3174,"style":1268},[613],[568,3176,3178,3181,3272],{"className":3177},[618],[568,3179],{"className":3180},[806,1278],[568,3182,3184],{"className":3183},[1054],[568,3185,3187,3264],{"className":3186},[631,632],[568,3188,3190,3261],{"className":3189},[636],[568,3191,3193,3204,3212],{"className":3192,"style":1291},[640],[568,3194,3195,3198],{"style":1294},[568,3196],{"className":3197,"style":1298},[648],[568,3199,3201],{"className":3200},[618],[568,3202,1081],{"className":3203},[618],[568,3205,3206,3209],{"style":1307},[568,3207],{"className":3208,"style":1298},[648],[568,3210],{"className":3211,"style":1315},[1314],[568,3213,3214,3217],{"style":1318},[568,3215],{"className":3216,"style":1298},[648],[568,3218,3220,3223,3226,3229,3232],{"className":3219},[618],[568,3221,2685],{"className":3222},[618],[568,3224],{"className":3225,"style":1199},[797],[568,3227,3099],{"className":3228},[1203],[568,3230],{"className":3231,"style":1199},[797],[568,3233,3235,3238],{"className":3234},[618],[568,3236,868],{"className":3237},[618,622],[568,3239,3241],{"className":3240},[627],[568,3242,3244],{"className":3243},[631],[568,3245,3247],{"className":3246},[636],[568,3248,3250],{"className":3249,"style":1367},[640],[568,3251,3252,3255],{"style":1370},[568,3253],{"className":3254,"style":649},[648],[568,3256,3258],{"className":3257},[653,654,655,656],[568,3259,1078],{"className":3260},[618,656],[568,3262,664],{"className":3263},[663],[568,3265,3267],{"className":3266},[636],[568,3268,3270],{"className":3269,"style":1389},[640],[568,3271],{},[568,3273],{"className":3274},[813,1278],[568,3276],{"className":3277,"style":1199},[797],[568,3279,3099],{"className":3280},[1203],[568,3282],{"className":3283,"style":1199},[797],[568,3285,3287,3291,3294,3297,3300],{"className":3286},[609],[568,3288],{"className":3289,"style":3290},[613],"height:0.7719em;vertical-align:-0.136em;",[568,3292,2690],{"className":3293},[618,622],[568,3295],{"className":3296,"style":965},[797],[568,3298,1888],{"className":3299},[969],[568,3301],{"className":3302,"style":965},[797],[568,3304,3306,3310,3313,3348,3352,3355,3358,3361],{"className":3305},[609],[568,3307],{"className":3308,"style":3309},[613],"height:0.8641em;",[568,3311,2685],{"className":3312},[618],[568,3314,3316,3319],{"className":3315},[618],[568,3317,1772],{"className":3318},[618],[568,3320,3322],{"className":3321},[627],[568,3323,3325],{"className":3324},[631],[568,3326,3328],{"className":3327},[636],[568,3329,3331],{"className":3330,"style":3309},[640],[568,3332,3333,3336],{"style":1419},[568,3334],{"className":3335,"style":649},[648],[568,3337,3339],{"className":3338},[653,654,655,656],[568,3340,3342,3345],{"className":3341},[618,656],[568,3343,1041],{"className":3344},[618,656],[568,3346,2830],{"className":3347},[618,656],[568,3349],{"className":3350,"style":3351},[797],"margin-right:1em;",[568,3353],{"className":3354,"style":965},[797],[568,3356,3129],{"className":3357},[969],[568,3359],{"className":3360,"style":3351},[797],[568,3362],{"className":3363,"style":965},[797],[568,3365,3367,3370,3373,3376,3379],{"className":3366},[609],[568,3368],{"className":3369,"style":1946},[613],[568,3371,868],{"className":3372},[618,622],[568,3374],{"className":3375,"style":965},[797],[568,3377,1888],{"className":3378},[969],[568,3380],{"className":3381,"style":965},[797],[568,3383,3385,3389,3554,3557,3560],{"className":3384},[609],[568,3386],{"className":3387,"style":3388},[613],"height:2.44em;vertical-align:-0.7406em;",[568,3390,3392],{"className":3391},[618,1969],[568,3393,3395,3545],{"className":3394},[631,632],[568,3396,3398,3542],{"className":3397},[636],[568,3399,3402,3525],{"className":3400,"style":3401},[640],"height:1.6994em;",[568,3403,3406,3410],{"className":3404,"style":3405},[1983],"top:-4.4em;",[568,3407],{"className":3408,"style":3409},[648],"height:4.4em;",[568,3411,3413],{"className":3412,"style":1992},[618],[568,3414,3416,3419,3522],{"className":3415},[618],[568,3417],{"className":3418},[806,1278],[568,3420,3422],{"className":3421},[1054],[568,3423,3425,3514],{"className":3424},[631,632],[568,3426,3428,3511],{"className":3427},[636],[568,3429,3432,3443,3451],{"className":3430,"style":3431},[640],"height:1.4171em;",[568,3433,3434,3437],{"style":1294},[568,3435],{"className":3436,"style":1298},[648],[568,3438,3440],{"className":3439},[618],[568,3441,2690],{"className":3442},[618,622],[568,3444,3445,3448],{"style":1307},[568,3446],{"className":3447,"style":1298},[648],[568,3449],{"className":3450,"style":1315},[1314],[568,3452,3453,3456],{"style":1318},[568,3454],{"className":3455,"style":1298},[648],[568,3457,3459,3462,3465,3468,3471,3474],{"className":3458},[618],[568,3460,1081],{"className":3461},[618],[568,3463],{"className":3464,"style":1199},[797],[568,3466,3099],{"className":3467},[1203],[568,3469],{"className":3470,"style":1199},[797],[568,3472,2685],{"className":3473},[618],[568,3475,3477,3480],{"className":3476},[618],[568,3478,1772],{"className":3479},[618],[568,3481,3483],{"className":3482},[627],[568,3484,3486],{"className":3485},[631],[568,3487,3489],{"className":3488},[636],[568,3490,3493],{"className":3491,"style":3492},[640],"height:0.7401em;",[568,3494,3496,3499],{"style":3495},"top:-2.989em;margin-right:0.05em;",[568,3497],{"className":3498,"style":649},[648],[568,3500,3502],{"className":3501},[653,654,655,656],[568,3503,3505,3508],{"className":3504},[618,656],[568,3506,1041],{"className":3507},[618,656],[568,3509,2830],{"className":3510},[618,656],[568,3512,664],{"className":3513},[663],[568,3515,3517],{"className":3516},[636],[568,3518,3520],{"className":3519,"style":1389},[640],[568,3521],{},[568,3523],{"className":3524},[813,1278],[568,3526,3528,3531],{"style":3527},"top:-3.6594em;",[568,3529],{"className":3530,"style":3409},[648],[568,3532,3535],{"className":3533,"style":3534},[2155],"min-width:1.02em;height:2.48em;",[2158,3536,3539],{"xmlns":2160,"width":2161,"height":3537,"viewBox":3538,"preserveAspectRatio":2164},"2.48em","0 0 400000 2592",[2166,3540],{"d":3541},"M424,2478\nc-1.3,-0.7,-38.5,-172,-111.5,-514c-73,-342,-109.8,-513.3,-110.5,-514\nc0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5,25c-5.7,9.3,-9.8,16,-12.5,20\ns-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13,-13s76,-122,76,-122s77,-121,77,-121\ns209,968,209,968c0,-2,84.7,-361.7,254,-1079c169.3,-717.3,254.7,-1077.7,256,-1081\nl0 -0c4,-6.7,10,-10,18,-10 H400000\nv40H1014.6\ns-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185\nc-2,6,-10,9,-24,9\nc-8,0,-12,-0.7,-12,-2z M1001 80\nh400000v40h-400000z",[568,3543,664],{"className":3544},[663],[568,3546,3548],{"className":3547},[636],[568,3549,3552],{"className":3550,"style":3551},[640],"height:0.7406em;",[568,3553],{},[568,3555],{"className":3556,"style":965},[797],[568,3558,2252],{"className":3559},[969],[568,3561],{"className":3562,"style":965},[797],[568,3564,3566,3570,3573,3579],{"className":3565},[609],[568,3567],{"className":3568,"style":3569},[613],"height:0.8389em;vertical-align:-0.1944em;",[568,3571,1772],{"className":3572},[618],[568,3574,3576],{"className":3575},[618],[568,3577,940],{"className":3578},[989],[568,3580,3582],{"className":3581},[618],"021",[564,3584,3585,3586,3707,3708,3760,3761,3813,3814,2181],{},"Wegen ",[568,3587,3589,3611],{"className":3588},[571],[568,3590,3592],{"className":3591},[575],[577,3593,3594],{"xmlns":579},[581,3595,3596,3608],{},[584,3597,3598,3600,3602],{},[590,3599,595],{},[691,3601,1050],{},[1054,3603,3604,3606],{},[1076,3605,2685],{},[590,3607,868],{},[597,3609,3610],{"encoding":599},"n = \\frac{1}{h}",[568,3612,3614,3632],{"className":3613,"ariaHidden":605},[604],[568,3615,3617,3620,3623,3626,3629],{"className":3616},[609],[568,3618],{"className":3619,"style":849},[613],[568,3621,595],{"className":3622},[618,622],[568,3624],{"className":3625,"style":965},[797],[568,3627,1050],{"className":3628},[969],[568,3630],{"className":3631,"style":965},[797],[568,3633,3635,3639],{"className":3634},[609],[568,3636],{"className":3637,"style":3638},[613],"height:1.1901em;vertical-align:-0.345em;",[568,3640,3642,3645,3704],{"className":3641},[618],[568,3643],{"className":3644},[806,1278],[568,3646,3648],{"className":3647},[1054],[568,3649,3651,3696],{"className":3650},[631,632],[568,3652,3654,3693],{"className":3653},[636],[568,3655,3657,3671,3679],{"className":3656,"style":2011},[640],[568,3658,3659,3662],{"style":2014},[568,3660],{"className":3661,"style":1298},[648],[568,3663,3665],{"className":3664},[653,654,655,656],[568,3666,3668],{"className":3667},[618,656],[568,3669,868],{"className":3670},[618,622,656],[568,3672,3673,3676],{"style":1307},[568,3674],{"className":3675,"style":1298},[648],[568,3677],{"className":3678,"style":1315},[1314],[568,3680,3681,3684],{"style":2112},[568,3682],{"className":3683,"style":1298},[648],[568,3685,3687],{"className":3686},[653,654,655,656],[568,3688,3690],{"className":3689},[618,656],[568,3691,2685],{"className":3692},[618,656],[568,3694,664],{"className":3695},[663],[568,3697,3699],{"className":3698},[636],[568,3700,3702],{"className":3701,"style":2541},[640],[568,3703],{},[568,3705],{"className":3706},[813,1278]," braucht man mindestens ",[568,3709,3711,3730],{"className":3710},[571],[568,3712,3714],{"className":3713},[575],[577,3715,3716],{"xmlns":579},[581,3717,3718,3727],{},[584,3719,3720,3722,3724],{},[590,3721,595],{},[691,3723,1050],{},[1076,3725,3726],{},"48",[597,3728,3729],{"encoding":599},"n = 48",[568,3731,3733,3751],{"className":3732,"ariaHidden":605},[604],[568,3734,3736,3739,3742,3745,3748],{"className":3735},[609],[568,3737],{"className":3738,"style":849},[613],[568,3740,595],{"className":3741},[618,622],[568,3743],{"className":3744,"style":965},[797],[568,3746,1050],{"className":3747},[969],[568,3749],{"className":3750,"style":965},[797],[568,3752,3754,3757],{"className":3753},[609],[568,3755],{"className":3756,"style":1833},[613],[568,3758,3726],{"className":3759},[618]," Teilintervalle. Mit ",[568,3762,3764,3783],{"className":3763},[571],[568,3765,3767],{"className":3766},[575],[577,3768,3769],{"xmlns":579},[581,3770,3771,3780],{},[584,3772,3773,3775,3777],{},[590,3774,595],{},[691,3776,1050],{},[1076,3778,3779],{},"47",[597,3781,3782],{"encoding":599},"n = 47",[568,3784,3786,3804],{"className":3785,"ariaHidden":605},[604],[568,3787,3789,3792,3795,3798,3801],{"className":3788},[609],[568,3790],{"className":3791,"style":849},[613],[568,3793,595],{"className":3794},[618,622],[568,3796],{"className":3797,"style":965},[797],[568,3799,1050],{"className":3800},[969],[568,3802],{"className":3803,"style":965},[797],[568,3805,3807,3810],{"className":3806},[609],[568,3808],{"className":3809,"style":1833},[613],[568,3811,3779],{"className":3812},[618]," wäre die Schranke knapp über 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\\sin x\\,dx = 2",[568,3929,3931,4021],{"className":3930,"ariaHidden":605},[604],[568,3932,3934,3938,3991,3994,3997,4000,4003,4006,4009,4012,4015,4018],{"className":3933},[609],[568,3935],{"className":3936,"style":3937},[613],"height:1.2151em;vertical-align:-0.3558em;",[568,3939,3941,3944],{"className":3940},[738],[568,3942,693],{"className":3943,"style":744},[738,742,743],[568,3945,3947],{"className":3946},[627],[568,3948,3950,3983],{"className":3949},[631,632],[568,3951,3953,3980],{"className":3952},[636],[568,3954,3957,3968],{"className":3955,"style":3956},[640],"height:0.8593em;",[568,3958,3959,3962],{"style":760},[568,3960],{"className":3961,"style":649},[648],[568,3963,3965],{"className":3964},[653,654,655,656],[568,3966,1772],{"className":3967},[618,656],[568,3969,3970,3973],{"style":772},[568,3971],{"className":3972,"style":649},[648],[568,3974,3976],{"className":3975},[653,654,655,656],[568,3977,3907],{"className":3978,"style":3979},[618,622,656],"margin-right:0.0359em;",[568,3981,664],{"className":3982},[663],[568,3984,3986],{"className":3985},[636],[568,3987,3989],{"className":3988,"style":791},[640],[568,3990],{},[568,3992],{"className":3993,"style":798},[797],[568,3995,3910],{"className":3996},[738],[568,3998],{"className":3999,"style":798},[797],[568,4001,709],{"className":4002},[618,622],[568,4004],{"className":4005,"style":798},[797],[568,4007,719],{"className":4008},[618,622],[568,4010,709],{"className":4011},[618,622],[568,4013],{"className":4014,"style":965},[797],[568,4016,1050],{"className":4017},[969],[568,4019],{"className":4020,"style":965},[797],[568,4022,4024,4027],{"className":4023},[609],[568,4025],{"className":4026,"style":1833},[613],[568,4028,1078],{"className":4029},[618],[568,4031,4033,4051],{"className":4032},[571],[568,4034,4036],{"className":4035},[575],[577,4037,4038],{"xmlns":579},[581,4039,4040,4048],{},[584,4041,4042,4044,4046],{},[590,4043,595],{},[691,4045,1050],{},[1076,4047,2830],{},[597,4049,4050],{"encoding":599},"n = 4",[568,4052,4054,4072],{"className":4053,"ariaHidden":605},[604],[568,4055,4057,4060,4063,4066,4069],{"className":4056},[609],[568,4058],{"className":4059,"style":849},[613],[568,4061,595],{"className":4062},[618,622],[568,4064],{"className":4065,"style":965},[797],[568,4067,1050],{"className":4068},[969],[568,4070],{"className":4071,"style":965},[797],[568,4073,4075,4078],{"className":4074},[609],[568,4076],{"className":4077,"style":1833},[613],[568,4079,2830],{"className":4080},[618],", also ",[568,4083,4085,4107],{"className":4084},[571],[568,4086,4088],{"className":4087},[575],[577,4089,4090],{"xmlns":579},[581,4091,4092,4104],{},[584,4093,4094,4096,4098],{},[590,4095,868],{},[691,4097,1050],{},[1054,4099,4100,4102],{},[590,4101,3907],{},[1076,4103,2830],{},[597,4105,4106],{"encoding":599},"h = \\frac{\\pi}{4}",[568,4108,4110,4128],{"className":4109,"ariaHidden":605},[604],[568,4111,4113,4116,4119,4122,4125],{"className":4112},[609],[568,4114],{"className":4115,"style":880},[613],[568,4117,868],{"className":4118},[618,622],[568,4120],{"className":4121,"style":965},[797],[568,4123,1050],{"className":4124},[969],[568,4126],{"className":4127,"style":965},[797],[568,4129,4131,4135],{"className":4130},[609],[568,4132],{"className":4133,"style":4134},[613],"height:1.0404em;vertical-align:-0.345em;",[568,4136,4138,4141,4201],{"className":4137},[618],[568,4139],{"className":4140},[806,1278],[568,4142,4144],{"className":4143},[1054],[568,4145,4147,4193],{"className":4146},[631,632],[568,4148,4150,4190],{"className":4149},[636],[568,4151,4154,4168,4176],{"className":4152,"style":4153},[640],"height:0.6954em;",[568,4155,4156,4159],{"style":2014},[568,4157],{"className":4158,"style":1298},[648],[568,4160,4162],{"className":4161},[653,654,655,656],[568,4163,4165],{"className":4164},[618,656],[568,4166,2830],{"className":4167},[618,656],[568,4169,4170,4173],{"style":1307},[568,4171],{"className":4172,"style":1298},[648],[568,4174],{"className":4175,"style":1315},[1314],[568,4177,4178,4181],{"style":2112},[568,4179],{"className":4180,"style":1298},[648],[568,4182,4184],{"className":4183},[653,654,655,656],[568,4185,4187],{"className":4186},[618,656],[568,4188,3907],{"className":4189,"style":3979},[618,622,656],[568,4191,664],{"className":4192},[663],[568,4194,4196],{"className":4195},[636],[568,4197,4199],{"className":4198,"style":2541},[640],[568,4200],{},[568,4202],{"className":4203},[813,1278],":",[568,4206,4208],{"className":4207},[1003],[568,4209,4211,4317],{"className":4210},[571],[568,4212,4214],{"className":4213},[575],[577,4215,4216],{"xmlns":579,"display":1012},[581,4217,4218,4314],{},[584,4219,4220,4226,4228,4234,4287,4289,4295,4297,4299,4301,4303,4307,4309,4311],{},[587,4221,4222,4224],{},[590,4223,592],{},[1076,4225,2830],{},[691,4227,1050],{},[1054,4229,4230,4232],{},[590,4231,3907],{},[1076,4233,2830],{},[584,4235,4236,4238,4240,4242,4251,4254,4256,4258,4266,4268,4270,4272,4285],{},[691,4237,706],{"fence":605},[590,4239,3910],{},[691,4241,1919],{},[4243,4244,4245],"mstyle",{"scriptlevel":1772,"displaystyle":705},[1054,4246,4247,4249],{},[590,4248,3907],{},[1076,4250,2830],{},[691,4252,4253],{},"+",[590,4255,3910],{},[691,4257,1919],{},[4243,4259,4260],{"scriptlevel":1772,"displaystyle":705},[1054,4261,4262,4264],{},[590,4263,3907],{},[1076,4265,1078],{},[691,4267,4253],{},[590,4269,3910],{},[691,4271,1919],{},[4243,4273,4274],{"scriptlevel":1772,"displaystyle":705},[1054,4275,4276,4283],{},[584,4277,4278,4281],{},[1076,4279,4280],{},"3",[590,4282,3907],{},[1076,4284,2830],{},[691,4286,712],{"fence":605},[691,4288,1050],{},[1054,4290,4291,4293],{},[590,4292,3907],{},[1076,4294,2830],{},[714,4296,716],{},[691,4298,706],{"stretchy":705},[1076,4300,2685],{},[691,4302,4253],{},[1890,4304,4305],{},[1076,4306,1078],{},[691,4308,712],{"stretchy":705},[691,4310,2252],{},[1076,4312,4313],{},"1,8961",[597,4315,4316],{"encoding":599},"T_4 = \\frac{\\pi}{4} \\left( \\sin\\tfrac{\\pi}{4} + \\sin\\tfrac{\\pi}{2} + \\sin\\tfrac{3\\pi}{4} \\right) = \\frac{\\pi}{4}\\,(1 + \\sqrt{2}) \\approx 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den Wert ",[568,5053,5055,5110],{"className":5054},[571],[568,5056,5058],{"className":5057},[575],[577,5059,5060],{"xmlns":579},[581,5061,5062,5107],{},[584,5063,5064,5089,5091,5102,5104],{},[1054,5065,5066,5087],{},[584,5067,5068,5070,5072,5074,5076,5079,5081],{},[590,5069,3907],{},[691,5071,3099],{},[691,5073,706],{"stretchy":705},[590,5075,3907],{},[590,5077,5078],{"mathvariant":1092},"\u002F",[1076,5080,2830],{},[1071,5082,5083,5085],{},[691,5084,712],{"stretchy":705},[1076,5086,1078],{},[1076,5088,1081],{},[691,5090,1050],{},[1054,5092,5093,5099],{},[1071,5094,5095,5097],{},[590,5096,3907],{},[1076,5098,4280],{},[1076,5100,5101],{},"192",[691,5103,2252],{},[1076,5105,5106],{},"0,1615",[597,5108,5109],{"encoding":599},"\\frac{\\pi \\cdot (\\pi\u002F4)^2}{12} = \\frac{\\pi^3}{192} \\approx 0{,}1615",[568,5111,5113,5241,5351],{"className":5112,"ariaHidden":605},[604],[568,5114,5116,5120,5232,5235,5238],{"className":5115},[609],[568,5117],{"className":5118,"style":5119},[613],"height:1.4539em;vertical-align:-0.345em;",[568,5121,5123,5126,5229],{"className":5122},[618],[568,5124],{"className":5125},[806,1278],[568,5127,5129],{"className":5128},[1054],[568,5130,5132,5221],{"className":5131},[631,632],[568,5133,5135,5218],{"className":5134},[636],[568,5136,5139,5153,5161],{"className":5137,"style":5138},[640],"height:1.1089em;",[568,5140,5141,5144],{"style":2014},[568,5142],{"className":5143,"style":1298},[648],[568,5145,5147],{"className":5146},[653,654,655,656],[568,5148,5150],{"className":5149},[618,656],[568,5151,1081],{"className":5152},[618,656],[568,5154,5155,5158],{"style":1307},[568,5156],{"className":5157,"style":1298},[648],[568,5159],{"className":5160,"style":1315},[1314],[568,5162,5164,5167],{"style":5163},"top:-3.485em;",[568,5165],{"className":5166,"style":1298},[648],[568,5168,5170],{"className":5169},[653,654,655,656],[568,5171,5173,5176,5179,5182,5185,5189],{"className":5172},[618,656],[568,5174,3907],{"className":5175,"style":3979},[618,622,656],[568,5177,3099],{"className":5178},[1203,656],[568,5180,706],{"className":5181},[806,656],[568,5183,3907],{"className":5184,"style":3979},[618,622,656],[568,5186,5188],{"className":5187},[618,656],"\u002F4",[568,5190,5192,5195],{"className":5191},[813,656],[568,5193,712],{"className":5194},[813,656],[568,5196,5198],{"className":5197},[627],[568,5199,5201],{"className":5200},[631],[568,5202,5204],{"className":5203},[636],[568,5205,5207],{"className":5206,"style":2519},[640],[568,5208,5209,5212],{"style":2522},[568,5210],{"className":5211,"style":2087},[648],[568,5213,5215],{"className":5214},[653,2091,2092,656],[568,5216,1078],{"className":5217},[618,656],[568,5219,664],{"className":5220},[663],[568,5222,5224],{"className":5223},[636],[568,5225,5227],{"className":5226,"style":2541},[640],[568,5228],{},[568,5230],{"className":5231},[813,1278],[568,5233],{"className":5234,"style":965},[797],[568,5236,1050],{"className":5237},[969],[568,5239],{"className":5240,"style":965},[797],[568,5242,5244,5248,5342,5345,5348],{"className":5243},[609],[568,5245],{"className":5246,"style":5247},[613],"height:1.3629em;vertical-align:-0.345em;",[568,5249,5251,5254,5339],{"className":5250},[618],[568,5252],{"className":5253},[806,1278],[568,5255,5257],{"className":5256},[1054],[568,5258,5260,5331],{"className":5259},[631,632],[568,5261,5263,5328],{"className":5262},[636],[568,5264,5266,5280,5288],{"className":5265,"style":2467},[640],[568,5267,5268,5271],{"style":2014},[568,5269],{"className":5270,"style":1298},[648],[568,5272,5274],{"className":5273},[653,654,655,656],[568,5275,5277],{"className":5276},[618,656],[568,5278,5101],{"className":5279},[618,656],[568,5281,5282,5285],{"style":1307},[568,5283],{"className":5284,"style":1298},[648],[568,5286],{"className":5287,"style":1315},[1314],[568,5289,5290,5293],{"style":2112},[568,5291],{"className":5292,"style":1298},[648],[568,5294,5296],{"className":5295},[653,654,655,656],[568,5297,5299],{"className":5298},[618,656],[568,5300,5302,5305],{"className":5301},[618,656],[568,5303,3907],{"className":5304,"style":3979},[618,622,656],[568,5306,5308],{"className":5307},[627],[568,5309,5311],{"className":5310},[631],[568,5312,5314],{"className":5313},[636],[568,5315,5317],{"className":5316,"style":2519},[640],[568,5318,5319,5322],{"style":2522},[568,5320],{"className":5321,"style":2087},[648],[568,5323,5325],{"className":5324},[653,2091,2092,656],[568,5326,4280],{"className":5327},[618,656],[568,5329,664],{"className":5330},[663],[568,5332,5334],{"className":5333},[636],[568,5335,5337],{"className":5336,"style":2541},[640],[568,5338],{},[568,5340],{"className":5341},[813,1278],[568,5343],{"className":5344,"style":965},[797],[568,5346,2252],{"className":5347},[969],[568,5349],{"className":5350,"style":965},[797],[568,5352,5354,5357,5360,5366],{"className":5353},[609],[568,5355],{"className":5356,"style":3569},[613],[568,5358,1772],{"className":5359},[618],[568,5361,5363],{"className":5362},[618],[568,5364,940],{"className":5365},[989],[568,5367,5369],{"className":5368},[618],"1615",". Die asymptotische Formel ",[568,5372,5374,5435],{"className":5373},[571],[568,5375,5377],{"className":5376},[575],[577,5378,5379],{"xmlns":579},[581,5380,5381,5432],{},[584,5382,5383,5385,5395,5397,5400,5402,5404,5406,5408,5410,5412,5414,5416,5427,5429],{},[691,5384,1041],{},[1054,5386,5387,5393],{},[1071,5388,5389,5391],{},[590,5390,868],{},[1076,5392,1078],{},[1076,5394,1081],{},[691,5396,706],{"stretchy":705},[590,5398,5399],{},"cos",[691,5401,1919],{},[590,5403,3907],{},[691,5405,1041],{},[590,5407,5399],{},[691,5409,1919],{},[1076,5411,1772],{},[691,5413,712],{"stretchy":705},[691,5415,1050],{},[1054,5417,5418,5424],{},[1071,5419,5420,5422],{},[590,5421,3907],{},[1076,5423,1078],{},[1076,5425,5426],{},"96",[691,5428,2252],{},[1076,5430,5431],{},"0,1028",[597,5433,5434],{"encoding":599},"-\\frac{h^2}{12}(\\cos\\pi - \\cos 0) = \\frac{\\pi^2}{96} \\approx 0{,}1028",[568,5436,5438,5562,5589,5698],{"className":5437,"ariaHidden":605},[604],[568,5439,5441,5444,5447,5541,5544,5547,5550,5553,5556,5559],{"className":5440},[609],[568,5442],{"className":5443,"style":5247},[613],[568,5445,1041],{"className":5446},[618],[568,5448,5450,5453,5538],{"className":5449},[618],[568,5451],{"className":5452},[806,1278],[568,5454,5456],{"className":5455},[1054],[568,5457,5459,5530],{"className":5458},[631,632],[568,5460,5462,5527],{"className":5461},[636],[568,5463,5465,5479,5487],{"className":5464,"style":2467},[640],[568,5466,5467,5470],{"style":2014},[568,5468],{"className":5469,"style":1298},[648],[568,5471,5473],{"className":5472},[653,654,655,656],[568,5474,5476],{"className":5475},[618,656],[568,5477,1081],{"className":5478},[618,656],[568,5480,5481,5484],{"style":1307},[568,5482],{"className":5483,"style":1298},[648],[568,5485],{"className":5486,"style":1315},[1314],[568,5488,5489,5492],{"style":2112},[568,5490],{"className":5491,"style":1298},[648],[568,5493,5495],{"className":5494},[653,654,655,656],[568,5496,5498],{"className":5497},[618,656],[568,5499,5501,5504],{"className":5500},[618,656],[568,5502,868],{"className":5503},[618,622,656],[568,5505,5507],{"className":5506},[627],[568,5508,5510],{"className":5509},[631],[568,5511,5513],{"className":5512},[636],[568,5514,5516],{"className":5515,"style":2519},[640],[568,5517,5518,5521],{"style":2522},[568,5519],{"className":5520,"style":2087},[648],[568,5522,5524],{"className":5523},[653,2091,2092,656],[568,5525,1078],{"className":5526},[618,656],[568,5528,664],{"className":5529},[663],[568,5531,5533],{"className":5532},[636],[568,5534,5536],{"className":5535,"style":2541},[640],[568,5537],{},[568,5539],{"className":5540},[813,1278],[568,5542,706],{"className":5543},[806],[568,5545,5399],{"className":5546},[738],[568,5548],{"className":5549,"style":798},[797],[568,5551,3907],{"className":5552,"style":3979},[618,622],[568,5554],{"className":5555,"style":1199},[797],[568,5557,1041],{"className":5558},[1203],[568,5560],{"className":5561,"style":1199},[797],[568,5563,5565,5568,5571,5574,5577,5580,5583,5586],{"className":5564},[609],[568,5566],{"className":5567,"style":979},[613],[568,5569,5399],{"className":5570},[738],[568,5572],{"className":5573,"style":798},[797],[568,5575,1772],{"className":5576},[618],[568,5578,712],{"className":5579},[813],[568,5581],{"className":5582,"style":965},[797],[568,5584,1050],{"className":5585},[969],[568,5587],{"className":5588,"style":965},[797],[568,5590,5592,5595,5689,5692,5695],{"className":5591},[609],[568,5593],{"className":5594,"style":5247},[613],[568,5596,5598,5601,5686],{"className":5597},[618],[568,5599],{"className":5600},[806,1278],[568,5602,5604],{"className":5603},[1054],[568,5605,5607,5678],{"className":5606},[631,632],[568,5608,5610,5675],{"className":5609},[636],[568,5611,5613,5627,5635],{"className":5612,"style":2467},[640],[568,5614,5615,5618],{"style":2014},[568,5616],{"className":5617,"style":1298},[648],[568,5619,5621],{"className":5620},[653,654,655,656],[568,5622,5624],{"className":5623},[618,656],[568,5625,5426],{"className":5626},[618,656],[568,5628,5629,5632],{"style":1307},[568,5630],{"className":5631,"style":1298},[648],[568,5633],{"className":5634,"style":1315},[1314],[568,5636,5637,5640],{"style":2112},[568,5638],{"className":5639,"style":1298},[648],[568,5641,5643],{"className":5642},[653,654,655,656],[568,5644,5646],{"className":5645},[618,656],[568,5647,5649,5652],{"className":5648},[618,656],[568,5650,3907],{"className":5651,"style":3979},[618,622,656],[568,5653,5655],{"className":5654},[627],[568,5656,5658],{"className":5657},[631],[568,5659,5661],{"className":5660},[636],[568,5662,5664],{"className":5663,"style":2519},[640],[568,5665,5666,5669],{"style":2522},[568,5667],{"className":5668,"style":2087},[648],[568,5670,5672],{"className":5671},[653,2091,2092,656],[568,5673,1078],{"className":5674},[618,656],[568,5676,664],{"className":5677},[663],[568,5679,5681],{"className":5680},[636],[568,5682,5684],{"className":5683,"style":2541},[640],[568,5685],{},[568,5687],{"className":5688},[813,1278],[568,5690],{"className":5691,"style":965},[797],[568,5693,2252],{"className":5694},[969],[568,5696],{"className":5697,"style":965},[797],[568,5699,5701,5704,5707,5713],{"className":5700},[609],[568,5702],{"className":5703,"style":3569},[613],[568,5705,1772],{"className":5706},[618],[568,5708,5710],{"className":5709},[618],[568,5711,940],{"className":5712},[989],[568,5714,5716],{"className":5715},[618],"1028"," trifft den Fehler fast genau. Mit ",[568,5719,5721,5740],{"className":5720},[571],[568,5722,5724],{"className":5723},[575],[577,5725,5726],{"xmlns":579},[581,5727,5728,5737],{},[584,5729,5730,5732,5734],{},[590,5731,595],{},[691,5733,1050],{},[1076,5735,5736],{},"8",[597,5738,5739],{"encoding":599},"n = 8",[568,5741,5743,5761],{"className":5742,"ariaHidden":605},[604],[568,5744,5746,5749,5752,5755,5758],{"className":5745},[609],[568,5747],{"className":5748,"style":849},[613],[568,5750,595],{"className":5751},[618,622],[568,5753],{"className":5754,"style":965},[797],[568,5756,1050],{"className":5757},[969],[568,5759],{"className":5760,"style":965},[797],[568,5762,5764,5767],{"className":5763},[609],[568,5765],{"className":5766,"style":1833},[613],[568,5768,5736],{"className":5769},[618]," sinkt der Fehler auf etwa ",[568,5772,5774,5789],{"className":5773},[571],[568,5775,5777],{"className":5776},[575],[577,5778,5779],{"xmlns":579},[581,5780,5781,5786],{},[584,5782,5783],{},[1076,5784,5785],{},"0,0258",[597,5787,5788],{"encoding":599},"0{,}0258",[568,5790,5792],{"className":5791,"ariaHidden":605},[604],[568,5793,5795,5798,5801,5807],{"className":5794},[609],[568,5796],{"className":5797,"style":3569},[613],[568,5799,1772],{"className":5800},[618],[568,5802,5804],{"className":5803},[618],[568,5805,940],{"className":5806},[989],[568,5808,5810],{"className":5809},[618],"0258",", also ungefähr auf ein Viertel.",[559,5813,5815],{"id":5814},"typische-fehler","Typische Fehler",[1704,5817,5818,6155,6234,6237],{},[1707,5819,5820,5848,5849,5877,5878,6095,6096,2181],{},[568,5821,5823,5836],{"className":5822},[571],[568,5824,5826],{"className":5825},[575],[577,5827,5828],{"xmlns":579},[581,5829,5830,5834],{},[584,5831,5832],{},[590,5833,868],{},[597,5835,868],{"encoding":599},[568,5837,5839],{"className":5838,"ariaHidden":605},[604],[568,5840,5842,5845],{"className":5841},[609],[568,5843],{"className":5844,"style":880},[613],[568,5846,868],{"className":5847},[618,622]," und ",[568,5850,5852,5865],{"className":5851},[571],[568,5853,5855],{"className":5854},[575],[577,5856,5857],{"xmlns":579},[581,5858,5859,5863],{},[584,5860,5861],{},[590,5862,595],{},[597,5864,595],{"encoding":599},[568,5866,5868],{"className":5867,"ariaHidden":605},[604],[568,5869,5871,5874],{"className":5870},[609],[568,5872],{"className":5873,"style":849},[613],[568,5875,595],{"className":5876},[618,622]," verwechseln: Die Schranke enthält ",[568,5879,5881,5923],{"className":5880},[571],[568,5882,5884],{"className":5883},[575],[577,5885,5886],{"xmlns":579},[581,5887,5888,5920],{},[584,5889,5890,5896,5898],{},[1071,5891,5892,5894],{},[590,5893,868],{},[1076,5895,1078],{},[691,5897,1050],{},[1071,5899,5900,5918],{},[584,5901,5902,5904,5916],{},[691,5903,706],{"fence":605},[1054,5905,5906,5914],{},[584,5907,5908,5910,5912],{},[590,5909,699],{},[691,5911,1041],{},[590,5913,696],{},[590,5915,595],{},[691,5917,712],{"fence":605},[1076,5919,1078],{},[597,5921,5922],{"encoding":599},"h^2 = \\left(\\frac{b - a}{n}\\right)^2",[568,5924,5926,5970],{"className":5925,"ariaHidden":605},[604],[568,5927,5929,5932,5961,5964,5967],{"className":5928},[609],[568,5930],{"className":5931,"style":1367},[613],[568,5933,5935,5938],{"className":5934},[618],[568,5936,868],{"className":5937},[618,622],[568,5939,5941],{"className":5940},[627],[568,5942,5944],{"className":5943},[631],[568,5945,5947],{"className":5946},[636],[568,5948,5950],{"className":5949,"style":1367},[640],[568,5951,5952,5955],{"style":1370},[568,5953],{"className":5954,"style":649},[648],[568,5956,5958],{"className":5957},[653,654,655,656],[568,5959,1078],{"className":5960},[618,656],[568,5962],{"className":5963,"style":965},[797],[568,5965,1050],{"className":5966},[969],[568,5968],{"className":5969,"style":965},[797],[568,5971,5973,5977],{"className":5972},[609],[568,5974],{"className":5975,"style":5976},[613],"height:1.4341em;vertical-align:-0.35em;",[568,5978,5980,6070],{"className":5979},[4452],[568,5981,5983,5989,6064],{"className":5982},[4452],[568,5984,5986],{"className":5985,"style":4457},[806,4456],[568,5987,706],{"className":5988},[2553,2092],[568,5990,5992,5995,6061],{"className":5991},[618],[568,5993],{"className":5994},[806,1278],[568,5996,5998],{"className":5997},[1054],[568,5999,6001,6053],{"className":6000},[631,632],[568,6002,6004,6050],{"className":6003},[636],[568,6005,6008,6022,6030],{"className":6006,"style":6007},[640],"height:0.8801em;",[568,6009,6010,6013],{"style":2014},[568,6011],{"className":6012,"style":1298},[648],[568,6014,6016],{"className":6015},[653,654,655,656],[568,6017,6019],{"className":6018},[618,656],[568,6020,595],{"className":6021},[618,622,656],[568,6023,6024,6027],{"style":1307},[568,6025],{"className":6026,"style":1298},[648],[568,6028],{"className":6029,"style":1315},[1314],[568,6031,6032,6035],{"style":2112},[568,6033],{"className":6034,"style":1298},[648],[568,6036,6038],{"className":6037},[653,654,655,656],[568,6039,6041,6044,6047],{"className":6040},[618,656],[568,6042,699],{"className":6043},[618,622,656],[568,6045,1041],{"className":6046},[1203,656],[568,6048,696],{"className":6049},[618,622,656],[568,6051,664],{"className":6052},[663],[568,6054,6056],{"className":6055},[636],[568,6057,6059],{"className":6058,"style":2541},[640],[568,6060],{},[568,6062],{"className":6063},[813,1278],[568,6065,6067],{"className":6066,"style":4457},[813,4456],[568,6068,712],{"className":6069},[2553,2092],[568,6071,6073],{"className":6072},[627],[568,6074,6076],{"className":6075},[631],[568,6077,6079],{"className":6078},[636],[568,6080,6083],{"className":6081,"style":6082},[640],"height:1.0841em;",[568,6084,6086,6089],{"style":6085},"top:-3.333em;margin-right:0.05em;",[568,6087],{"className":6088,"style":649},[648],[568,6090,6092],{"className":6091},[653,654,655,656],[568,6093,1078],{"className":6094},[618,656],", nicht ",[568,6097,6099,6117],{"className":6098},[571],[568,6100,6102],{"className":6101},[575],[577,6103,6104],{"xmlns":579},[581,6105,6106,6114],{},[584,6107,6108],{},[1071,6109,6110,6112],{},[590,6111,595],{},[1076,6113,1078],{},[597,6115,6116],{"encoding":599},"n^2",[568,6118,6120],{"className":6119,"ariaHidden":605},[604],[568,6121,6123,6126],{"className":6122},[609],[568,6124],{"className":6125,"style":1367},[613],[568,6127,6129,6132],{"className":6128},[618],[568,6130,595],{"className":6131},[618,622],[568,6133,6135],{"className":6134},[627],[568,6136,6138],{"className":6137},[631],[568,6139,6141],{"className":6140},[636],[568,6142,6144],{"className":6143,"style":1367},[640],[568,6145,6146,6149],{"style":1370},[568,6147],{"className":6148,"style":649},[648],[568,6150,6152],{"className":6151},[653,654,655,656],[568,6153,1078],{"className":6154},[618,656],[1707,6156,6157,6158,6233],{},"Das Maximum von ",[568,6159,6161,6186],{"className":6160},[571],[568,6162,6164],{"className":6163},[575],[577,6165,6166],{"xmlns":579},[581,6167,6168,6184],{},[584,6169,6170,6172,6182],{},[590,6171,1489],{"mathvariant":1092},[1071,6173,6174,6176],{},[590,6175,702],{},[584,6177,6178,6180],{},[691,6179,1093],{"mathvariant":1092},[691,6181,1093],{"mathvariant":1092},[590,6183,1489],{"mathvariant":1092},[597,6185,1598],{"encoding":599},[568,6187,6189],{"className":6188,"ariaHidden":605},[604],[568,6190,6192,6195,6198,6230],{"className":6191},[609],[568,6193],{"className":6194,"style":1520},[613],[568,6196,1489],{"className":6197},[618],[568,6199,6201,6204],{"className":6200},[618],[568,6202,702],{"className":6203,"style":802},[618,622],[568,6205,6207],{"className":6206},[627],[568,6208,6210],{"className":6209},[631],[568,6211,6213],{"className":6212},[636],[568,6214,6216],{"className":6215,"style":1542},[640],[568,6217,6218,6221],{"style":1370},[568,6219],{"className":6220,"style":649},[648],[568,6222,6224],{"className":6223},[653,654,655,656],[568,6225,6227],{"className":6226},[618,656],[568,6228,1432],{"className":6229},[618,656],[568,6231,1489],{"className":6232},[618]," nur an den Randpunkten suchen. Es kann auch im Inneren liegen.",[1707,6235,6236],{},"Die Schranke für den tatsächlichen Fehler halten. Sie ist eine obere Grenze, der echte Fehler kann deutlich kleiner sein.",[1707,6238,6239,6240,6268],{},"Bei der Bestimmung von ",[568,6241,6243,6256],{"className":6242},[571],[568,6244,6246],{"className":6245},[575],[577,6247,6248],{"xmlns":579},[581,6249,6250,6254],{},[584,6251,6252],{},[590,6253,595],{},[597,6255,595],{"encoding":599},[568,6257,6259],{"className":6258,"ariaHidden":605},[604],[568,6260,6262,6265],{"className":6261},[609],[568,6263],{"className":6264,"style":849},[613],[568,6266,595],{"className":6267},[618,622]," abrunden. Man muss auf die nächste ganze Zahl aufrunden.",{"title":6270,"searchDepth":6271,"depth":6271,"links":6272},"",2,[6273,6274,6275],{"id":561,"depth":6271,"text":562},{"id":2661,"depth":6271,"text":2662},{"id":5814,"depth":6271,"text":5815},[6277,6280,6282,6285,6288,6291,6294,6297,6300,6303,6306,6309],{"lhs":6278,"rhs":6279},"round(sqrt(12*1e-4\u002Fexp(1)), 4)","0.021",{"lhs":6281,"rhs":3726},"ceil(1\u002Fsqrt(12*1e-4\u002Fexp(1)))",{"lhs":6283,"rhs":6284},"round(exp(1)*(1\u002F48)^2\u002F12*1e5, 2)","9.83",{"lhs":6286,"rhs":6287},"round(exp(1)*(1\u002F47)^2\u002F12*1e5, 2)","10.25",{"lhs":6289,"rhs":6290},"pi\u002F4*(sin(0)\u002F2 + sin(pi\u002F4) + sin(pi\u002F2) + sin(3*pi\u002F4) + sin(pi)\u002F2)","pi\u002F4*(1 + sqrt(2))",{"lhs":6292,"rhs":6293},"round(pi\u002F4*(1 + sqrt(2)), 4)","1.8961",{"lhs":6295,"rhs":6296},"round(2 - pi\u002F4*(1 + sqrt(2)), 4)","0.1039",{"lhs":6298,"rhs":6299},"pi*(pi\u002F4)^2\u002F12*1","pi^3\u002F192",{"lhs":6301,"rhs":6302},"round(pi^3\u002F192, 4)","0.1615",{"lhs":6304,"rhs":6305},"-((pi\u002F4)^2\u002F12)*(cos(pi) - cos(0))","pi^2\u002F96",{"lhs":6307,"rhs":6308},"round(pi^2\u002F96, 4)","0.1028",{"lhs":6310,"rhs":6311},"round((2 - pi\u002F8*(sin(pi\u002F8) + sin(pi\u002F4) + sin(3*pi\u002F8) + sin(pi\u002F2) + sin(5*pi\u002F8) + sin(3*pi\u002F4) + sin(7*pi\u002F8)))*1000, 1)","25.8","f \\text{ zweimal stetig differenzierbar auf } [a, b],\\ h = \\frac{b - a}{n}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">zweimal stetig differenzierbar auf\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo stretchy=\"false\">[\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">]\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">[a, b],\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">[\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">]\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>h\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">h = \\frac{b - a}{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:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.2251em;vertical-align:-0.345em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8801em;\">\u003Cspan style=\"top:-2.655em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.394em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">b\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">a\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:0.345em;\">\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>",null,"md","composite-trapezoidal-error","\\left| \\int_a^b f(x)\\,dx - T_n \\right| \\leq \\frac{(b - a)\\,h^2}{12} \\max_{x \\in [a, b]} |f''(x)|","\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>\u003Cmrow>\u003Cmo fence=\"true\">∣\u003C\u002Fmo>\u003Cmsubsup>\u003Cmo>∫\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmsubsup>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>T\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo fence=\"true\">∣\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmo>≤\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmsup>\u003Cmi>h\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cmn>12\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmunder>\u003Cmrow>\u003Cmi>max\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmo stretchy=\"false\">[\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">]\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmunder>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmsup>\u003Cmi>f\u003C\u002Fmi>\u003Cmrow>\u003Cmo mathvariant=\"normal\">′\u003C\u002Fmo>\u003Cmo mathvariant=\"normal\">′\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\left| \\int_a^b f(x)\\,dx - T_n \\right| \\leq \\frac{(b - a)\\,h^2}{12} \\max_{x \\in [a, b]} |f''(x)|\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:3em;vertical-align:-1.25em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen\">\u003Cspan class=\"delimsizing mult\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.75em;\">\u003Cspan style=\"top:-3.75em;\">\u003Cspan class=\"pstrut\" style=\"height:5em;\">\u003C\u002Fspan>\u003Cspan 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