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f''(\\xi)",[574,1041,1043,1144,1174],{"className":1042,"ariaHidden":603},[619],[574,1044,1046,1050,1111,1114,1117,1120,1123,1126,1129,1132,1135,1138,1141],{"className":1045},[623],[574,1047],{"className":1048,"style":1049},[627],"height:2.511em;vertical-align:-0.9119em;",[574,1051,1054,1060],{"className":1052},[1053],"mop",[574,1055,953],{"className":1056,"style":1059},[1053,1057,1058],"op-symbol","large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[574,1061,1064],{"className":1062},[1063],"msupsub",[574,1065,1067,1102],{"className":1066},[808,809],[574,1068,1070,1099],{"className":1069},[813],[574,1071,1074,1087],{"className":1072,"style":1073},[817],"height:1.599em;",[574,1075,1077,1081],{"style":1076},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[574,1078],{"className":1079,"style":1080},[825],"height:2.7em;",[574,1082,1084],{"className":1083},[830,831,832,833],[574,1085,600],{"className":1086},[636,637,833],[574,1088,1090,1093],{"style":1089},"top:-3.8129em;margin-right:0.05em;",[574,1091],{"className":1092,"style":1080},[825],[574,1094,1096],{"className":1095},[830,831,832,833],[574,1097,607],{"className":1098},[636,637,833],[574,1100,870],{"className":1101},[869],[574,1103,1105],{"className":1104},[813],[574,1106,1109],{"className":1107,"style":1108},[817],"height:0.9119em;",[574,1110],{},[574,1112],{"className":1113,"style":646},[645],[574,1115,913],{"className":1116,"style":929},[636,637],[574,1118,711],{"className":1119},[632],[574,1121,964],{"className":1122},[636,637],[574,1124,730],{"className":1125},[653],[574,1127],{"className":1128,"style":646},[645],[574,1130,973],{"className":1131},[636,637],[574,1133,964],{"className":1134},[636,637],[574,1136],{"className":1137,"style":753},[645],[574,1139,717],{"className":1140},[757],[574,1142],{"className":1143,"style":753},[645],[574,1145,1147,1150,1154,1157,1160,1163,1167,1171],{"className":1146},[623],[574,1148],{"className":1149,"style":628},[627],[574,1151,980],{"className":1152,"style":1153},[636,637],"margin-right:0.109em;",[574,1155,711],{"className":1156},[632],[574,1158,733],{"className":1159},[636,637],[574,1161,730],{"className":1162},[653],[574,1164],{"className":1165,"style":1166},[645],"margin-right:0.2778em;",[574,1168,989],{"className":1169},[1170],"mrel",[574,1172],{"className":1173,"style":1166},[645],[574,1175,1177,1181,1299,1302,1337,1340,1344],{"className":1176},[623],[574,1178],{"className":1179,"style":1180},[627],"height:2.1771em;vertical-align:-0.686em;",[574,1182,1184,1187,1296],{"className":1183},[636],[574,1185],{"className":1186},[632,801],[574,1188,1190],{"className":1189},[719],[574,1191,1193,1287],{"className":1192},[808,809],[574,1194,1196,1284],{"className":1195},[813],[574,1197,1200,1212,1220],{"className":1198,"style":1199},[817],"height:1.4911em;",[574,1201,1203,1206],{"style":1202},"top:-2.314em;",[574,1204],{"className":1205,"style":826},[825],[574,1207,1209],{"className":1208},[636],[574,1210,1015],{"className":1211},[636],[574,1213,1214,1217],{"style":842},[574,1215],{"className":1216,"style":826},[825],[574,1218],{"className":1219,"style":850},[849],[574,1221,1223,1226],{"style":1222},"top:-3.677em;",[574,1224],{"className":1225,"style":826},[825],[574,1227,1229,1232,1235,1238,1241,1244,1247,1250,1253],{"className":1228},[636],[574,1230,711],{"className":1231},[632],[574,1233,607],{"className":1234},[636,637],[574,1236],{"className":1237,"style":753},[645],[574,1239,717],{"className":1240},[757],[574,1242],{"className":1243,"style":753},[645],[574,1245,600],{"className":1246},[636,637],[574,1248,730],{"className":1249},[653],[574,1251],{"className":1252,"style":646},[645],[574,1254,1256,1259],{"className":1255},[636],[574,1257,733],{"className":1258},[636,637],[574,1260,1262],{"className":1261},[1063],[574,1263,1265],{"className":1264},[808],[574,1266,1268],{"className":1267},[813],[574,1269,1272],{"className":1270,"style":1271},[817],"height:0.8141em;",[574,1273,1275,1278],{"style":1274},"top:-3.063em;margin-right:0.05em;",[574,1276],{"className":1277,"style":1080},[825],[574,1279,1281],{"className":1280},[830,831,832,833],[574,1282,727],{"className":1283},[636,833],[574,1285,870],{"className":1286},[869],[574,1288,1290],{"className":1289},[813],[574,1291,1294],{"className":1292,"style":1293},[817],"height:0.686em;",[574,1295],{},[574,1297],{"className":1298},[653,801],[574,1300],{"className":1301,"style":646},[645],[574,1303,1305,1308],{"className":1304},[636],[574,1306,913],{"className":1307,"style":929},[636,637],[574,1309,1311],{"className":1310},[1063],[574,1312,1314],{"className":1313},[808],[574,1315,1317],{"className":1316},[813],[574,1318,1321],{"className":1319,"style":1320},[817],"height:0.8019em;",[574,1322,1324,1327],{"style":1323},"top:-3.113em;margin-right:0.05em;",[574,1325],{"className":1326,"style":1080},[825],[574,1328,1330],{"className":1329},[830,831,832,833],[574,1331,1333],{"className":1332},[636,833],[574,1334,1336],{"className":1335},[636,833],"′′",[574,1338,711],{"className":1339},[632],[574,1341,1034],{"className":1342,"style":1343},[636,637],"margin-right:0.046em;",[574,1345,730],{"className":1346},[653],[563,1348,1349,1350,1425,1426,1429,1430,1433,1434,1554],{},"für ein ",[574,1351,1353,1380],{"className":1352},[577],[574,1354,1356],{"className":1355},[581],[583,1357,1358],{"xmlns":585},[587,1359,1360,1377],{},[590,1361,1362,1364,1367,1369,1371,1373,1375],{},[598,1363,1034],{},[593,1365,1366],{},"∈",[593,1368,596],{"stretchy":595},[598,1370,600],{},[593,1372,604],{"separator":603},[598,1374,607],{},[593,1376,610],{"stretchy":595},[612,1378,1379],{"encoding":614},"\\xi \\in [a, b]",[574,1381,1383,1401],{"className":1382,"ariaHidden":603},[619],[574,1384,1386,1389,1392,1395,1398],{"className":1385},[623],[574,1387],{"className":1388,"style":925},[627],[574,1390,1034],{"className":1391,"style":1343},[636,637],[574,1393],{"className":1394,"style":1166},[645],[574,1396,1366],{"className":1397},[1170],[574,1399],{"className":1400,"style":1166},[645],[574,1402,1404,1407,1410,1413,1416,1419,1422],{"className":1403},[623],[574,1405],{"className":1406,"style":628},[627],[574,1408,596],{"className":1409},[632],[574,1411,600],{"className":1412},[636,637],[574,1414,604],{"className":1415},[641],[574,1417],{"className":1418,"style":646},[645],[574,1420,607],{"className":1421},[636,637],[574,1423,610],{"className":1424},[653],". Das ist ungefähr ",[567,1427,1428],{},"halb so groß"," wie bei der Trapezregel und hat das ",[567,1431,1432],{},"umgekehrte Vorzeichen",": Bei konvexen Funktionen unterschätzt die Mittelpunktregel, die Trapezregel überschätzt. Daher liegt der wahre Wert oft zwischen beiden, und die Kombination ",[574,1435,1437,1465],{"className":1436},[577],[574,1438,1440],{"className":1439},[581],[583,1441,1442],{"xmlns":585},[587,1443,1444,1462],{},[590,1445,1446],{},[719,1447,1448,1459],{},[590,1449,1450,1452,1454,1456],{},[722,1451,727],{},[598,1453,980],{},[593,1455,706],{},[598,1457,1458],{},"T",[722,1460,1461],{},"3",[612,1463,1464],{"encoding":614},"\\frac{2M + T}{3}",[574,1466,1468],{"className":1467,"ariaHidden":603},[619],[574,1469,1471,1475],{"className":1470},[623],[574,1472],{"className":1473,"style":1474},[627],"height:1.2173em;vertical-align:-0.345em;",[574,1476,1478,1481,1551],{"className":1477},[636],[574,1479],{"className":1480},[632,801],[574,1482,1484],{"className":1483},[719],[574,1485,1487,1543],{"className":1486},[808,809],[574,1488,1490,1540],{"className":1489},[813],[574,1491,1494,1508,1516],{"className":1492,"style":1493},[817],"height:0.8723em;",[574,1495,1496,1499],{"style":821},[574,1497],{"className":1498,"style":826},[825],[574,1500,1502],{"className":1501},[830,831,832,833],[574,1503,1505],{"className":1504},[636,833],[574,1506,1461],{"className":1507},[636,833],[574,1509,1510,1513],{"style":842},[574,1511],{"className":1512,"style":826},[825],[574,1514],{"className":1515,"style":850},[849],[574,1517,1518,1521],{"style":853},[574,1519],{"className":1520,"style":826},[825],[574,1522,1524],{"className":1523},[830,831,832,833],[574,1525,1527,1530,1533,1536],{"className":1526},[636,833],[574,1528,727],{"className":1529},[636,833],[574,1531,980],{"className":1532,"style":1153},[636,637,833],[574,1534,706],{"className":1535},[757,833],[574,1537,1458],{"className":1538,"style":1539},[636,637,833],"margin-right:0.1389em;",[574,1541,870],{"className":1542},[869],[574,1544,1546],{"className":1545},[813],[574,1547,1549],{"className":1548,"style":877},[817],[574,1550],{},[574,1552],{"className":1553},[653,801]," ergibt die Simpsonregel.",[563,1556,1557,1558,1586,1587,1836],{},"Lineare Funktionen werden exakt integriert, obwohl nur Rechtecke verwendet werden. Ein Vorteil gegenüber der Trapezregel: Die Randpunkte werden nicht ausgewertet. Deshalb funktioniert die Regel auch, wenn ",[574,1559,1561,1574],{"className":1560},[577],[574,1562,1564],{"className":1563},[581],[583,1565,1566],{"xmlns":585},[587,1567,1568,1572],{},[590,1569,1570],{},[598,1571,913],{},[612,1573,913],{"encoding":614},[574,1575,1577],{"className":1576,"ariaHidden":603},[619],[574,1578,1580,1583],{"className":1579},[623],[574,1581],{"className":1582,"style":925},[627],[574,1584,913],{"className":1585,"style":929},[636,637]," am Rand nicht definiert ist, etwa bei ",[574,1588,1590,1626],{"className":1589},[577],[574,1591,1593],{"className":1592},[581],[583,1594,1595],{"xmlns":585},[587,1596,1597,1623],{},[590,1598,1599,1608,1617,1619,1621],{},[949,1600,1601,1603,1606],{},[593,1602,953],{},[722,1604,1605],{},"0",[722,1607,724],{},[719,1609,1610,1612],{},[722,1611,724],{},[1613,1614,1615],"msqrt",{},[598,1616,964],{},[968,1618,970],{},[598,1620,973],{},[598,1622,964],{},[612,1624,1625],{"encoding":614},"\\int_0^1 \\frac{1}{\\sqrt{x}}\\,dx",[574,1627,1629],{"className":1628,"ariaHidden":603},[619],[574,1630,1632,1636,1693,1696,1827,1830,1833],{"className":1631},[623],[574,1633],{"className":1634,"style":1635},[627],"height:1.547em;vertical-align:-0.538em;",[574,1637,1639,1644],{"className":1638},[1053],[574,1640,953],{"className":1641,"style":1643},[1053,1057,1642],"small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[574,1645,1647],{"className":1646},[1063],[574,1648,1650,1684],{"className":1649},[808,809],[574,1651,1653,1681],{"className":1652},[813],[574,1654,1657,1669],{"className":1655,"style":1656},[817],"height:1.009em;",[574,1658,1660,1663],{"style":1659},"top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;",[574,1661],{"className":1662,"style":1080},[825],[574,1664,1666],{"className":1665},[830,831,832,833],[574,1667,1605],{"className":1668},[636,833],[574,1670,1672,1675],{"style":1671},"top:-3.2579em;margin-right:0.05em;",[574,1673],{"className":1674,"style":1080},[825],[574,1676,1678],{"className":1677},[830,831,832,833],[574,1679,724],{"className":1680},[636,833],[574,1682,870],{"className":1683},[869],[574,1685,1687],{"className":1686},[813],[574,1688,1691],{"className":1689,"style":1690},[817],"height:0.3558em;",[574,1692],{},[574,1694],{"className":1695,"style":646},[645],[574,1697,1699,1702,1824],{"className":1698},[636],[574,1700],{"className":1701},[632,801],[574,1703,1705],{"className":1704},[719],[574,1706,1708,1815],{"className":1707},[808,809],[574,1709,1711,1812],{"className":1710},[813],[574,1712,1714,1790,1798],{"className":1713,"style":818},[817],[574,1715,1717,1720],{"style":1716},"top:-2.6259em;",[574,1718],{"className":1719,"style":826},[825],[574,1721,1723],{"className":1722},[830,831,832,833],[574,1724,1726],{"className":1725},[636,833],[574,1727,1730],{"className":1728},[636,1729,833],"sqrt",[574,1731,1733,1781],{"className":1732},[808,809],[574,1734,1736,1778],{"className":1735},[813],[574,1737,1740,1755],{"className":1738,"style":1739},[817],"height:0.8059em;",[574,1741,1745,1748],{"className":1742,"style":1744},[1743],"svg-align","top:-3em;",[574,1746],{"className":1747,"style":826},[825],[574,1749,1752],{"className":1750,"style":1751},[636,833],"padding-left:0.833em;",[574,1753,964],{"className":1754},[636,637,833],[574,1756,1758,1761],{"style":1757},"top:-2.7659em;",[574,1759],{"className":1760,"style":826},[825],[574,1762,1766],{"className":1763,"style":1765},[1764,833],"hide-tail","min-width:0.853em;height:1.08em;",[1767,1768,1774],"svg",{"xmlns":1769,"width":1770,"height":1771,"viewBox":1772,"preserveAspectRatio":1773},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[1775,1776],"path",{"d":1777},"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",[574,1779,870],{"className":1780},[869],[574,1782,1784],{"className":1783},[813],[574,1785,1788],{"className":1786,"style":1787},[817],"height:0.2341em;",[574,1789],{},[574,1791,1792,1795],{"style":842},[574,1793],{"className":1794,"style":826},[825],[574,1796],{"className":1797,"style":850},[849],[574,1799,1800,1803],{"style":853},[574,1801],{"className":1802,"style":826},[825],[574,1804,1806],{"className":1805},[830,831,832,833],[574,1807,1809],{"className":1808},[636,833],[574,1810,724],{"className":1811},[636,833],[574,1813,870],{"className":1814},[869],[574,1816,1818],{"className":1817},[813],[574,1819,1822],{"className":1820,"style":1821},[817],"height:0.538em;",[574,1823],{},[574,1825],{"className":1826},[653,801],[574,1828],{"className":1829,"style":646},[645],[574,1831,973],{"className":1832},[636,637],[574,1834,964],{"className":1835},[636,637]," (dort allerdings mit schlechterer Genauigkeit).",[563,1838,1839,1840,895],{},"Nicht zu verwechseln ist die Mittelpunktregel mit Ober- und Untersummen oder mit Rechtecksummen, die den linken oder rechten Rand jedes Teilintervalls verwenden. Diese haben nur einen Fehler der Ordnung ",[574,1841,1843,1856],{"className":1842},[577],[574,1844,1846],{"className":1845},[581],[583,1847,1848],{"xmlns":585},[587,1849,1850,1854],{},[590,1851,1852],{},[598,1853,733],{},[612,1855,733],{"encoding":614},[574,1857,1859],{"className":1858,"ariaHidden":603},[619],[574,1860,1862,1866],{"className":1861},[623],[574,1863],{"className":1864,"style":1865},[627],"height:0.6944em;",[574,1867,733],{"className":1868},[636,637],[558,1870,1872],{"id":1871},"beispiele","Beispiele",[563,1874,1875,2104,2105,2158,2159,2222,2223,2158,2263,2158,2303,2343,2344,2384],{},[574,1876,1878,1918],{"className":1877},[577],[574,1879,1881],{"className":1880},[581],[583,1882,1883],{"xmlns":585},[587,1884,1885,1915],{},[590,1886,1887,1895,1901,1903,1905,1907,1909],{},[949,1888,1889,1891,1893],{},[593,1890,953],{},[722,1892,1605],{},[722,1894,724],{},[1007,1896,1897,1899],{},[598,1898,964],{},[722,1900,727],{},[968,1902,970],{},[598,1904,973],{},[598,1906,964],{},[593,1908,989],{},[719,1910,1911,1913],{},[722,1912,724],{},[722,1914,1461],{},[612,1916,1917],{"encoding":614},"\\int_0^1 x^2\\,dx = \\frac{1}{3}",[574,1919,1921,2029],{"className":1920,"ariaHidden":603},[619],[574,1922,1924,1928,1979,1982,2011,2014,2017,2020,2023,2026],{"className":1923},[623],[574,1925],{"className":1926,"style":1927},[627],"height:1.3648em;vertical-align:-0.3558em;",[574,1929,1931,1934],{"className":1930},[1053],[574,1932,953],{"className":1933,"style":1643},[1053,1057,1642],[574,1935,1937],{"className":1936},[1063],[574,1938,1940,1971],{"className":1939},[808,809],[574,1941,1943,1968],{"className":1942},[813],[574,1944,1946,1957],{"className":1945,"style":1656},[817],[574,1947,1948,1951],{"style":1659},[574,1949],{"className":1950,"style":1080},[825],[574,1952,1954],{"className":1953},[830,831,832,833],[574,1955,1605],{"className":1956},[636,833],[574,1958,1959,1962],{"style":1671},[574,1960],{"className":1961,"style":1080},[825],[574,1963,1965],{"className":1964},[830,831,832,833],[574,1966,724],{"className":1967},[636,833],[574,1969,870],{"className":1970},[869],[574,1972,1974],{"className":1973},[813],[574,1975,1977],{"className":1976,"style":1690},[817],[574,1978],{},[574,1980],{"className":1981,"style":646},[645],[574,1983,1985,1988],{"className":1984},[636],[574,1986,964],{"className":1987},[636,637],[574,1989,1991],{"className":1990},[1063],[574,1992,1994],{"className":1993},[808],[574,1995,1997],{"className":1996},[813],[574,1998,2000],{"className":1999,"style":1271},[817],[574,2001,2002,2005],{"style":1274},[574,2003],{"className":2004,"style":1080},[825],[574,2006,2008],{"className":2007},[830,831,832,833],[574,2009,727],{"className":2010},[636,833],[574,2012],{"className":2013,"style":646},[645],[574,2015,973],{"className":2016},[636,637],[574,2018,964],{"className":2019},[636,637],[574,2021],{"className":2022,"style":1166},[645],[574,2024,989],{"className":2025},[1170],[574,2027],{"className":2028,"style":1166},[645],[574,2030,2032,2036],{"className":2031},[623],[574,2033],{"className":2034,"style":2035},[627],"height:1.1901em;vertical-align:-0.345em;",[574,2037,2039,2042,2101],{"className":2038},[636],[574,2040],{"className":2041},[632,801],[574,2043,2045],{"className":2044},[719],[574,2046,2048,2093],{"className":2047},[808,809],[574,2049,2051,2090],{"className":2050},[813],[574,2052,2054,2068,2076],{"className":2053,"style":818},[817],[574,2055,2056,2059],{"style":821},[574,2057],{"className":2058,"style":826},[825],[574,2060,2062],{"className":2061},[830,831,832,833],[574,2063,2065],{"className":2064},[636,833],[574,2066,1461],{"className":2067},[636,833],[574,2069,2070,2073],{"style":842},[574,2071],{"className":2072,"style":826},[825],[574,2074],{"className":2075,"style":850},[849],[574,2077,2078,2081],{"style":853},[574,2079],{"className":2080,"style":826},[825],[574,2082,2084],{"className":2083},[830,831,832,833],[574,2085,2087],{"className":2086},[636,833],[574,2088,724],{"className":2089},[636,833],[574,2091,870],{"className":2092},[869],[574,2094,2096],{"className":2095},[813],[574,2097,2099],{"className":2098,"style":877},[817],[574,2100],{},[574,2102],{"className":2103},[653,801]," mit ",[574,2106,2108,2127],{"className":2107},[577],[574,2109,2111],{"className":2110},[581],[583,2112,2113],{"xmlns":585},[587,2114,2115,2124],{},[590,2116,2117,2119,2121],{},[598,2118,669],{},[593,2120,989],{},[722,2122,2123],{},"4",[612,2125,2126],{"encoding":614},"n = 4",[574,2128,2130,2148],{"className":2129,"ariaHidden":603},[619],[574,2131,2133,2136,2139,2142,2145],{"className":2132},[623],[574,2134],{"className":2135,"style":681},[627],[574,2137,669],{"className":2138},[636,637],[574,2140],{"className":2141,"style":1166},[645],[574,2143,989],{"className":2144},[1170],[574,2146],{"className":2147,"style":1166},[645],[574,2149,2151,2155],{"className":2150},[623],[574,2152],{"className":2153,"style":2154},[627],"height:0.6444em;",[574,2156,2123],{"className":2157},[636],", ",[574,2160,2162,2181],{"className":2161},[577],[574,2163,2165],{"className":2164},[581],[583,2166,2167],{"xmlns":585},[587,2168,2169,2178],{},[590,2170,2171,2173,2175],{},[598,2172,733],{},[593,2174,989],{},[722,2176,2177],{},"0,25",[612,2179,2180],{"encoding":614},"h = 0{,}25",[574,2182,2184,2202],{"className":2183,"ariaHidden":603},[619],[574,2185,2187,2190,2193,2196,2199],{"className":2186},[623],[574,2188],{"className":2189,"style":1865},[627],[574,2191,733],{"className":2192},[636,637],[574,2194],{"className":2195,"style":1166},[645],[574,2197,989],{"className":2198},[1170],[574,2200],{"className":2201,"style":1166},[645],[574,2203,2205,2209,2212,2218],{"className":2204},[623],[574,2206],{"className":2207,"style":2208},[627],"height:0.8389em;vertical-align:-0.1944em;",[574,2210,1605],{"className":2211},[636],[574,2213,2215],{"className":2214},[636],[574,2216,604],{"className":2217},[641],[574,2219,2221],{"className":2220},[636],"25",". Die Mittelpunkte sind ",[574,2224,2226,2241],{"className":2225},[577],[574,2227,2229],{"className":2228},[581],[583,2230,2231],{"xmlns":585},[587,2232,2233,2238],{},[590,2234,2235],{},[722,2236,2237],{},"0,125",[612,2239,2240],{"encoding":614},"0{,}125",[574,2242,2244],{"className":2243,"ariaHidden":603},[619],[574,2245,2247,2250,2253,2259],{"className":2246},[623],[574,2248],{"className":2249,"style":2208},[627],[574,2251,1605],{"className":2252},[636],[574,2254,2256],{"className":2255},[636],[574,2257,604],{"className":2258},[641],[574,2260,2262],{"className":2261},[636],"125",[574,2264,2266,2281],{"className":2265},[577],[574,2267,2269],{"className":2268},[581],[583,2270,2271],{"xmlns":585},[587,2272,2273,2278],{},[590,2274,2275],{},[722,2276,2277],{},"0,375",[612,2279,2280],{"encoding":614},"0{,}375",[574,2282,2284],{"className":2283,"ariaHidden":603},[619],[574,2285,2287,2290,2293,2299],{"className":2286},[623],[574,2288],{"className":2289,"style":2208},[627],[574,2291,1605],{"className":2292},[636],[574,2294,2296],{"className":2295},[636],[574,2297,604],{"className":2298},[641],[574,2300,2302],{"className":2301},[636],"375",[574,2304,2306,2321],{"className":2305},[577],[574,2307,2309],{"className":2308},[581],[583,2310,2311],{"xmlns":585},[587,2312,2313,2318],{},[590,2314,2315],{},[722,2316,2317],{},"0,625",[612,2319,2320],{"encoding":614},"0{,}625",[574,2322,2324],{"className":2323,"ariaHidden":603},[619],[574,2325,2327,2330,2333,2339],{"className":2326},[623],[574,2328],{"className":2329,"style":2208},[627],[574,2331,1605],{"className":2332},[636],[574,2334,2336],{"className":2335},[636],[574,2337,604],{"className":2338},[641],[574,2340,2342],{"className":2341},[636],"625"," und ",[574,2345,2347,2362],{"className":2346},[577],[574,2348,2350],{"className":2349},[581],[583,2351,2352],{"xmlns":585},[587,2353,2354,2359],{},[590,2355,2356],{},[722,2357,2358],{},"0,875",[612,2360,2361],{"encoding":614},"0{,}875",[574,2363,2365],{"className":2364,"ariaHidden":603},[619],[574,2366,2368,2371,2374,2380],{"className":2367},[623],[574,2369],{"className":2370,"style":2208},[627],[574,2372,1605],{"className":2373},[636],[574,2375,2377],{"className":2376},[636],[574,2378,604],{"className":2379},[641],[574,2381,2383],{"className":2382},[636],"875",":",[574,2386,2388],{"className":2387},[934],[574,2389,2391,2453],{"className":2390},[577],[574,2392,2394],{"className":2393},[581],[583,2395,2396],{"xmlns":585,"display":943},[587,2397,2398,2450],{},[590,2399,2400,2402,2404,2406,2409,2445,2447],{},[598,2401,980],{},[593,2403,989],{},[722,2405,2177],{},[593,2407,2408],{},"⋅",[590,2410,2411,2413,2419,2421,2427,2429,2435,2437,2443],{},[593,2412,711],{"fence":603},[1007,2414,2415,2417],{},[722,2416,2237],{},[722,2418,727],{},[593,2420,706],{},[1007,2422,2423,2425],{},[722,2424,2277],{},[722,2426,727],{},[593,2428,706],{},[1007,2430,2431,2433],{},[722,2432,2317],{},[722,2434,727],{},[593,2436,706],{},[1007,2438,2439,2441],{},[722,2440,2358],{},[722,2442,727],{},[593,2444,730],{"fence":603},[593,2446,989],{},[722,2448,2449],{},"0,328125",[612,2451,2452],{"encoding":614},"M = 0{,}25 \\cdot \\left( 0{,}125^2 + 0{,}375^2 + 0{,}625^2 + 0{,}875^2 \\right) = 0{,}328125",[574,2454,2456,2475,2502,2730],{"className":2455,"ariaHidden":603},[619],[574,2457,2459,2463,2466,2469,2472],{"className":2458},[623],[574,2460],{"className":2461,"style":2462},[627],"height:0.6833em;",[574,2464,980],{"className":2465,"style":1153},[636,637],[574,2467],{"className":2468,"style":1166},[645],[574,2470,989],{"className":2471},[1170],[574,2473],{"className":2474,"style":1166},[645],[574,2476,2478,2481,2484,2490,2493,2496,2499],{"className":2477},[623],[574,2479],{"className":2480,"style":2208},[627],[574,2482,1605],{"className":2483},[636],[574,2485,2487],{"className":2486},[636],[574,2488,604],{"className":2489},[641],[574,2491,2221],{"className":2492},[636],[574,2494],{"className":2495,"style":753},[645],[574,2497,2408],{"className":2498},[757],[574,2500],{"className":2501,"style":753},[645],[574,2503,2505,2509,2721,2724,2727],{"className":2504},[623],[574,2506],{"className":2507,"style":2508},[627],"height:1.2141em;vertical-align:-0.35em;",[574,2510,2512,2518,2521,2527,2531,2562,2565,2568,2571,2574,2580,2584,2613,2616,2619,2622,2625,2631,2635,2664,2667,2670,2673,2676,2682,2686,2715],{"className":2511},[771],[574,2513,2515],{"className":2514,"style":776},[632,775],[574,2516,711],{"className":2517},[780,781],[574,2519,1605],{"className":2520},[636],[574,2522,2524],{"className":2523},[636],[574,2525,604],{"className":2526},[641],[574,2528,2530],{"className":2529},[636],"12",[574,2532,2534,2538],{"className":2533},[636],[574,2535,2537],{"className":2536},[636],"5",[574,2539,2541],{"className":2540},[1063],[574,2542,2544],{"className":2543},[808],[574,2545,2547],{"className":2546},[813],[574,2548,2551],{"className":2549,"style":2550},[817],"height:0.8641em;",[574,2552,2553,2556],{"style":1323},[574,2554],{"className":2555,"style":1080},[825],[574,2557,2559],{"className":2558},[830,831,832,833],[574,2560,727],{"className":2561},[636,833],[574,2563],{"className":2564,"style":753},[645],[574,2566,706],{"className":2567},[757],[574,2569],{"className":2570,"style":753},[645],[574,2572,1605],{"className":2573},[636],[574,2575,2577],{"className":2576},[636],[574,2578,604],{"className":2579},[641],[574,2581,2583],{"className":2582},[636],"37",[574,2585,2587,2590],{"className":2586},[636],[574,2588,2537],{"className":2589},[636],[574,2591,2593],{"className":2592},[1063],[574,2594,2596],{"className":2595},[808],[574,2597,2599],{"className":2598},[813],[574,2600,2602],{"className":2601,"style":2550},[817],[574,2603,2604,2607],{"style":1323},[574,2605],{"className":2606,"style":1080},[825],[574,2608,2610],{"className":2609},[830,831,832,833],[574,2611,727],{"className":2612},[636,833],[574,2614],{"className":2615,"style":753},[645],[574,2617,706],{"className":2618},[757],[574,2620],{"className":2621,"style":753},[645],[574,2623,1605],{"className":2624},[636],[574,2626,2628],{"className":2627},[636],[574,2629,604],{"className":2630},[641],[574,2632,2634],{"className":2633},[636],"62",[574,2636,2638,2641],{"className":2637},[636],[574,2639,2537],{"className":2640},[636],[574,2642,2644],{"className":2643},[1063],[574,2645,2647],{"className":2646},[808],[574,2648,2650],{"className":2649},[813],[574,2651,2653],{"className":2652,"style":2550},[817],[574,2654,2655,2658],{"style":1323},[574,2656],{"className":2657,"style":1080},[825],[574,2659,2661],{"className":2660},[830,831,832,833],[574,2662,727],{"className":2663},[636,833],[574,2665],{"className":2666,"style":753},[645],[574,2668,706],{"className":2669},[757],[574,2671],{"className":2672,"style":753},[645],[574,2674,1605],{"className":2675},[636],[574,2677,2679],{"className":2678},[636],[574,2680,604],{"className":2681},[641],[574,2683,2685],{"className":2684},[636],"87",[574,2687,2689,2692],{"className":2688},[636],[574,2690,2537],{"className":2691},[636],[574,2693,2695],{"className":2694},[1063],[574,2696,2698],{"className":2697},[808],[574,2699,2701],{"className":2700},[813],[574,2702,2704],{"className":2703,"style":2550},[817],[574,2705,2706,2709],{"style":1323},[574,2707],{"className":2708,"style":1080},[825],[574,2710,2712],{"className":2711},[830,831,832,833],[574,2713,727],{"className":2714},[636,833],[574,2716,2718],{"className":2717,"style":776},[653,775],[574,2719,730],{"className":2720},[780,781],[574,2722],{"className":2723,"style":1166},[645],[574,2725,989],{"className":2726},[1170],[574,2728],{"className":2729,"style":1166},[645],[574,2731,2733,2736,2739,2745],{"className":2732},[623],[574,2734],{"className":2735,"style":2208},[627],[574,2737,1605],{"className":2738},[636],[574,2740,2742],{"className":2741},[636],[574,2743,604],{"className":2744},[641],[574,2746,2748],{"className":2747},[636],"328125",[563,2750,2751,2752,3007,3008,3107],{},"Der Fehler ist ",[574,2753,2755,2792],{"className":2754},[577],[574,2756,2758],{"className":2757},[581],[583,2759,2760],{"xmlns":585},[587,2761,2762,2789],{},[590,2763,2764,2770,2772,2774,2776,2783,2786],{},[719,2765,2766,2768],{},[722,2767,724],{},[722,2769,1461],{},[593,2771,717],{},[722,2773,2449],{},[593,2775,989],{},[719,2777,2778,2780],{},[722,2779,724],{},[722,2781,2782],{},"192",[593,2784,2785],{},"≈",[722,2787,2788],{},"0,0052",[612,2790,2791],{"encoding":614},"\\frac{1}{3} - 0{,}328125 = \\frac{1}{192} \\approx 0{,}0052",[574,2793,2795,2878,2905,2988],{"className":2794,"ariaHidden":603},[619],[574,2796,2798,2801,2869,2872,2875],{"className":2797},[623],[574,2799],{"className":2800,"style":2035},[627],[574,2802,2804,2807,2866],{"className":2803},[636],[574,2805],{"className":2806},[632,801],[574,2808,2810],{"className":2809},[719],[574,2811,2813,2858],{"className":2812},[808,809],[574,2814,2816,2855],{"className":2815},[813],[574,2817,2819,2833,2841],{"className":2818,"style":818},[817],[574,2820,2821,2824],{"style":821},[574,2822],{"className":2823,"style":826},[825],[574,2825,2827],{"className":2826},[830,831,832,833],[574,2828,2830],{"className":2829},[636,833],[574,2831,1461],{"className":2832},[636,833],[574,2834,2835,2838],{"style":842},[574,2836],{"className":2837,"style":826},[825],[574,2839],{"className":2840,"style":850},[849],[574,2842,2843,2846],{"style":853},[574,2844],{"className":2845,"style":826},[825],[574,2847,2849],{"className":2848},[830,831,832,833],[574,2850,2852],{"className":2851},[636,833],[574,2853,724],{"className":2854},[636,833],[574,2856,870],{"className":2857},[869],[574,2859,2861],{"className":2860},[813],[574,2862,2864],{"className":2863,"style":877},[817],[574,2865],{},[574,2867],{"className":2868},[653,801],[574,2870],{"className":2871,"style":753},[645],[574,2873,717],{"className":2874},[757],[574,2876],{"className":2877,"style":753},[645],[574,2879,2881,2884,2887,2893,2896,2899,2902],{"className":2880},[623],[574,2882],{"className":2883,"style":2208},[627],[574,2885,1605],{"className":2886},[636],[574,2888,2890],{"className":2889},[636],[574,2891,604],{"className":2892},[641],[574,2894,2748],{"className":2895},[636],[574,2897],{"className":2898,"style":1166},[645],[574,2900,989],{"className":2901},[1170],[574,2903],{"className":2904,"style":1166},[645],[574,2906,2908,2911,2979,2982,2985],{"className":2907},[623],[574,2909],{"className":2910,"style":2035},[627],[574,2912,2914,2917,2976],{"className":2913},[636],[574,2915],{"className":2916},[632,801],[574,2918,2920],{"className":2919},[719],[574,2921,2923,2968],{"className":2922},[808,809],[574,2924,2926,2965],{"className":2925},[813],[574,2927,2929,2943,2951],{"className":2928,"style":818},[817],[574,2930,2931,2934],{"style":821},[574,2932],{"className":2933,"style":826},[825],[574,2935,2937],{"className":2936},[830,831,832,833],[574,2938,2940],{"className":2939},[636,833],[574,2941,2782],{"className":2942},[636,833],[574,2944,2945,2948],{"style":842},[574,2946],{"className":2947,"style":826},[825],[574,2949],{"className":2950,"style":850},[849],[574,2952,2953,2956],{"style":853},[574,2954],{"className":2955,"style":826},[825],[574,2957,2959],{"className":2958},[830,831,832,833],[574,2960,2962],{"className":2961},[636,833],[574,2963,724],{"className":2964},[636,833],[574,2966,870],{"className":2967},[869],[574,2969,2971],{"className":2970},[813],[574,2972,2974],{"className":2973,"style":877},[817],[574,2975],{},[574,2977],{"className":2978},[653,801],[574,2980],{"className":2981,"style":1166},[645],[574,2983,2785],{"className":2984},[1170],[574,2986],{"className":2987,"style":1166},[645],[574,2989,2991,2994,2997,3003],{"className":2990},[623],[574,2992],{"className":2993,"style":2208},[627],[574,2995,1605],{"className":2996},[636],[574,2998,3000],{"className":2999},[636],[574,3001,604],{"className":3002},[641],[574,3004,3006],{"className":3005},[636],"0052",", genau halb so groß wie bei der Trapezregel mit denselben Teilintervallen (",[574,3009,3011,3030],{"className":3010},[577],[574,3012,3014],{"className":3013},[581],[583,3015,3016],{"xmlns":585},[587,3017,3018,3027],{},[590,3019,3020],{},[719,3021,3022,3024],{},[722,3023,724],{},[722,3025,3026],{},"96",[612,3028,3029],{"encoding":614},"\\frac{1}{96}",[574,3031,3033],{"className":3032,"ariaHidden":603},[619],[574,3034,3036,3039],{"className":3035},[623],[574,3037],{"className":3038,"style":2035},[627],[574,3040,3042,3045,3104],{"className":3041},[636],[574,3043],{"className":3044},[632,801],[574,3046,3048],{"className":3047},[719],[574,3049,3051,3096],{"className":3050},[808,809],[574,3052,3054,3093],{"className":3053},[813],[574,3055,3057,3071,3079],{"className":3056,"style":818},[817],[574,3058,3059,3062],{"style":821},[574,3060],{"className":3061,"style":826},[825],[574,3063,3065],{"className":3064},[830,831,832,833],[574,3066,3068],{"className":3067},[636,833],[574,3069,3026],{"className":3070},[636,833],[574,3072,3073,3076],{"style":842},[574,3074],{"className":3075,"style":826},[825],[574,3077],{"className":3078,"style":850},[849],[574,3080,3081,3084],{"style":853},[574,3082],{"className":3083,"style":826},[825],[574,3085,3087],{"className":3086},[830,831,832,833],[574,3088,3090],{"className":3089},[636,833],[574,3091,724],{"className":3092},[636,833],[574,3094,870],{"className":3095},[869],[574,3097,3099],{"className":3098},[813],[574,3100,3102],{"className":3101,"style":877},[817],[574,3103],{},[574,3105],{"className":3106},[653,801],").",[563,3109,3110,2104,3319,2158,3370,3431,3432,2343,3471,2384],{},[574,3111,3113,3155],{"className":3112},[577],[574,3114,3116],{"className":3115},[581],[583,3117,3118],{"xmlns":585},[587,3119,3120,3152],{},[590,3121,3122,3130,3136,3138,3140,3142,3144,3147,3150],{},[949,3123,3124,3126,3128],{},[593,3125,953],{},[722,3127,724],{},[722,3129,727],{},[719,3131,3132,3134],{},[722,3133,724],{},[598,3135,964],{},[968,3137,970],{},[598,3139,973],{},[598,3141,964],{},[593,3143,989],{},[598,3145,3146],{},"ln",[593,3148,3149],{},"⁡",[722,3151,727],{},[612,3153,3154],{"encoding":614},"\\int_1^2 \\frac{1}{x}\\,dx = \\ln 2",[574,3156,3158,3304],{"className":3157,"ariaHidden":603},[619],[574,3159,3161,3164,3215,3218,3286,3289,3292,3295,3298,3301],{"className":3160},[623],[574,3162],{"className":3163,"style":1927},[627],[574,3165,3167,3170],{"className":3166},[1053],[574,3168,953],{"className":3169,"style":1643},[1053,1057,1642],[574,3171,3173],{"className":3172},[1063],[574,3174,3176,3207],{"className":3175},[808,809],[574,3177,3179,3204],{"className":3178},[813],[574,3180,3182,3193],{"className":3181,"style":1656},[817],[574,3183,3184,3187],{"style":1659},[574,3185],{"className":3186,"style":1080},[825],[574,3188,3190],{"className":3189},[830,831,832,833],[574,3191,724],{"className":3192},[636,833],[574,3194,3195,3198],{"style":1671},[574,3196],{"className":3197,"style":1080},[825],[574,3199,3201],{"className":3200},[830,831,832,833],[574,3202,727],{"className":3203},[636,833],[574,3205,870],{"className":3206},[869],[574,3208,3210],{"className":3209},[813],[574,3211,3213],{"className":3212,"style":1690},[817],[574,3214],{},[574,3216],{"className":3217,"style":646},[645],[574,3219,3221,3224,3283],{"className":3220},[636],[574,3222],{"className":3223},[632,801],[574,3225,3227],{"className":3226},[719],[574,3228,3230,3275],{"className":3229},[808,809],[574,3231,3233,3272],{"className":3232},[813],[574,3234,3236,3250,3258],{"className":3235,"style":818},[817],[574,3237,3238,3241],{"style":821},[574,3239],{"className":3240,"style":826},[825],[574,3242,3244],{"className":3243},[830,831,832,833],[574,3245,3247],{"className":3246},[636,833],[574,3248,964],{"className":3249},[636,637,833],[574,3251,3252,3255],{"style":842},[574,3253],{"className":3254,"style":826},[825],[574,3256],{"className":3257,"style":850},[849],[574,3259,3260,3263],{"style":853},[574,3261],{"className":3262,"style":826},[825],[574,3264,3266],{"className":3265},[830,831,832,833],[574,3267,3269],{"className":3268},[636,833],[574,3270,724],{"className":3271},[636,833],[574,3273,870],{"className":3274},[869],[574,3276,3278],{"className":3277},[813],[574,3279,3281],{"className":3280,"style":877},[817],[574,3282],{},[574,3284],{"className":3285},[653,801],[574,3287],{"className":3288,"style":646},[645],[574,3290,973],{"className":3291},[636,637],[574,3293,964],{"className":3294},[636,637],[574,3296],{"className":3297,"style":1166},[645],[574,3299,989],{"className":3300},[1170],[574,3302],{"className":3303,"style":1166},[645],[574,3305,3307,3310,3313,3316],{"className":3306},[623],[574,3308],{"className":3309,"style":1865},[627],[574,3311,3146],{"className":3312},[1053],[574,3314],{"className":3315,"style":646},[645],[574,3317,727],{"className":3318},[636],[574,3320,3322,3340],{"className":3321},[577],[574,3323,3325],{"className":3324},[581],[583,3326,3327],{"xmlns":585},[587,3328,3329,3337],{},[590,3330,3331,3333,3335],{},[598,3332,669],{},[593,3334,989],{},[722,3336,727],{},[612,3338,3339],{"encoding":614},"n = 2",[574,3341,3343,3361],{"className":3342,"ariaHidden":603},[619],[574,3344,3346,3349,3352,3355,3358],{"className":3345},[623],[574,3347],{"className":3348,"style":681},[627],[574,3350,669],{"className":3351},[636,637],[574,3353],{"className":3354,"style":1166},[645],[574,3356,989],{"className":3357},[1170],[574,3359],{"className":3360,"style":1166},[645],[574,3362,3364,3367],{"className":3363},[623],[574,3365],{"className":3366,"style":2154},[627],[574,3368,727],{"className":3369},[636],[574,3371,3373,3392],{"className":3372},[577],[574,3374,3376],{"className":3375},[581],[583,3377,3378],{"xmlns":585},[587,3379,3380,3389],{},[590,3381,3382,3384,3386],{},[598,3383,733],{},[593,3385,989],{},[722,3387,3388],{},"0,5",[612,3390,3391],{"encoding":614},"h = 0{,}5",[574,3393,3395,3413],{"className":3394,"ariaHidden":603},[619],[574,3396,3398,3401,3404,3407,3410],{"className":3397},[623],[574,3399],{"className":3400,"style":1865},[627],[574,3402,733],{"className":3403},[636,637],[574,3405],{"className":3406,"style":1166},[645],[574,3408,989],{"className":3409},[1170],[574,3411],{"className":3412,"style":1166},[645],[574,3414,3416,3419,3422,3428],{"className":3415},[623],[574,3417],{"className":3418,"style":2208},[627],[574,3420,1605],{"className":3421},[636],[574,3423,3425],{"className":3424},[636],[574,3426,604],{"className":3427},[641],[574,3429,2537],{"className":3430},[636]," und den Mittelpunkten ",[574,3433,3435,3450],{"className":3434},[577],[574,3436,3438],{"className":3437},[581],[583,3439,3440],{"xmlns":585},[587,3441,3442,3447],{},[590,3443,3444],{},[722,3445,3446],{},"1,25",[612,3448,3449],{"encoding":614},"1{,}25",[574,3451,3453],{"className":3452,"ariaHidden":603},[619],[574,3454,3456,3459,3462,3468],{"className":3455},[623],[574,3457],{"className":3458,"style":2208},[627],[574,3460,724],{"className":3461},[636],[574,3463,3465],{"className":3464},[636],[574,3466,604],{"className":3467},[641],[574,3469,2221],{"className":3470},[636],[574,3472,3474,3489],{"className":3473},[577],[574,3475,3477],{"className":3476},[581],[583,3478,3479],{"xmlns":585},[587,3480,3481,3486],{},[590,3482,3483],{},[722,3484,3485],{},"1,75",[612,3487,3488],{"encoding":614},"1{,}75",[574,3490,3492],{"className":3491,"ariaHidden":603},[619],[574,3493,3495,3498,3501,3507],{"className":3494},[623],[574,3496],{"className":3497,"style":2208},[627],[574,3499,724],{"className":3500},[636],[574,3502,3504],{"className":3503},[636],[574,3505,604],{"className":3506},[641],[574,3508,3510],{"className":3509},[636],"75",[574,3512,3514],{"className":3513},[934],[574,3515,3517,3572],{"className":3516},[577],[574,3518,3520],{"className":3519},[581],[583,3521,3522],{"xmlns":585,"display":943},[587,3523,3524,3569],{},[590,3525,3526,3528,3530,3532,3534,3554,3556,3564,3566],{},[598,3527,980],{},[593,3529,989],{},[722,3531,3388],{},[593,3533,2408],{},[590,3535,3536,3538,3544,3546,3552],{},[593,3537,711],{"fence":603},[719,3539,3540,3542],{},[722,3541,724],{},[722,3543,3446],{},[593,3545,706],{},[719,3547,3548,3550],{},[722,3549,724],{},[722,3551,3485],{},[593,3553,730],{"fence":603},[593,3555,989],{},[719,3557,3558,3561],{},[722,3559,3560],{},"48",[722,3562,3563],{},"70",[593,3565,2785],{},[722,3567,3568],{},"0,6857",[612,3570,3571],{"encoding":614},"M = 0{,}5 \\cdot \\left( \\frac{1}{1{,}25} + \\frac{1}{1{,}75} \\right) = \\frac{48}{70} \\approx 0{,}6857",[574,3573,3575,3593,3620,3804,3882],{"className":3574,"ariaHidden":603},[619],[574,3576,3578,3581,3584,3587,3590],{"className":3577},[623],[574,3579],{"className":3580,"style":2462},[627],[574,3582,980],{"className":3583,"style":1153},[636,637],[574,3585],{"className":3586,"style":1166},[645],[574,3588,989],{"className":3589},[1170],[574,3591],{"className":3592,"style":1166},[645],[574,3594,3596,3599,3602,3608,3611,3614,3617],{"className":3595},[623],[574,3597],{"className":3598,"style":2208},[627],[574,3600,1605],{"className":3601},[636],[574,3603,3605],{"className":3604},[636],[574,3606,604],{"className":3607},[641],[574,3609,2537],{"className":3610},[636],[574,3612],{"className":3613,"style":753},[645],[574,3615,2408],{"className":3616},[757],[574,3618],{"className":3619,"style":753},[645],[574,3621,3623,3627,3795,3798,3801],{"className":3622},[623],[574,3624],{"className":3625,"style":3626},[627],"height:2.4em;vertical-align:-0.95em;",[574,3628,3630,3636,3709,3712,3715,3718,3789],{"className":3629},[771],[574,3631,3633],{"className":3632,"style":776},[632,775],[574,3634,711],{"className":3635},[780,832],[574,3637,3639,3642,3706],{"className":3638},[636],[574,3640],{"className":3641},[632,801],[574,3643,3645],{"className":3644},[719],[574,3646,3648,3697],{"className":3647},[808,809],[574,3649,3651,3694],{"className":3650},[813],[574,3652,3655,3675,3683],{"className":3653,"style":3654},[817],"height:1.3214em;",[574,3656,3657,3660],{"style":1202},[574,3658],{"className":3659,"style":826},[825],[574,3661,3663,3666,3672],{"className":3662},[636],[574,3664,724],{"className":3665},[636],[574,3667,3669],{"className":3668},[636],[574,3670,604],{"className":3671},[641],[574,3673,2221],{"className":3674},[636],[574,3676,3677,3680],{"style":842},[574,3678],{"className":3679,"style":826},[825],[574,3681],{"className":3682,"style":850},[849],[574,3684,3685,3688],{"style":1222},[574,3686],{"className":3687,"style":826},[825],[574,3689,3691],{"className":3690},[636],[574,3692,724],{"className":3693},[636],[574,3695,870],{"className":3696},[869],[574,3698,3700],{"className":3699},[813],[574,3701,3704],{"className":3702,"style":3703},[817],"height:0.8804em;",[574,3705],{},[574,3707],{"className":3708},[653,801],[574,3710],{"className":3711,"style":753},[645],[574,3713,706],{"className":3714},[757],[574,3716],{"className":3717,"style":753},[645],[574,3719,3721,3724,3786],{"className":3720},[636],[574,3722],{"className":3723},[632,801],[574,3725,3727],{"className":3726},[719],[574,3728,3730,3778],{"className":3729},[808,809],[574,3731,3733,3775],{"className":3732},[813],[574,3734,3736,3756,3764],{"className":3735,"style":3654},[817],[574,3737,3738,3741],{"style":1202},[574,3739],{"className":3740,"style":826},[825],[574,3742,3744,3747,3753],{"className":3743},[636],[574,3745,724],{"className":3746},[636],[574,3748,3750],{"className":3749},[636],[574,3751,604],{"className":3752},[641],[574,3754,3510],{"className":3755},[636],[574,3757,3758,3761],{"style":842},[574,3759],{"className":3760,"style":826},[825],[574,3762],{"className":3763,"style":850},[849],[574,3765,3766,3769],{"style":1222},[574,3767],{"className":3768,"style":826},[825],[574,3770,3772],{"className":3771},[636],[574,3773,724],{"className":3774},[636],[574,3776,870],{"className":3777},[869],[574,3779,3781],{"className":3780},[813],[574,3782,3784],{"className":3783,"style":3703},[817],[574,3785],{},[574,3787],{"className":3788},[653,801],[574,3790,3792],{"className":3791,"style":776},[653,775],[574,3793,730],{"className":3794},[780,832],[574,3796],{"className":3797,"style":1166},[645],[574,3799,989],{"className":3800},[1170],[574,3802],{"className":3803,"style":1166},[645],[574,3805,3807,3811,3873,3876,3879],{"className":3806},[623],[574,3808],{"className":3809,"style":3810},[627],"height:2.0074em;vertical-align:-0.686em;",[574,3812,3814,3817,3870],{"className":3813},[636],[574,3815],{"className":3816},[632,801],[574,3818,3820],{"className":3819},[719],[574,3821,3823,3862],{"className":3822},[808,809],[574,3824,3826,3859],{"className":3825},[813],[574,3827,3829,3840,3848],{"className":3828,"style":3654},[817],[574,3830,3831,3834],{"style":1202},[574,3832],{"className":3833,"style":826},[825],[574,3835,3837],{"className":3836},[636],[574,3838,3563],{"className":3839},[636],[574,3841,3842,3845],{"style":842},[574,3843],{"className":3844,"style":826},[825],[574,3846],{"className":3847,"style":850},[849],[574,3849,3850,3853],{"style":1222},[574,3851],{"className":3852,"style":826},[825],[574,3854,3856],{"className":3855},[636],[574,3857,3560],{"className":3858},[636],[574,3860,870],{"className":3861},[869],[574,3863,3865],{"className":3864},[813],[574,3866,3868],{"className":3867,"style":1293},[817],[574,3869],{},[574,3871],{"className":3872},[653,801],[574,3874],{"className":3875,"style":1166},[645],[574,3877,2785],{"className":3878},[1170],[574,3880],{"className":3881,"style":1166},[645],[574,3883,3885,3888,3891,3897],{"className":3884},[623],[574,3886],{"className":3887,"style":2208},[627],[574,3889,1605],{"className":3890},[636],[574,3892,3894],{"className":3893},[636],[574,3895,604],{"className":3896},[641],[574,3898,3900],{"className":3899},[636],"6857",[563,3902,3903,3904,895],{},"Der Fehler ist etwa ",[574,3905,3907,3922],{"className":3906},[577],[574,3908,3910],{"className":3909},[581],[583,3911,3912],{"xmlns":585},[587,3913,3914,3919],{},[590,3915,3916],{},[722,3917,3918],{},"0,0074",[612,3920,3921],{"encoding":614},"0{,}0074",[574,3923,3925],{"className":3924,"ariaHidden":603},[619],[574,3926,3928,3931,3934,3940],{"className":3927},[623],[574,3929],{"className":3930,"style":2208},[627],[574,3932,1605],{"className":3933},[636],[574,3935,3937],{"className":3936},[636],[574,3938,604],{"className":3939},[641],[574,3941,3943],{"className":3942},[636],"0074",[558,3945,3947],{"id":3946},"typische-fehler","Typische Fehler",[3949,3950,3951,3955,4132],"ul",{},[3952,3953,3954],"li",{},"Die Funktion am linken oder rechten Rand statt in der Mitte auswerten. Dann sinkt die Genauigkeit deutlich.",[3952,3956,3957,3958,4080,4081,895],{},"Die Mittelpunkte falsch berechnen: Der erste liegt bei ",[574,3959,3961,3983],{"className":3960},[577],[574,3962,3964],{"className":3963},[581],[583,3965,3966],{"xmlns":585},[587,3967,3968,3980],{},[590,3969,3970,3972,3974],{},[598,3971,600],{},[593,3973,706],{},[719,3975,3976,3978],{},[598,3977,733],{},[722,3979,727],{},[612,3981,3982],{"encoding":614},"a + \\frac{h}{2}",[574,3984,3986,4004],{"className":3985,"ariaHidden":603},[619],[574,3987,3989,3992,3995,3998,4001],{"className":3988},[623],[574,3990],{"className":3991,"style":746},[627],[574,3993,600],{"className":3994},[636,637],[574,3996],{"className":3997,"style":753},[645],[574,3999,706],{"className":4000},[757],[574,4002],{"className":4003,"style":753},[645],[574,4005,4007,4011],{"className":4006},[623],[574,4008],{"className":4009,"style":4010},[627],"height:1.2251em;vertical-align:-0.345em;",[574,4012,4014,4017,4077],{"className":4013},[636],[574,4015],{"className":4016},[632,801],[574,4018,4020],{"className":4019},[719],[574,4021,4023,4069],{"className":4022},[808,809],[574,4024,4026,4066],{"className":4025},[813],[574,4027,4030,4044,4052],{"className":4028,"style":4029},[817],"height:0.8801em;",[574,4031,4032,4035],{"style":821},[574,4033],{"className":4034,"style":826},[825],[574,4036,4038],{"className":4037},[830,831,832,833],[574,4039,4041],{"className":4040},[636,833],[574,4042,727],{"className":4043},[636,833],[574,4045,4046,4049],{"style":842},[574,4047],{"className":4048,"style":826},[825],[574,4050],{"className":4051,"style":850},[849],[574,4053,4054,4057],{"style":853},[574,4055],{"className":4056,"style":826},[825],[574,4058,4060],{"className":4059},[830,831,832,833],[574,4061,4063],{"className":4062},[636,833],[574,4064,733],{"className":4065},[636,637,833],[574,4067,870],{"className":4068},[869],[574,4070,4072],{"className":4071},[813],[574,4073,4075],{"className":4074,"style":877},[817],[574,4076],{},[574,4078],{"className":4079},[653,801],", nicht bei ",[574,4082,4084,4102],{"className":4083},[577],[574,4085,4087],{"className":4086},[581],[583,4088,4089],{"xmlns":585},[587,4090,4091,4099],{},[590,4092,4093,4095,4097],{},[598,4094,600],{},[593,4096,706],{},[598,4098,733],{},[612,4100,4101],{"encoding":614},"a + h",[574,4103,4105,4123],{"className":4104,"ariaHidden":603},[619],[574,4106,4108,4111,4114,4117,4120],{"className":4107},[623],[574,4109],{"className":4110,"style":746},[627],[574,4112,600],{"className":4113},[636,637],[574,4115],{"className":4116,"style":753},[645],[574,4118,706],{"className":4119},[757],[574,4121],{"className":4122,"style":753},[645],[574,4124,4126,4129],{"className":4125},[623],[574,4127],{"className":4128,"style":1865},[627],[574,4130,733],{"className":4131},[636,637],[3952,4133,4134,4135,4163],{},"Mit ",[574,4136,4138,4151],{"className":4137},[577],[574,4139,4141],{"className":4140},[581],[583,4142,4143],{"xmlns":585},[587,4144,4145,4149],{},[590,4146,4147],{},[598,4148,733],{},[612,4150,733],{"encoding":614},[574,4152,4154],{"className":4153,"ariaHidden":603},[619],[574,4155,4157,4160],{"className":4156},[623],[574,4158],{"className":4159,"style":1865},[627],[574,4161,733],{"className":4162},[636,637]," multiplizieren vergessen und nur die Funktionswerte addieren.",{"title":4165,"searchDepth":4166,"depth":4166,"links":4167},"",2,[4168,4169,4170],{"id":560,"depth":4166,"text":561},{"id":1871,"depth":4166,"text":1872},{"id":3946,"depth":4166,"text":3947},[4172,4175,4178,4181,4183,4186,4188,4191,4194],{"lhs":4173,"rhs":4174},"(b - a)*(m*(a + b)\u002F2 + k)","m*(b^2 - a^2)\u002F2 + k*(b - a)",{"lhs":4176,"rhs":4177},"0.25*(0.125^2 + 0.375^2 + 0.625^2 + 0.875^2)","0.328125",{"lhs":4179,"rhs":4180},"1\u002F3 - 0.328125","1\u002F192",{"lhs":4182,"rhs":4180},"(1 - 0)*0.25^2\u002F24*2",{"lhs":4184,"rhs":4185},"round(1\u002F192, 4)","0.0052",{"lhs":4187,"rhs":727},"(1\u002F96)\u002F(1\u002F192)",{"lhs":4189,"rhs":4190},"0.5*(1\u002F1.25 + 1\u002F1.75)","48\u002F70",{"lhs":4192,"rhs":4193},"round(48\u002F70, 4)","0.6857",{"lhs":4195,"rhs":4196},"round(log(2) - 48\u002F70, 4)","0.0074","h = \\frac{b - a}{n},\\ n \\in \\mathbb{N},\\ n \\geq 1","\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>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\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>\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>n\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">N\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\in \\mathbb{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:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">N\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>n\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\geq 1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","midpoint-rule","\\int_a^b f(x)\\,dx \\approx h \\sum_{k=1}^{n} f\\!\\left( a + \\left(k - \\tfrac{1}{2}\\right) h \\right)","\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>\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>\u003Cmi>h\u003C\u002Fmi>\u003Cmunderover>\u003Cmo>∑\u003C\u002Fmo>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmunderover>\u003Cmi>f\u003C\u002Fmi>\u003Cmtext> ⁣\u003C\u002Fmtext>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003C\u002Fmstyle>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmi>h\u003C\u002Fmi>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\int_a^b f(x)\\,dx \\approx h \\sum_{k=1}^{n} f\\!\\left( a + \\left(k - \\tfrac{1}{2}\\right) h \\right)\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:2.511em;vertical-align:-0.9119em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">∫\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.599em;\">\u003Cspan style=\"top:-1.7881em;margin-left:-0.4445em;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\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8129em;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\">b\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:0.9119em;\">\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 mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.9535em;vertical-align:-1.3021em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.6514em;\">\u003Cspan style=\"top:-1.8479em;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\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">=\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\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\" style=\"height:1.3021em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:-0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\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=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\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=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8451em;\">\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 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