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\\frac{1}{x^p}\\,dx",[594,1079,1081],{"className":1080,"ariaHidden":624},[623],[594,1082,1084,1088,1143,1146,1250,1253,1256],{"className":1083},[628],[594,1085],{"className":1086,"style":1087},[632],"height:1.2151em;vertical-align:-0.3558em;",[594,1089,1091,1094],{"className":1090},[754],[594,1092,658],{"className":1093,"style":760},[754,758,759],[594,1095,1097],{"className":1096},[764],[594,1098,1100,1135],{"className":1099},[768,769],[594,1101,1103,1132],{"className":1102},[773],[594,1104,1107,1118],{"className":1105,"style":1106},[777],"height:0.8593em;",[594,1108,1109,1112],{"style":781},[594,1110],{"className":1111,"style":786},[785],[594,1113,1115],{"className":1114},[790,791,792,793],[594,1116,1053],{"className":1117},[637,793],[594,1119,1120,1123],{"style":799},[594,1121],{"className":1122,"style":786},[785],[594,1124,1126],{"className":1125},[790,791,792,793],[594,1127,1129],{"className":1128},[637,793],[594,1130,1057],{"className":1131},[637,793],[594,1133,813],{"className":1134},[812],[594,1136,1138],{"className":1137},[773],[594,1139,1141],{"className":1140,"style":820},[777],[594,1142],{},[594,1144],{"className":1145,"style":827},[826],[594,1147,1149,1153,1247],{"className":1148},[637],[594,1150],{"className":1151},[835,1152],"nulldelimiter",[594,1154,1156],{"className":1155},[1059],[594,1157,1159,1238],{"className":1158},[768,769],[594,1160,1162,1235],{"className":1161},[773],[594,1163,1166,1209,1220],{"className":1164,"style":1165},[777],"height:0.8451em;",[594,1167,1169,1173],{"style":1168},"top:-2.655em;",[594,1170],{"className":1171,"style":1172},[785],"height:3em;",[594,1174,1176],{"className":1175},[790,791,792,793],[594,1177,1179],{"className":1178},[637,793],[594,1180,1182,1185],{"className":1181},[637,793],[594,1183,673],{"className":1184},[637,638,793],[594,1186,1188],{"className":1187},[764],[594,1189,1191],{"className":1190},[768],[594,1192,1194],{"className":1193},[773],[594,1195,1198],{"className":1196,"style":1197},[777],"height:0.5935em;",[594,1199,1200,1203],{"style":927},[594,1201],{"className":1202,"style":931},[785],[594,1204,1206],{"className":1205},[790,935,936,793],[594,1207,564],{"className":1208},[637,638,793],[594,1210,1212,1215],{"style":1211},"top:-3.23em;",[594,1213],{"className":1214,"style":1172},[785],[594,1216],{"className":1217,"style":1219},[1218],"frac-line","border-bottom-width:0.04em;",[594,1221,1223,1226],{"style":1222},"top:-3.394em;",[594,1224],{"className":1225,"style":1172},[785],[594,1227,1229],{"className":1228},[790,791,792,793],[594,1230,1232],{"className":1231},[637,793],[594,1233,1053],{"className":1234},[637,793],[594,1236,813],{"className":1237},[812],[594,1239,1241],{"className":1240},[773],[594,1242,1245],{"className":1243,"style":1244},[777],"height:0.345em;",[594,1246],{},[594,1248],{"className":1249},[842,1152],[594,1251],{"className":1252,"style":827},[826],[594,1254,683],{"className":1255},[637,638],[594,1257,673],{"className":1258},[637,638]," genau für ",[594,1261,1263,1282],{"className":1262},[597],[594,1264,1266],{"className":1265},[601],[603,1267,1268],{"xmlns":605},[607,1269,1270,1279],{},[610,1271,1272,1274,1277],{},[613,1273,564],{},[656,1275,1276],{},">",[1051,1278,1053],{},[617,1280,1281],{"encoding":619},"p > 1",[594,1283,1285,1304],{"className":1284,"ariaHidden":624},[623],[594,1286,1288,1292,1295,1298,1301],{"className":1287},[628],[594,1289],{"className":1290,"style":1291},[632],"height:0.7335em;vertical-align:-0.1944em;",[594,1293,564],{"className":1294},[637,638],[594,1296],{"className":1297,"style":855},[826],[594,1299,1276],{"className":1300},[859],[594,1302],{"className":1303,"style":855},[826],[594,1305,1307,1311],{"className":1306},[628],[594,1308],{"className":1309,"style":1310},[632],"height:0.6444em;",[594,1312,1053],{"className":1313},[637]," und hat dann den Wert ",[594,1316,1318,1343],{"className":1317},[597],[594,1319,1321],{"className":1320},[601],[603,1322,1323],{"xmlns":605},[607,1324,1325,1340],{},[610,1326,1327],{},[1059,1328,1329,1331],{},[1051,1330,1053],{},[610,1332,1333,1335,1338],{},[613,1334,564],{},[656,1336,1337],{},"−",[1051,1339,1053],{},[617,1341,1342],{"encoding":619},"\\frac{1}{p - 1}",[594,1344,1346],{"className":1345,"ariaHidden":624},[623],[594,1347,1349,1353],{"className":1348},[628],[594,1350],{"className":1351,"style":1352},[632],"height:1.3262em;vertical-align:-0.4811em;",[594,1354,1356,1359,1425],{"className":1355},[637],[594,1357],{"className":1358},[835,1152],[594,1360,1362],{"className":1361},[1059],[594,1363,1365,1416],{"className":1364},[768,769],[594,1366,1368,1413],{"className":1367},[773],[594,1369,1371,1391,1399],{"className":1370,"style":1165},[777],[594,1372,1373,1376],{"style":1168},[594,1374],{"className":1375,"style":1172},[785],[594,1377,1379],{"className":1378},[790,791,792,793],[594,1380,1382,1385,1388],{"className":1381},[637,793],[594,1383,564],{"className":1384},[637,638,793],[594,1386,1337],{"className":1387},[940,793],[594,1389,1053],{"className":1390},[637,793],[594,1392,1393,1396],{"style":1211},[594,1394],{"className":1395,"style":1172},[785],[594,1397],{"className":1398,"style":1219},[1218],[594,1400,1401,1404],{"style":1222},[594,1402],{"className":1403,"style":1172},[785],[594,1405,1407],{"className":1406},[790,791,792,793],[594,1408,1410],{"className":1409},[637,793],[594,1411,1053],{"className":1412},[637,793],[594,1414,813],{"className":1415},[812],[594,1417,1419],{"className":1418},[773],[594,1420,1423],{"className":1421,"style":1422},[777],"height:0.4811em;",[594,1424],{},[594,1426],{"className":1427},[842,1152],". Für ",[594,1430,1432,1451],{"className":1431},[597],[594,1433,1435],{"className":1434},[601],[603,1436,1437],{"xmlns":605},[607,1438,1439,1448],{},[610,1440,1441,1443,1446],{},[613,1442,564],{},[656,1444,1445],{},"≤",[1051,1447,1053],{},[617,1449,1450],{"encoding":619},"p \\leq 1",[594,1452,1454,1473],{"className":1453,"ariaHidden":624},[623],[594,1455,1457,1461,1464,1467,1470],{"className":1456},[628],[594,1458],{"className":1459,"style":1460},[632],"height:0.8304em;vertical-align:-0.1944em;",[594,1462,564],{"className":1463},[637,638],[594,1465],{"className":1466,"style":855},[826],[594,1468,1445],{"className":1469},[859],[594,1471],{"className":1472,"style":855},[826],[594,1474,1476,1479],{"className":1475},[628],[594,1477],{"className":1478,"style":1310},[632],[594,1480,1053],{"className":1481},[637]," divergiert es. Zum Beispiel ist ",[594,1484,1486,1505],{"className":1485},[597],[594,1487,1489],{"className":1488},[601],[603,1490,1491],{"xmlns":605},[607,1492,1493,1502],{},[610,1494,1495,1497,1499],{},[613,1496,564],{},[656,1498,688],{},[1051,1500,1501],{},"3",[617,1503,1504],{"encoding":619},"p = 3",[594,1506,1508,1527],{"className":1507,"ariaHidden":624},[623],[594,1509,1511,1515,1518,1521,1524],{"className":1510},[628],[594,1512],{"className":1513,"style":1514},[632],"height:0.625em;vertical-align:-0.1944em;",[594,1516,564],{"className":1517},[637,638],[594,1519],{"className":1520,"style":855},[826],[594,1522,688],{"className":1523},[859],[594,1525],{"className":1526,"style":855},[826],[594,1528,1530,1533],{"className":1529},[628],[594,1531],{"className":1532,"style":1310},[632],[594,1534,1501],{"className":1535},[637]," konvergent mit Wert ",[594,1538,1540,1559],{"className":1539},[597],[594,1541,1543],{"className":1542},[601],[603,1544,1545],{"xmlns":605},[607,1546,1547,1556],{},[610,1548,1549],{},[1059,1550,1551,1553],{},[1051,1552,1053],{},[1051,1554,1555],{},"2",[617,1557,1558],{"encoding":619},"\\frac{1}{2}",[594,1560,1562],{"className":1561,"ariaHidden":624},[623],[594,1563,1565,1569],{"className":1564},[628],[594,1566],{"className":1567,"style":1568},[632],"height:1.1901em;vertical-align:-0.345em;",[594,1570,1572,1575,1634],{"className":1571},[637],[594,1573],{"className":1574},[835,1152],[594,1576,1578],{"className":1577},[1059],[594,1579,1581,1626],{"className":1580},[768,769],[594,1582,1584,1623],{"className":1583},[773],[594,1585,1587,1601,1609],{"className":1586,"style":1165},[777],[594,1588,1589,1592],{"style":1168},[594,1590],{"className":1591,"style":1172},[785],[594,1593,1595],{"className":1594},[790,791,792,793],[594,1596,1598],{"className":1597},[637,793],[594,1599,1555],{"className":1600},[637,793],[594,1602,1603,1606],{"style":1211},[594,1604],{"className":1605,"style":1172},[785],[594,1607],{"className":1608,"style":1219},[1218],[594,1610,1611,1614],{"style":1222},[594,1612],{"className":1613,"style":1172},[785],[594,1615,1617],{"className":1616},[790,791,792,793],[594,1618,1620],{"className":1619},[637,793],[594,1621,1053],{"className":1622},[637,793],[594,1624,813],{"className":1625},[812],[594,1627,1629],{"className":1628},[773],[594,1630,1632],{"className":1631,"style":1244},[777],[594,1633],{},[594,1635],{"className":1636},[842,1152],", ",[594,1639,1641,1660],{"className":1640},[597],[594,1642,1644],{"className":1643},[601],[603,1645,1646],{"xmlns":605},[607,1647,1648,1657],{},[610,1649,1650,1652,1654],{},[613,1651,564],{},[656,1653,688],{},[1051,1655,1656],{},"1,5",[617,1658,1659],{"encoding":619},"p = 1{,}5",[594,1661,1663,1681],{"className":1662,"ariaHidden":624},[623],[594,1664,1666,1669,1672,1675,1678],{"className":1665},[628],[594,1667],{"className":1668,"style":1514},[632],[594,1670,564],{"className":1671},[637,638],[594,1673],{"className":1674,"style":855},[826],[594,1676,688],{"className":1677},[859],[594,1679],{"className":1680,"style":855},[826],[594,1682,1684,1688,1691,1699],{"className":1683},[628],[594,1685],{"className":1686,"style":1687},[632],"height:0.8389em;vertical-align:-0.1944em;",[594,1689,1053],{"className":1690},[637],[594,1692,1694],{"className":1693},[637],[594,1695,1698],{"className":1696},[1697],"mpunct",",",[594,1700,1702],{"className":1701},[637],"5"," mit Wert ",[594,1705,1707,1720],{"className":1706},[597],[594,1708,1710],{"className":1709},[601],[603,1711,1712],{"xmlns":605},[607,1713,1714,1718],{},[610,1715,1716],{},[1051,1717,1555],{},[617,1719,1555],{"encoding":619},[594,1721,1723],{"className":1722,"ariaHidden":624},[623],[594,1724,1726,1729],{"className":1725},[628],[594,1727],{"className":1728,"style":1310},[632],[594,1730,1555],{"className":1731},[637],". Bei der Polstelle in ",[594,1734,1736,1750],{"className":1735},[597],[594,1737,1739],{"className":1738},[601],[603,1740,1741],{"xmlns":605},[607,1742,1743,1748],{},[610,1744,1745],{},[1051,1746,1747],{},"0",[617,1749,1747],{"encoding":619},[594,1751,1753],{"className":1752,"ariaHidden":624},[623],[594,1754,1756,1759],{"className":1755},[628],[594,1757],{"className":1758,"style":1310},[632],[594,1760,1747],{"className":1761},[637]," ist es umgekehrt: ",[594,1764,1766,1802],{"className":1765},[597],[594,1767,1769],{"className":1768},[601],[603,1770,1771],{"xmlns":605},[607,1772,1773,1799],{},[610,1774,1775,1783,1793,1795,1797],{},[653,1776,1777,1779,1781],{},[656,1778,658],{},[1051,1780,1747],{},[1051,1782,1053],{},[1059,1784,1785,1787],{},[1051,1786,1053],{},[709,1788,1789,1791],{},[613,1790,673],{},[613,1792,564],{},[678,1794,680],{},[613,1796,683],{},[613,1798,673],{},[617,1800,1801],{"encoding":619},"\\int_0^1 \\frac{1}{x^p}\\,dx",[594,1803,1805],{"className":1804,"ariaHidden":624},[623],[594,1806,1808,1812,1864,1867,1961,1964,1967],{"className":1807},[628],[594,1809],{"className":1810,"style":1811},[632],"height:1.3648em;vertical-align:-0.3558em;",[594,1813,1815,1818],{"className":1814},[754],[594,1816,658],{"className":1817,"style":760},[754,758,759],[594,1819,1821],{"className":1820},[764],[594,1822,1824,1856],{"className":1823},[768,769],[594,1825,1827,1853],{"className":1826},[773],[594,1828,1831,1842],{"className":1829,"style":1830},[777],"height:1.009em;",[594,1832,1833,1836],{"style":781},[594,1834],{"className":1835,"style":786},[785],[594,1837,1839],{"className":1838},[790,791,792,793],[594,1840,1747],{"className":1841},[637,793],[594,1843,1844,1847],{"style":799},[594,1845],{"className":1846,"style":786},[785],[594,1848,1850],{"className":1849},[790,791,792,793],[594,1851,1053],{"className":1852},[637,793],[594,1854,813],{"className":1855},[812],[594,1857,1859],{"className":1858},[773],[594,1860,1862],{"className":1861,"style":820},[777],[594,1863],{},[594,1865],{"className":1866,"style":827},[826],[594,1868,1870,1873,1958],{"className":1869},[637],[594,1871],{"className":1872},[835,1152],[594,1874,1876],{"className":1875},[1059],[594,1877,1879,1950],{"className":1878},[768,769],[594,1880,1882,1947],{"className":1881},[773],[594,1883,1885,1925,1933],{"className":1884,"style":1165},[777],[594,1886,1887,1890],{"style":1168},[594,1888],{"className":1889,"style":1172},[785],[594,1891,1893],{"className":1892},[790,791,792,793],[594,1894,1896],{"className":1895},[637,793],[594,1897,1899,1902],{"className":1898},[637,793],[594,1900,673],{"className":1901},[637,638,793],[594,1903,1905],{"className":1904},[764],[594,1906,1908],{"className":1907},[768],[594,1909,1911],{"className":1910},[773],[594,1912,1914],{"className":1913,"style":1197},[777],[594,1915,1916,1919],{"style":927},[594,1917],{"className":1918,"style":931},[785],[594,1920,1922],{"className":1921},[790,935,936,793],[594,1923,564],{"className":1924},[637,638,793],[594,1926,1927,1930],{"style":1211},[594,1928],{"className":1929,"style":1172},[785],[594,1931],{"className":1932,"style":1219},[1218],[594,1934,1935,1938],{"style":1222},[594,1936],{"className":1937,"style":1172},[785],[594,1939,1941],{"className":1940},[790,791,792,793],[594,1942,1944],{"className":1943},[637,793],[594,1945,1053],{"className":1946},[637,793],[594,1948,813],{"className":1949},[812],[594,1951,1953],{"className":1952},[773],[594,1954,1956],{"className":1955,"style":1244},[777],[594,1957],{},[594,1959],{"className":1960},[842,1152],[594,1962],{"className":1963,"style":827},[826],[594,1965,683],{"className":1966},[637,638],[594,1968,673],{"className":1969},[637,638]," konvergiert genau für ",[594,1972,1974,1993],{"className":1973},[597],[594,1975,1977],{"className":1976},[601],[603,1978,1979],{"xmlns":605},[607,1980,1981,1990],{},[610,1982,1983,1985,1988],{},[613,1984,564],{},[656,1986,1987],{},"\u003C",[1051,1989,1053],{},[617,1991,1992],{"encoding":619},"p \u003C 1",[594,1994,1996,2014],{"className":1995,"ariaHidden":624},[623],[594,1997,1999,2002,2005,2008,2011],{"className":1998},[628],[594,2000],{"className":2001,"style":1291},[632],[594,2003,564],{"className":2004},[637,638],[594,2006],{"className":2007,"style":855},[826],[594,2009,1987],{"className":2010},[859],[594,2012],{"className":2013,"style":855},[826],[594,2015,2017,2020],{"className":2016},[628],[594,2018],{"className":2019,"style":1310},[632],[594,2021,1053],{"className":2022},[637]," und hat den Wert ",[594,2025,2027,2051],{"className":2026},[597],[594,2028,2030],{"className":2029},[601],[603,2031,2032],{"xmlns":605},[607,2033,2034,2048],{},[610,2035,2036],{},[1059,2037,2038,2040],{},[1051,2039,1053],{},[610,2041,2042,2044,2046],{},[1051,2043,1053],{},[656,2045,1337],{},[613,2047,564],{},[617,2049,2050],{"encoding":619},"\\frac{1}{1 - p}",[594,2052,2054],{"className":2053,"ariaHidden":624},[623],[594,2055,2057,2060],{"className":2056},[628],[594,2058],{"className":2059,"style":1352},[632],[594,2061,2063,2066,2131],{"className":2062},[637],[594,2064],{"className":2065},[835,1152],[594,2067,2069],{"className":2068},[1059],[594,2070,2072,2123],{"className":2071},[768,769],[594,2073,2075,2120],{"className":2074},[773],[594,2076,2078,2098,2106],{"className":2077,"style":1165},[777],[594,2079,2080,2083],{"style":1168},[594,2081],{"className":2082,"style":1172},[785],[594,2084,2086],{"className":2085},[790,791,792,793],[594,2087,2089,2092,2095],{"className":2088},[637,793],[594,2090,1053],{"className":2091},[637,793],[594,2093,1337],{"className":2094},[940,793],[594,2096,564],{"className":2097},[637,638,793],[594,2099,2100,2103],{"style":1211},[594,2101],{"className":2102,"style":1172},[785],[594,2104],{"className":2105,"style":1219},[1218],[594,2107,2108,2111],{"style":1222},[594,2109],{"className":2110,"style":1172},[785],[594,2112,2114],{"className":2113},[790,791,792,793],[594,2115,2117],{"className":2116},[637,793],[594,2118,1053],{"className":2119},[637,793],[594,2121,813],{"className":2122},[812],[594,2124,2126],{"className":2125},[773],[594,2127,2129],{"className":2128,"style":1422},[777],[594,2130],{},[594,2132],{"className":2133},[842,1152],[559,2135,2137],{"id":2136},"beispiele","Beispiele",[594,2139,2142],{"className":2140},[2141],"katex-display",[594,2143,2145,2261],{"className":2144},[597],[594,2146,2148],{"className":2147},[601],[603,2149,2151],{"xmlns":605,"display":2150},"block",[607,2152,2153,2258],{},[610,2154,2155,2163,2173,2175,2177,2179,2181,2198,2220,2222,2238,2254,2256],{},[653,2156,2157,2159,2161],{},[656,2158,658],{},[1051,2160,1053],{},[613,2162,1057],{"mathvariant":1056},[1059,2164,2165,2167],{},[1051,2166,1053],{},[709,2168,2169,2171],{},[613,2170,673],{},[1051,2172,1555],{},[678,2174,680],{},[613,2176,683],{},[613,2178,673],{},[656,2180,688],{},[2182,2183,2184,2190],"munder",{},[610,2185,2186,2188],{},[613,2187,696],{},[656,2189,699],{},[610,2191,2192,2194,2196],{},[613,2193,663],{},[656,2195,707],{},[613,2197,1057],{"mathvariant":1056},[653,2199,2200,2216,2218],{},[610,2201,2202,2205,2207,2213],{},[656,2203,2204],{"fence":624},"[",[656,2206,1337],{},[1059,2208,2209,2211],{},[1051,2210,1053],{},[613,2212,673],{},[656,2214,2215],{"fence":624},"]",[1051,2217,1053],{},[613,2219,663],{},[656,2221,688],{},[2182,2223,2224,2230],{},[610,2225,2226,2228],{},[613,2227,696],{},[656,2229,699],{},[610,2231,2232,2234,2236],{},[613,2233,663],{},[656,2235,707],{},[613,2237,1057],{"mathvariant":1056},[610,2239,2240,2242,2244,2246,2252],{},[656,2241,670],{"fence":624},[1051,2243,1053],{},[656,2245,1337],{},[1059,2247,2248,2250],{},[1051,2249,1053],{},[613,2251,663],{},[656,2253,676],{"fence":624},[656,2255,688],{},[1051,2257,1053],{},[617,2259,2260],{"encoding":619},"\\int_1^{\\infty} \\frac{1}{x^2}\\,dx = \\lim_{b \\to \\infty} \\left[-\\frac{1}{x}\\right]_1^b = \\lim_{b \\to \\infty} \\left(1 - \\frac{1}{b}\\right) = 1",[594,2262,2264,2446,2659,2821],{"className":2263,"ariaHidden":624},[623],[594,2265,2267,2271,2331,2334,2428,2431,2434,2437,2440,2443],{"className":2266},[628],[594,2268],{"className":2269,"style":2270},[632],"height:2.3262em;vertical-align:-0.9119em;",[594,2272,2274,2279],{"className":2273},[754],[594,2275,658],{"className":2276,"style":2278},[754,758,2277],"large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[594,2280,2282],{"className":2281},[764],[594,2283,2285,2322],{"className":2284},[768,769],[594,2286,2288,2319],{"className":2287},[773],[594,2289,2292,2304],{"className":2290,"style":2291},[777],"height:1.4143em;",[594,2293,2295,2298],{"style":2294},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[594,2296],{"className":2297,"style":786},[785],[594,2299,2301],{"className":2300},[790,791,792,793],[594,2302,1053],{"className":2303},[637,793],[594,2305,2307,2310],{"style":2306},"top:-3.8129em;margin-right:0.05em;",[594,2308],{"className":2309,"style":786},[785],[594,2311,2313],{"className":2312},[790,791,792,793],[594,2314,2316],{"className":2315},[637,793],[594,2317,1057],{"className":2318},[637,793],[594,2320,813],{"className":2321},[812],[594,2323,2325],{"className":2324},[773],[594,2326,2329],{"className":2327,"style":2328},[777],"height:0.9119em;",[594,2330],{},[594,2332],{"className":2333,"style":827},[826],[594,2335,2337,2340,2425],{"className":2336},[637],[594,2338],{"className":2339},[835,1152],[594,2341,2343],{"className":2342},[1059],[594,2344,2346,2416],{"className":2345},[768,769],[594,2347,2349,2413],{"className":2348},[773],[594,2350,2353,2393,2401],{"className":2351,"style":2352},[777],"height:1.3214em;",[594,2354,2356,2359],{"style":2355},"top:-2.314em;",[594,2357],{"className":2358,"style":1172},[785],[594,2360,2362],{"className":2361},[637],[594,2363,2365,2368],{"className":2364},[637],[594,2366,673],{"className":2367},[637,638],[594,2369,2371],{"className":2370},[764],[594,2372,2374],{"className":2373},[768],[594,2375,2377],{"className":2376},[773],[594,2378,2381],{"className":2379,"style":2380},[777],"height:0.7401em;",[594,2382,2384,2387],{"style":2383},"top:-2.989em;margin-right:0.05em;",[594,2385],{"className":2386,"style":786},[785],[594,2388,2390],{"className":2389},[790,791,792,793],[594,2391,1555],{"className":2392},[637,793],[594,2394,2395,2398],{"style":1211},[594,2396],{"className":2397,"style":1172},[785],[594,2399],{"className":2400,"style":1219},[1218],[594,2402,2404,2407],{"style":2403},"top:-3.677em;",[594,2405],{"className":2406,"style":1172},[785],[594,2408,2410],{"className":2409},[637],[594,2411,1053],{"className":2412},[637],[594,2414,813],{"className":2415},[812],[594,2417,2419],{"className":2418},[773],[594,2420,2423],{"className":2421,"style":2422},[777],"height:0.686em;",[594,2424],{},[594,2426],{"className":2427},[842,1152],[594,2429],{"className":2430,"style":827},[826],[594,2432,683],{"className":2433},[637,638],[594,2435,673],{"className":2436},[637,638],[594,2438],{"className":2439,"style":855},[826],[594,2441,688],{"className":2442},[859],[594,2444],{"className":2445,"style":855},[826],[594,2447,2449,2453,2511,2514,2650,2653,2656],{"className":2448},[628],[594,2450],{"className":2451,"style":2452},[632],"height:2.6887em;vertical-align:-0.9997em;",[594,2454,2457],{"className":2455},[754,2456],"op-limits",[594,2458,2460,2502],{"className":2459},[768,769],[594,2461,2463,2499],{"className":2462},[773],[594,2464,2467,2488],{"className":2465,"style":2466},[777],"height:0.6944em;",[594,2468,2470,2473],{"style":2469},"top:-2.3479em;margin-left:0em;",[594,2471],{"className":2472,"style":1172},[785],[594,2474,2476],{"className":2475},[790,791,792,793],[594,2477,2479,2482,2485],{"className":2478},[637,793],[594,2480,663],{"className":2481},[637,638,793],[594,2483,707],{"className":2484},[859,793],[594,2486,1057],{"className":2487},[637,793],[594,2489,2491,2494],{"style":2490},"top:-3em;",[594,2492],{"className":2493,"style":1172},[785],[594,2495,2496],{},[594,2497,696],{"className":2498},[754],[594,2500,813],{"className":2501},[812],[594,2503,2505],{"className":2504},[773],[594,2506,2509],{"className":2507,"style":2508},[777],"height:0.7521em;",[594,2510],{},[594,2512],{"className":2513,"style":827},[826],[594,2515,2518,2601],{"className":2516},[2517],"minner",[594,2519,2521,2530,2533,2595],{"className":2520},[2517],[594,2522,2526],{"className":2523,"style":2525},[835,2524],"delimcenter","top:0em;",[594,2527,2204],{"className":2528},[2529,792],"delimsizing",[594,2531,1337],{"className":2532},[637],[594,2534,2536,2539,2592],{"className":2535},[637],[594,2537],{"className":2538},[835,1152],[594,2540,2542],{"className":2541},[1059],[594,2543,2545,2584],{"className":2544},[768,769],[594,2546,2548,2581],{"className":2547},[773],[594,2549,2551,2562,2570],{"className":2550,"style":2352},[777],[594,2552,2553,2556],{"style":2355},[594,2554],{"className":2555,"style":1172},[785],[594,2557,2559],{"className":2558},[637],[594,2560,673],{"className"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e^{-x}\\,dx = \\lim_{b \\to \\infty} \\left[-e^{-x}\\right]_0^b = \\lim_{b \\to \\infty} \\left(1 - e^{-b}\\right) = 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Integral von 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divergiert, obwohl der Graph sich der ",[594,3502,3504,3517],{"className":3503},[597],[594,3505,3507],{"className":3506},[601],[603,3508,3509],{"xmlns":605},[607,3510,3511,3515],{},[610,3512,3513],{},[613,3514,673],{},[617,3516,673],{"encoding":619},[594,3518,3520],{"className":3519,"ariaHidden":624},[623],[594,3521,3523,3526],{"className":3522},[628],[594,3524],{"className":3525,"style":633},[632],[594,3527,673],{"className":3528},[637,638],"-Achse nähert:",[594,3531,3533],{"className":3532},[2141],[594,3534,3536,3605],{"className":3535},[597],[594,3537,3539],{"className":3538},[601],[603,3540,3541],{"xmlns":605,"display":2150},[607,3542,3543,3602],{},[610,3544,3545,3553,3559,3561,3563,3565,3567,3570,3572,3574,3576,3578,3581,3596,3598,3600],{},[653,3546,3547,3549,3551],{},[656,3548,658],{},[1051,3550,1053],{},[613,3552,663],{},[1059,3554,3555,3557],{},[1051,3556,1053],{},[613,3558,673],{},[678,3560,680],{},[613,3562,683],{},[613,3564,673],{},[656,3566,688],{},[613,3568,3569],{},"ln",[656,3571,699],{},[613,3573,663],{},[656,3575,707],{},[613,3577,1057],{"mathvariant":1056},[826,3579],{"width":3580},"1em",[610,3582,3583,3585,3593],{},[678,3584,666],{},[3586,3587,3588,3590],"mover",{"accent":624},[678,3589,704],{},[656,3591,3592],{},"¨",[678,3594,3595],{},"r ",[613,3597,663],{},[656,3599,707],{},[613,3601,1057],{"mathvariant":1056},[617,3603,3604],{"encoding":619},"\\int_1^{b} \\frac{1}{x}\\,dx = \\ln b \\to \\infty \\quad \\text{für } b \\to \\infty",[594,3606,3608,3753,3777,3847],{"className":3607,"ariaHidden":624},[623],[594,3609,3611,3615,3670,3673,3735,3738,3741,3744,3747,3750],{"className":3610},[628],[594,3612],{"className":3613,"style":3614},[632],"height:2.511em;vertical-align:-0.9119em;",[594,3616,3618,3621],{"className":3617},[754],[594,3619,658],{"className":3620,"style":2278},[754,758,2277],[594,3622,3624],{"className":3623},[764],[594,3625,3627,3662],{"className":3626},[768,769],[594,3628,3630,3659],{"className":3629},[773],[594,3631,3634,3645],{"className":3632,"style":3633},[777],"height:1.599em;",[594,3635,3636,3639],{"style":2294},[594,3637],{"className":3638,"style":786},[785],[594,3640,3642],{"className":3641},[790,791,792,793],[594,3643,1053],{"className":3644},[637,793],[594,3646,3647,3650],{"style":2306},[594,3648],{"className":3649,"style":786},[785],[594,3651,3653],{"className":3652},[790,791,792,793],[594,3654,3656],{"className":3655},[637,793],[594,3657,663],{"className":3658},[637,638,793],[594,3660,813],{"className":3661},[812],[594,3663,3665],{"className":3664},[773],[594,3666,3668],{"className":3667,"style":2328},[777],[594,3669],{},[594,3671],{"className":3672,"style":827},[826],[594,3674,3676,3679,3732],{"className":3675},[637],[594,3677],{"className":3678},[835,1152],[594,3680,3682],{"className":3681},[1059],[594,3683,3685,3724],{"className":3684},[768,769],[594,3686,3688,3721],{"className":3687},[773],[594,3689,3691,3702,3710],{"className":3690,"style":2352},[777],[594,3692,3693,3696],{"style":2355},[594,3694],{"className":3695,"style":1172},[785],[594,3697,3699],{"className":3698},[637],[594,3700,673],{"className":3701},[637,638],[594,3703,3704,3707],{"style":1211},[594,3705],{"className":3706,"style":1172},[785],[594,3708],{"className":3709,"style":1219},[1218],[594,3711,3712,3715],{"style":2403},[594,3713],{"className":3714,"style":1172},[785],[594,3716,3718],{"className":3717},[637],[594,3719,1053],{"className":3720},[637],[594,3722,813],{"className":3723},[812],[594,3725,3727],{"className":3726},[773],[594,3728,3730],{"className":3729,"style":2422},[777],[594,3731],{},[594,3733],{"className":3734},[842,1152],[594,3736],{"className":3737,"style":827},[826],[594,3739,683],{"className":3740},[637,638],[594,3742,673],{"className":3743},[637,638],[594,3745],{"className":3746,"style":855},[826],[594,3748,688],{"className":3749},[859],[594,3751],{"className":3752,"style":855},[826],[594,3754,3756,3759,3762,3765,3768,3771,3774],{"className":3755},[628],[594,3757],{"className":3758,"style":2466},[632],[594,3760,3569],{"className":3761},[754],[594,3763],{"className":3764,"style":827},[826],[594,3766,663],{"className":3767},[637,638],[594,3769],{"className":3770,"style":855},[826],[594,3772,707],{"className":3773},[859],[594,3775],{"className":3776,"style":855},[826],[594,3778,3780,3783,3786,3790,3835,3838,3841,3844],{"className":3779},[628],[594,3781],{"className":3782,"style":2466},[632],[594,3784,1057],{"className":3785},[637],[594,3787],{"className":3788,"style":3789},[826],"margin-right:1em;",[594,3791,3794,3797,3832],{"className":3792},[637,3793],"text",[594,3795,666],{"className":3796},[637],[594,3798,3801],{"className":3799},[637,3800],"accent",[594,3802,3804],{"className":3803},[768],[594,3805,3807],{"className":3806},[773],[594,3808,3811,3819],{"className":3809,"style":3810},[777],"height:0.6679em;",[594,3812,3813,3816],{"style":2490},[594,3814],{"className":3815,"style":1172},[785],[594,3817,704],{"className":3818},[637],[594,3820,3821,3824],{"style":2490},[594,3822],{"className":3823,"style":1172},[785],[594,3825,3829],{"className":3826,"style":3828},[3827],"accent-body","left:-0.25em;",[594,3830,3592],{"className":3831},[637],[594,3833,3595],{"className":3834},[637],[594,3836,663],{"className":3837},[637,638],[594,3839],{"className":3840,"style":855},[826],[594,3842,707],{"className":3843},[859],[594,3845],{"className":3846,"style":855},[826],[594,3848,3850,3853],{"className":3849},[628],[594,3851],{"className":3852,"style":633},[632],[594,3854,1057],{"className":3855},[637],[564,3857,3858,3859,3911,3912,3986],{},"Schon für ",[594,3860,3862,3881],{"className":3861},[597],[594,3863,3865],{"className":3864},[601],[603,3866,3867],{"xmlns":605},[607,3868,3869,3878],{},[610,3870,3871,3873,3875],{},[613,3872,663],{},[656,3874,688],{},[1051,3876,3877],{},"1000",[617,3879,3880],{"encoding":619},"b = 1000",[594,3882,3884,3902],{"className":3883,"ariaHidden":624},[623],[594,3885,3887,3890,3893,3896,3899],{"className":3886},[628],[594,3888],{"className":3889,"style":2466},[632],[594,3891,663],{"className":3892},[637,638],[594,3894],{"className":3895,"style":855},[826],[594,3897,688],{"className":3898},[859],[594,3900],{"className":3901,"style":855},[826],[594,3903,3905,3908],{"className":3904},[628],[594,3906],{"className":3907,"style":1310},[632],[594,3909,3877],{"className":3910},[637]," ist ",[594,3913,3915,3939],{"className":3914},[597],[594,3916,3918],{"className":3917},[601],[603,3919,3920],{"xmlns":605},[607,3921,3922,3936],{},[610,3923,3924,3926,3928,3930,3933],{},[613,3925,3569],{},[656,3927,699],{},[1051,3929,3877],{},[656,3931,3932],{},"≈",[1051,3934,3935],{},"6,91",[617,3937,3938],{"encoding":619},"\\ln 1000 \\approx 6{,}91",[594,3940,3942,3966],{"className":3941,"ariaHidden":624},[623],[594,3943,3945,3948,3951,3954,3957,3960,3963],{"className":3944},[628],[594,3946],{"className":3947,"style":2466},[632],[594,3949,3569],{"className":3950},[754],[594,3952],{"className":3953,"style":827},[826],[594,3955,3877],{"className":3956},[637],[594,3958],{"className":3959,"style":855},[826],[594,3961,3932],{"className":3962},[859],[594,3964],{"className":3965,"style":855},[826],[594,3967,3969,3972,3976,3982],{"className":3968},[628],[594,3970],{"className":3971,"style":1687},[632],[594,3973,3975],{"className":3974},[637],"6",[594,3977,3979],{"className":3978},[637],[594,3980,1698],{"className":3981},[1697],[594,3983,3985],{"className":3984},[637],"91",", und der Wert wächst unbeschränkt weiter.",[564,3988,3989],{},"Eine Polstelle an der unteren Grenze:",[594,3991,3993],{"className":3992},[2141],[594,3994,3996,4113],{"className":3995},[597],[594,3997,3999],{"className":3998},[601],[603,4000,4001],{"xmlns":605,"display":2150},[607,4002,4003,4110],{},[610,4004,4005,4013,4022,4024,4026,4028,4030,4050,4068,4070,4090,4106,4108],{},[653,4006,4007,4009,4011],{},[656,4008,658],{},[1051,4010,1747],{},[1051,4012,1053],{},[1059,4014,4015,4017],{},[1051,4016,1053],{},[4018,4019,4020],"msqrt",{},[613,4021,673],{},[678,4023,680],{},[613,4025,683],{},[613,4027,673],{},[656,4029,688],{},[2182,4031,4032,4038],{},[610,4033,4034,4036],{},[613,4035,696],{},[656,4037,699],{},[610,4039,4040,4042,4044],{},[613,4041,704],{},[656,4043,707],{},[709,4045,4046,4048],{},[1051,4047,1747],{},[656,4049,715],{},[653,4051,4052,4064,4066],{},[610,4053,4054,4056,4058,4062],{},[656,4055,2204],{"fence":624},[1051,4057,1555],{},[4018,4059,4060],{},[613,4061,673],{},[656,4063,2215],{"fence":624},[613,4065,704],{},[1051,4067,1053],{},[656,4069,688],{},[2182,4071,4072,4078],{},[610,4073,4074,4076],{},[613,4075,696],{},[656,4077,699],{},[610,4079,4080,4082,4084],{},[613,4081,704],{},[656,4083,707],{},[709,4085,4086,4088],{},[1051,4087,1747],{},[656,4089,715],{},[610,4091,4092,4094,4096,4098,4100,4104],{},[656,4093,670],{"fence":624},[1051,4095,1555],{},[656,4097,1337],{},[1051,4099,1555],{},[4018,4101,4102],{},[613,4103,704],{},[656,4105,676],{"fence":624},[656,4107,688],{},[1051,4109,1555],{},[617,4111,4112],{"encoding":619},"\\int_0^1 \\frac{1}{\\sqrt{x}}\\,dx = \\lim_{u \\to 0^+} \\left[2\\sqrt{x}\\right]_u^1 = \\lim_{u \\to 0^+} \\left(2 - 2\\sqrt{u}\\right) = 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Fehler",[573,4726,4727,4759,4928],{},[576,4728,4729,4758],{},[594,4730,4732,4746],{"className":4731},[597],[594,4733,4735],{"className":4734},[601],[603,4736,4737],{"xmlns":605},[607,4738,4739,4743],{},[610,4740,4741],{},[613,4742,1057],{"mathvariant":1056},[617,4744,4745],{"encoding":619},"\\infty",[594,4747,4749],{"className":4748,"ariaHidden":624},[623],[594,4750,4752,4755],{"className":4751},[628],[594,4753],{"className":4754,"style":633},[632],[594,4756,1057],{"className":4757},[637]," wie eine Zahl in die Stammfunktion einsetzen. Richtig ist, mit einer Variablen zu rechnen und den Grenzwert zu bilden.",[576,4760,4761,4762,4829,4830,4927],{},"Annehmen, dass das Integral konvergiert, weil ",[594,4763,4765,4789],{"className":4764},[597],[594,4766,4768],{"className":4767},[601],[603,4769,4770],{"xmlns":605},[607,4771,4772,4786],{},[610,4773,4774,4776,4778,4780,4782,4784],{},[613,4775,666],{},[656,4777,670],{"stretchy":669},[613,4779,673],{},[656,4781,676],{"stretchy":669},[656,4783,707],{},[1051,4785,1747],{},[617,4787,4788],{"encoding":619},"f(x) \\to 0",[594,4790,4792,4820],{"className":4791,"ariaHidden":624},[623],[594,4793,4795,4799,4802,4805,4808,4811,4814,4817],{"className":4794},[628],[594,4796],{"className":4797,"style":4798},[632],"height:1em;vertical-align:-0.25em;",[594,4800,666],{"className":4801,"style":831},[637,638],[594,4803,670],{"className":4804},[835],[594,4806,673],{"className":4807},[637,638],[594,4809,676],{"className":4810},[842],[594,4812],{"className":4813,"style":855},[826],[594,4815,707],{"className":4816},[859],[594,4818],{"className":4819,"style":855},[826],[594,4821,4823,4826],{"className":4822},[628],[594,4824],{"className":4825,"style":1310},[632],[594,4827,1747],{"className":4828},[637]," geht. Das Beispiel ",[594,4831,4833,4850],{"className":4832},[597],[594,4834,4836],{"className":4835},[601],[603,4837,4838],{"xmlns":605},[607,4839,4840,4848],{},[610,4841,4842],{},[1059,4843,4844,4846],{},[1051,4845,1053],{},[613,4847,673],{},[617,4849,3422],{"encoding":619},[594,4851,4853],{"className":4852,"ariaHidden":624},[623],[594,4854,4856,4859],{"className":4855},[628],[594,4857],{"className":4858,"style":1568},[632],[594,4860,4862,4865,4924],{"className":4861},[637],[594,4863],{"className":4864},[835,1152],[594,4866,4868],{"className":4867},[1059],[594,4869,4871,4916],{"className":4870},[768,769],[594,4872,4874,4913],{"className":4873},[773],[594,4875,4877,4891,4899],{"className":4876,"style":1165},[777],[594,4878,4879,4882],{"style":1168},[594,4880],{"className":4881,"style":1172},[785],[594,4883,4885],{"className":4884},[790,791,792,793],[594,4886,4888],{"className":4887},[637,793],[594,4889,673],{"className":4890},[637,638,793],[594,4892,4893,4896],{"style":1211},[594,4894],{"className":4895,"style":1172},[785],[594,4897],{"className":4898,"style":1219},[1218],[594,4900,4901,4904],{"style":1222},[594,4902],{"className":4903,"style":1172},[785],[594,4905,4907],{"className":4906},[790,791,792,793],[594,4908,4910],{"className":4909},[637,793],[594,4911,1053],{"className":4912},[637,793],[594,4914,813],{"className":4915},[812],[594,4917,4919],{"className":4918},[773],[594,4920,4922],{"className":4921,"style":1244},[777],[594,4923],{},[594,4925],{"className":4926},[842,1152]," zeigt, dass das nicht reicht.",[576,4929,4930,4931,3911,5366,5369],{},"Eine Polstelle im Inneren übersehen: ",[594,4932,4934,5006],{"className":4933},[597],[594,4935,4937],{"className":4936},[601],[603,4938,4939],{"xmlns":605},[607,4940,4941,5003],{},[610,4942,4943,4955,4965,4967,4969,4971,4973,4997,4999,5001],{},[653,4944,4945,4947,4953],{},[656,4946,658],{},[610,4948,4949,4951],{},[656,4950,1337],{},[1051,4952,1053],{},[1051,4954,1053],{},[1059,4956,4957,4959],{},[1051,4958,1053],{},[709,4960,4961,4963],{},[613,4962,673],{},[1051,4964,1555],{},[678,4966,680],{},[613,4968,683],{},[613,4970,673],{},[656,4972,688],{},[653,4974,4975,4989,4995],{},[610,4976,4977,4979,4981,4987],{},[656,4978,2204],{"fence":624},[656,4980,1337],{},[1059,4982,4983,4985],{},[1051,4984,1053],{},[613,4986,673],{},[656,4988,2215],{"fence":624},[610,4990,4991,4993],{},[656,4992,1337],{},[1051,4994,1053],{},[1051,4996,1053],{},[656,4998,688],{},[656,5000,1337],{},[1051,5002,1555],{},[617,5004,5005],{"encoding":619},"\\int_{-1}^{1} \\frac{1}{x^2}\\,dx = \\left[-\\frac{1}{x}\\right]_{-1}^{1} = 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Der Integrand ist positiv, das Integral divergiert.",{"title":5371,"searchDepth":5372,"depth":5372,"links":5373},"",2,[5374,5375,5376],{"id":561,"depth":5372,"text":562},{"id":2136,"depth":5372,"text":2137},{"id":4723,"depth":5372,"text":4724},[5378,5381,5384,5387,5390,5393,5396,5401,5404,5407,5412,5416],{"lhs":5379,"rhs":5380},"-1\u002Fb - (-1\u002F1)","1 - 1\u002Fb",{"lhs":5382,"rhs":5383},"round(sum(map(0:999, f(k) = 1 \u002F (1 + (k + 0.5) * 9 \u002F 1000)^2)) * 9 \u002F 1000, 4)","1 - 1\u002F10",{"lhs":5385,"rhs":5386},"-exp(-b) - (-exp(0))","1 - exp(-b)",{"lhs":5388,"rhs":5389},"log(b) - log(1)","log(b)",{"lhs":5391,"rhs":5392},"round(log(1000), 2)","6.91",{"lhs":5394,"rhs":5395},"2*sqrt(1) - 2*sqrt(u)","2 - 2*sqrt(u)",{"lhs":5397,"rhs":5398,"where":5399},"1\u002F(p - 1)","1\u002F2",{"p":5400},3,{"lhs":5397,"rhs":1555,"where":5402},{"p":5403},1.5,{"lhs":5405,"rhs":5406},"round(sum(map(0:999, f(k) = (1 + (k + 0.5) * 9 \u002F 1000)^(-3))) * 9 \u002F 1000, 4)","round((1 - 10^(-2)) 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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>",{"symbol":615,"meaning":5490,"symbolHtml":5491},"feste untere Grenze","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation 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style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","pek0pkGIN8FDRebeqCYo7OelaJ6roJOJR5GDJsr2kMI",[5497,5500,5503,5506],{"stem":5498,"title":5499,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fhauptsatz-der-differential-und-integralrechnung","Hauptsatz der Differential- und Integralrechnung",{"stem":5501,"title":5502,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fintegral-e-funktion","Integral der e-Funktion",{"stem":5504,"title":5505,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fintegral-von-1-durch-x","Integral von 1\u002Fx",{"stem":5507,"title":5508,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fstammfunktion-potenzfunktion","Stammfunktion einer Potenzfunktion",1793824284204]