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Man erhält sie auch, indem man die Sinusreihe gliedweise ableitet.",[564,850,851,852,880],{},"Wichtige Näherungen für kleine ",[572,853,855,868],{"className":854},[575],[572,856,858],{"className":857},[579],[581,859,860],{"xmlns":583},[585,861,862,866],{},[588,863,864],{},[591,865,832],{},[599,867,832],{"encoding":601},[572,869,871],{"className":870,"ariaHidden":607},[606],[572,872,874,877],{"className":873},[611],[572,875],{"className":876,"style":616},[615],[572,878,832],{"className":879},[653,847],":",[882,883,884,1292],"ul",{},[885,886,887,1108,1109,1291],"li",{},[572,888,890,928],{"className":889},[575],[572,891,893],{"className":892},[579],[581,894,895],{"xmlns":583},[585,896,897,925],{},[588,898,899,901,903,905,908,910,912],{},[591,900,593],{},[595,902,597],{},[591,904,832],{},[595,906,907],{},"≈",[635,909,698],{},[595,911,708],{},[913,914,915,923],"mfrac",{},[916,917,918,920],"msup",{},[591,919,832],{},[635,921,922],{},"2",[635,924,922],{},[599,926,927],{"encoding":601},"\\cos x \\approx 1 - 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\\cos x \\approx \\frac{x^2}{2}",[572,1147,1149,1167,1191],{"className":1148,"ariaHidden":607},[606],[572,1150,1152,1155,1158,1161,1164],{"className":1151},[611],[572,1153],{"className":1154,"style":964},[615],[572,1156,698],{"className":1157},[653],[572,1159],{"className":1160,"style":971},[743],[572,1162,708],{"className":1163},[975],[572,1165],{"className":1166,"style":971},[743],[572,1168,1170,1173,1176,1179,1182,1185,1188],{"className":1169},[611],[572,1171],{"className":1172,"style":937},[615],[572,1174,593],{"className":1175},[620],[572,1177],{"className":1178,"style":744},[743],[572,1180,832],{"className":1181},[653,847],[572,1183],{"className":1184,"style":950},[743],[572,1186,907],{"className":1187},[954],[572,1189],{"className":1190,"style":950},[743],[572,1192,1194,1197],{"className":1193},[611],[572,1195],{"className":1196,"style":985},[615],[572,1198,1200,1203,1288],{"className":1199},[653],[572,1201],{"className":1202},[992,993],[572,1204,1206],{"className":1205},[913],[572,1207,1209,1280],{"className":1208},[1000,1001],[572,1210,1212,1277],{"className":1211},[1005],[572,1213,1215,1229,1237],{"className":1214,"style":1010},[1009],[572,1216,1217,1220],{"style":1013},[572,1218],{"className":1219,"style":1018},[1017],[572,1221,1223],{"className":1222},[1022,1023,1024,1025],[572,1224,1226],{"className":1225},[653,1025],[572,1227,922],{"className":1228},[653,1025],[572,1230,1231,1234],{"style":1034},[572,1232],{"className":1233,"style":1018},[1017],[572,1235],{"className":1236,"style":1042},[1041],[572,1238,1239,1242],{"style":1045},[572,1240],{"className":1241,"style":1018},[1017],[572,1243,1245],{"className":1244},[1022,1023,1024,1025],[572,1246,1248],{"className":1247},[653,1025],[572,1249,1251,1254],{"className":1250},[653,1025],[572,1252,832],{"className":1253},[653,847,1025],[572,1255,1257],{"className":1256},[1064],[572,1258,1260],{"className":1259},[1000],[572,1261,1263],{"className":1262},[1005],[572,1264,1266],{"className":1265,"style":1074},[1009],[572,1267,1268,1271],{"style":1077},[572,1269],{"className":1270,"style":1081},[1017],[572,1272,1274],{"className":1273},[1022,1085,1086,1025],[572,1275,922],{"className":1276},[653,1025],[572,1278,1094],{"className":1279},[1093],[572,1281,1283],{"className":1282},[1005],[572,1284,1286],{"className":1285,"style":1101},[1009],[572,1287],{},[572,1289],{"className":1290},[1107,993],".",[885,1293,1294,1295,1554,1555,1606,1607],{},"Daraus folgt der Grenzwert ",[572,1296,1298,1339],{"className":1297},[575],[572,1299,1301],{"className":1300},[579],[581,1302,1303],{"xmlns":583},[585,1304,1305,1336],{},[588,1306,1307,1327,1330],{},[913,1308,1309,1321],{},[588,1310,1311,1313,1315,1317,1319],{},[635,1312,698],{},[595,1314,708],{},[591,1316,593],{},[595,1318,597],{},[591,1320,832],{},[916,1322,1323,1325],{},[591,1324,832],{},[635,1326,922],{},[595,1328,1329],{},"→",[913,1331,1332,1334],{},[635,1333,698],{},[635,1335,922],{},[599,1337,1338],{"encoding":601},"\\frac{1 - \\cos x}{x^2} \\to \\frac{1}{2}",[572,1340,1342,1480],{"className":1341,"ariaHidden":607},[606],[572,1343,1345,1349,1471,1474,1477],{"className":1344},[611],[572,1346],{"className":1347,"style":1348},[615],"height:1.1901em;vertical-align:-0.345em;",[572,1350,1352,1355,1468],{"className":1351},[653],[572,1353],{"className":1354},[992,993],[572,1356,1358],{"className":1357},[913],[572,1359,1361,1460],{"className":1360},[1000,1001],[572,1362,1364,1457],{"className":1363},[1005],[572,1365,1368,1410,1418],{"className":1366,"style":1367},[1009],"height:0.8451em;",[572,1369,1370,1373],{"style":1013},[572,1371],{"className":1372,"style":1018},[1017],[572,1374,1376],{"className":1375},[1022,1023,1024,1025],[572,1377,1379],{"className":1378},[653,1025],[572,1380,1382,1385],{"className":1381},[653,1025],[572,1383,832],{"className":1384},[653,847,1025],[572,1386,1388],{"className":1387},[1064],[572,1389,1391],{"className":1390},[1000],[572,1392,1394],{"className":1393},[1005],[572,1395,1398],{"className":1396,"style":1397},[1009],"height:0.7463em;",[572,1399,1401,1404],{"style":1400},"top:-2.786em;margin-right:0.0714em;",[572,1402],{"className":1403,"style":1081},[1017],[572,1405,1407],{"className":1406},[1022,1085,1086,1025],[572,1408,922],{"className":1409},[653,1025],[572,1411,1412,1415],{"style":1034},[572,1413],{"className":1414,"style":1018},[1017],[572,1416],{"className":1417,"style":1042},[1041],[572,1419,1420,1423],{"style":1045},[572,1421],{"className":1422,"style":1018},[1017],[572,1424,1426],{"className":1425},[1022,1023,1024,1025],[572,1427,1429,1432,1435,1450,1454],{"className":1428},[653,1025],[572,1430,698],{"className":1431},[653,1025],[572,1433,708],{"className":1434},[975,1025],[572,1436,1438,1442,1446],{"className":1437},[620,1025],[572,1439,1441],{"className":1440},[1025],"c",[572,1443,1445],{"className":1444},[1025],"o",[572,1447,1449],{"className":1448},[1025],"s",[572,1451],{"className":1452,"style":1453},[743,1025],"margin-right:0.1952em;",[572,1455,832],{"className":1456},[653,847,1025],[572,1458,1094],{"className":1459},[1093],[572,1461,1463],{"className":1462},[1005],[572,1464,1466],{"className":1465,"style":1101},[1009],[572,1467],{},[572,1469],{"className":1470},[1107,993],[572,1472],{"className":1473,"style":950},[743],[572,1475,1329],{"className":1476},[954],[572,1478],{"className":1479,"style":950},[743],[572,1481,1483,1486],{"className":1482},[611],[572,1484],{"className":1485,"style":1348},[615],[572,1487,1489,1492,1551],{"className":1488},[653],[572,1490],{"className":1491},[992,993],[572,1493,1495],{"className":1494},[913],[572,1496,1498,1543],{"className":1497},[1000,1001],[572,1499,1501,1540],{"className":1500},[1005],[572,1502,1504,1518,1526],{"className":1503,"style":1367},[1009],[572,1505,1506,1509],{"style":1013},[572,1507],{"className":1508,"style":1018},[1017],[572,1510,1512],{"className":1511},[1022,1023,1024,1025],[572,1513,1515],{"className":1514},[653,1025],[572,1516,922],{"className":1517},[653,1025],[572,1519,1520,1523],{"style":1034},[572,1521],{"className":1522,"style":1018},[1017],[572,1524],{"className":1525,"style":1042},[1041],[572,1527,1528,1531],{"style":1045},[572,1529],{"className":1530,"style":1018},[1017],[572,1532,1534],{"className":1533},[1022,1023,1024,1025],[572,1535,1537],{"className":1536},[653,1025],[572,1538,698],{"className":1539},[653,1025],[572,1541,1094],{"className":1542},[1093],[572,1544,1546],{"className":1545},[1005],[572,1547,1549],{"className":1548,"style":1101},[1009],[572,1550],{},[572,1552],{"className":1553},[1107,993]," für ",[572,1556,1558,1576],{"className":1557},[575],[572,1559,1561],{"className":1560},[579],[581,1562,1563],{"xmlns":583},[585,1564,1565,1573],{},[588,1566,1567,1569,1571],{},[591,1568,832],{},[595,1570,1329],{},[635,1572,637],{},[599,1574,1575],{"encoding":601},"x \\to 0",[572,1577,1579,1597],{"className":1578,"ariaHidden":607},[606],[572,1580,1582,1585,1588,1591,1594],{"className":1581},[611],[572,1583],{"className":1584,"style":616},[615],[572,1586,832],{"className":1587},[653,847],[572,1589],{"className":1590,"style":950},[743],[572,1592,1329],{"className":1593},[954],[572,1595],{"className":1596,"style":950},[743],[572,1598,1600,1603],{"className":1599},[611],[572,1601],{"className":1602,"style":649},[615],[572,1604,637],{"className":1605},[653],". Genauer ist ",[572,1608,1610,1669],{"className":1609},[575],[572,1611,1613],{"className":1612},[579],[581,1614,1615],{"xmlns":583},[585,1616,1617,1666],{},[588,1618,1619,1639,1642,1648,1650,1661,1664],{},[913,1620,1621,1633],{},[588,1622,1623,1625,1627,1629,1631],{},[635,1624,698],{},[595,1626,708],{},[591,1628,593],{},[595,1630,597],{},[591,1632,832],{},[916,1634,1635,1637],{},[591,1636,832],{},[635,1638,922],{},[595,1640,1641],{},"=",[913,1643,1644,1646],{},[635,1645,698],{},[635,1647,922],{},[595,1649,708],{},[913,1651,1652,1658],{},[916,1653,1654,1656],{},[591,1655,832],{},[635,1657,922],{},[635,1659,1660],{},"24",[595,1662,1663],{},"+",[595,1665,719],{},[599,1667,1668],{"encoding":601},"\\frac{1 - \\cos x}{x^2} = \\frac{1}{2} - \\frac{x^2}{24} + \\ldots",[572,1670,1672,1802,1885,1994],{"className":1671,"ariaHidden":607},[606],[572,1673,1675,1678,1793,1796,1799],{"className":1674},[611],[572,1676],{"className":1677,"style":1348},[615],[572,1679,1681,1684,1790],{"className":1680},[653],[572,1682],{"className":1683},[992,993],[572,1685,1687],{"className":1686},[913],[572,1688,1690,1782],{"className":1689},[1000,1001],[572,1691,1693,1779],{"className":1692},[1005],[572,1694,1696,1736,1744],{"className":1695,"style":1367},[1009],[572,1697,1698,1701],{"style":1013},[572,1699],{"className":1700,"style":1018},[1017],[572,1702,1704],{"className":1703},[1022,1023,1024,1025],[572,1705,1707],{"className":1706},[653,1025],[572,1708,1710,1713],{"className":1709},[653,1025],[572,1711,832],{"className":1712},[653,847,1025],[572,1714,1716],{"className":1715},[1064],[572,1717,1719],{"className":1718},[1000],[572,1720,1722],{"className":1721},[1005],[572,1723,1725],{"className":1724,"style":1397},[1009],[572,1726,1727,1730],{"style":1400},[572,1728],{"className":1729,"style":1081},[1017],[572,1731,1733],{"className":1732},[1022,1085,1086,1025],[572,1734,922],{"className":1735},[653,1025],[572,1737,1738,1741],{"style":1034},[572,1739],{"className":1740,"style":1018},[1017],[572,1742],{"className":1743,"style":1042},[1041],[572,1745,1746,1749],{"style":1045},[572,1747],{"className":1748,"style":1018},[1017],[572,1750,1752],{"className":1751},[1022,1023,1024,1025],[572,1753,1755,1758,1761,1773,1776],{"className":1754},[653,1025],[572,1756,698],{"className":1757},[653,1025],[572,1759,708],{"className":1760},[975,1025],[572,1762,1764,1767,1770],{"className":1763},[620,1025],[572,1765,1441],{"className":1766},[1025],[572,1768,1445],{"className":1769},[1025],[572,1771,1449],{"className":1772},[1025],[572,1774],{"className":1775,"style":1453},[743,1025],[572,1777,832],{"className":1778},[653,847,1025],[572,1780,1094],{"className":1781},[1093],[572,1783,1785],{"className":1784},[1005],[572,1786,1788],{"className":1787,"style":1101},[1009],[572,1789],{},[572,1791],{"className":1792},[1107,993],[572,1794],{"className":1795,"style":950},[743],[572,1797,1641],{"className":1798},[954],[572,1800],{"className":1801,"style":950},[743],[572,1803,1805,1808,1876,1879,1882],{"className":1804},[611],[572,1806],{"className":1807,"style":1348},[615],[572,1809,1811,1814,1873],{"className":1810},[653],[572,1812],{"className":1813},[992,993],[572,1815,1817],{"className":1816},[913],[572,1818,1820,1865],{"className":1819},[1000,1001],[572,1821,1823,1862],{"className":1822},[1005],[572,1824,1826,1840,1848],{"className":1825,"style":1367},[1009],[572,1827,1828,1831],{"style":1013},[572,1829],{"className":1830,"style":1018},[1017],[572,1832,1834],{"className":1833},[1022,1023,1024,1025],[572,1835,1837],{"className":1836},[653,1025],[572,1838,922],{"className":1839},[653,1025],[572,1841,1842,1845],{"style":1034},[572,1843],{"className":1844,"style":1018},[1017],[572,1846],{"className":1847,"style":1042},[1041],[572,1849,1850,1853],{"style":1045},[572,1851],{"className":1852,"style":1018},[1017],[572,1854,1856],{"className":1855},[1022,1023,1024,1025],[572,1857,1859],{"className":1858},[653,1025],[572,1860,698],{"className":1861},[653,1025],[572,1863,1094],{"className":1864},[1093],[572,1866,1868],{"className":1867},[1005],[572,1869,1871],{"className":1870,"style":1101},[1009],[572,1872],{},[572,1874],{"className":1875},[1107,993],[572,1877],{"className":1878,"style":971},[743],[572,1880,708],{"className":1881},[975],[572,1883],{"className":1884,"style":971},[743],[572,1886,1888,1891,1985,1988,1991],{"className":1887},[611],[572,1889],{"className":1890,"style":985},[615],[572,1892,1894,1897,1982],{"className":1893},[653],[572,1895],{"className":1896},[992,993],[572,1898,1900],{"className":1899},[913],[572,1901,1903,1974],{"className":1902},[1000,1001],[572,1904,1906,1971],{"className":1905},[1005],[572,1907,1909,1923,1931],{"className":1908,"style":1010},[1009],[572,1910,1911,1914],{"style":1013},[572,1912],{"className":1913,"style":1018},[1017],[572,1915,1917],{"className":1916},[1022,1023,1024,1025],[572,1918,1920],{"className":1919},[653,1025],[572,1921,1660],{"className":1922},[653,1025],[572,1924,1925,1928],{"style":1034},[572,1926],{"className":1927,"style":1018},[1017],[572,1929],{"className":1930,"style":1042},[1041],[572,1932,1933,1936],{"style":1045},[572,1934],{"className":1935,"style":1018},[1017],[572,1937,1939],{"className":1938},[1022,1023,1024,1025],[572,1940,1942],{"className":1941},[653,1025],[572,1943,1945,1948],{"className":1944},[653,1025],[572,1946,832],{"className":1947},[653,847,1025],[572,1949,1951],{"className":1950},[1064],[572,1952,1954],{"className":1953},[1000],[572,1955,1957],{"className":1956},[1005],[572,1958,1960],{"className":1959,"style":1074},[1009],[572,1961,1962,1965],{"style":1077},[572,1963],{"className":1964,"style":1081},[1017],[572,1966,1968],{"className":1967},[1022,1085,1086,1025],[572,1969,922],{"className":1970},[653,1025],[572,1972,1094],{"className":1973},[1093],[572,1975,1977],{"className":1976},[1005],[572,1978,1980],{"className":1979,"style":1101},[1009],[572,1981],{},[572,1983],{"className":1984},[1107,993],[572,1986],{"className":1987,"style":971},[743],[572,1989,1663],{"className":1990},[975],[572,1992],{"className":1993,"style":971},[743],[572,1995,1997,2001],{"className":1996},[611],[572,1998],{"className":1999,"style":2000},[615],"height:0.123em;",[572,2002,719],{"className":2003},[778],[564,2005,2006,2007,2072],{},"Für ",[572,2008,2010,2035],{"className":2009},[575],[572,2011,2013],{"className":2012},[579],[581,2014,2015],{"xmlns":583},[585,2016,2017,2032],{},[588,2018,2019,2023,2025,2027,2030],{},[591,2020,2022],{"mathvariant":2021},"normal","∣",[591,2024,832],{},[591,2026,2022],{"mathvariant":2021},[595,2028,2029],{},"≤",[635,2031,698],{},[599,2033,2034],{"encoding":601},"|x| \\leq 1",[572,2036,2038,2063],{"className":2037,"ariaHidden":607},[606],[572,2039,2041,2045,2048,2051,2054,2057,2060],{"className":2040},[611],[572,2042],{"className":2043,"style":2044},[615],"height:1em;vertical-align:-0.25em;",[572,2046,2022],{"className":2047},[653],[572,2049,832],{"className":2050},[653,847],[572,2052,2022],{"className":2053},[653],[572,2055],{"className":2056,"style":950},[743],[572,2058,2029],{"className":2059},[954],[572,2061],{"className":2062,"style":950},[743],[572,2064,2066,2069],{"className":2065},[611],[572,2067],{"className":2068,"style":649},[615],[572,2070,698],{"className":2071},[653]," fallen die Glieder betragsmäßig, und der Fehler beim Abbrechen ist höchstens das erste weggelassene Glied.",[559,2074,2076],{"id":2075},"beispiele","Beispiele",[564,2078,2079,2129],{},[572,2080,2082,2101],{"className":2081},[575],[572,2083,2085],{"className":2084},[579],[581,2086,2087],{"xmlns":583},[585,2088,2089,2098],{},[588,2090,2091,2093,2095],{},[591,2092,593],{},[595,2094,597],{},[635,2096,2097],{},"0,5",[599,2099,2100],{"encoding":601},"\\cos 0{,}5",[572,2102,2104],{"className":2103,"ariaHidden":607},[606],[572,2105,2107,2110,2113,2116,2119,2125],{"className":2106},[611],[572,2108],{"className":2109,"style":732},[615],[572,2111,593],{"className":2112},[620],[572,2114],{"className":2115,"style":744},[743],[572,2117,637],{"className":2118},[653],[572,2120,2122],{"className":2121},[653],[572,2123,701],{"className":2124},[739],[572,2126,2128],{"className":2127},[653],"5"," mit drei Gliedern:",[572,2131,2134],{"className":2132},[2133],"katex-display",[572,2135,2137,2183],{"className":2136},[575],[572,2138,2140],{"className":2139},[579],[581,2141,2143],{"xmlns":583,"display":2142},"block",[585,2144,2145,2180],{},[588,2146,2147,2149,2151,2153,2155,2157,2159,2166,2168,2175,2177],{},[591,2148,593],{},[595,2150,597],{},[635,2152,2097],{},[595,2154,907],{},[635,2156,698],{},[595,2158,708],{},[913,2160,2161,2164],{},[635,2162,2163],{},"0,25",[635,2165,922],{},[595,2167,1663],{},[913,2169,2170,2173],{},[635,2171,2172],{},"0,0625",[635,2174,1660],{},[595,2176,907],{},[635,2178,2179],{},"0,877604",[599,2181,2182],{"encoding":601},"\\cos 0{,}5 \\approx 1 - \\frac{0{,}25}{2} + \\frac{0{,}0625}{24} \\approx 0{,}877604",[572,2184,2186,2219,2237,2329,2416],{"className":2185,"ariaHidden":607},[606],[572,2187,2189,2192,2195,2198,2201,2207,2210,2213,2216],{"className":2188},[611],[572,2190],{"className":2191,"style":732},[615],[572,2193,593],{"className":2194},[620],[572,2196],{"className":2197,"style":744},[743],[572,2199,637],{"className":2200},[653],[572,2202,2204],{"className":2203},[653],[572,2205,701],{"className":2206},[739],[572,2208,2128],{"className":2209},[653],[572,2211],{"className":2212,"style":950},[743],[572,2214,907],{"className":2215},[954],[572,2217],{"className":2218,"style":950},[743],[572,2220,2222,2225,2228,2231,2234],{"className":2221},[611],[572,2223],{"className":2224,"style":964},[615],[572,2226,698],{"className":2227},[653],[572,2229],{"className":2230,"style":971},[743],[572,2232,708],{"className":2233},[975],[572,2235],{"className":2236,"style":971},[743],[572,2238,2240,2244,2320,2323,2326],{"className":2239},[611],[572,2241],{"className":2242,"style":2243},[615],"height:2.0074em;vertical-align:-0.686em;",[572,2245,2247,2250,2317],{"className":2246},[653],[572,2248],{"className":2249},[992,993],[572,2251,2253],{"className":2252},[913],[572,2254,2256,2308],{"className":2255},[1000,1001],[572,2257,2259,2305],{"className":2258},[1005],[572,2260,2263,2275,2283],{"className":2261,"style":2262},[1009],"height:1.3214em;",[572,2264,2266,2269],{"style":2265},"top:-2.314em;",[572,2267],{"className":2268,"style":1018},[1017],[572,2270,2272],{"className":2271},[653],[572,2273,922],{"className":2274},[653],[572,2276,2277,2280],{"style":1034},[572,2278],{"className":2279,"style":1018},[1017],[572,2281],{"className":2282,"style":1042},[1041],[572,2284,2286,2289],{"style":2285},"top:-3.677em;",[572,2287],{"className":2288,"style":1018},[1017],[572,2290,2292,2295,2301],{"className":2291},[653],[572,2293,637],{"className":2294},[653],[572,2296,2298],{"className":2297},[653],[572,2299,701],{"className":2300},[739],[572,2302,2304],{"className":2303},[653],"25",[572,2306,1094],{"className":2307},[1093],[572,2309,2311],{"className":2310},[1005],[572,2312,2315],{"className":2313,"style":2314},[1009],"height:0.686em;",[572,2316],{},[572,2318],{"className":2319},[1107,993],[572,2321],{"className":2322,"style":971},[743],[572,2324,1663],{"className":2325},[975],[572,2327],{"className":2328,"style":971},[743],[572,2330,2332,2335,2407,2410,2413],{"className":2331},[611],[572,2333],{"className":2334,"style":2243},[615],[572,2336,2338,2341,2404],{"className":2337},[653],[572,2339],{"className":2340},[992,993],[572,2342,2344],{"className":2343},[913],[572,2345,2347,2396],{"className":2346},[1000,1001],[572,2348,2350,2393],{"className":2349},[1005],[572,2351,2353,2364,2372],{"className":2352,"style":2262},[1009],[572,2354,2355,2358],{"style":2265},[572,2356],{"className":2357,"style":1018},[1017],[572,2359,2361],{"className":2360},[653],[572,2362,1660],{"className":2363},[653],[572,2365,2366,2369],{"style":1034},[572,2367],{"className":2368,"style":1018},[1017],[572,2370],{"className":2371,"style":1042},[1041],[572,2373,2374,2377],{"style":2285},[572,2375],{"className":2376,"style":1018},[1017],[572,2378,2380,2383,2389],{"className":2379},[653],[572,2381,637],{"className":2382},[653],[572,2384,2386],{"className":2385},[653],[572,2387,701],{"className":2388},[739],[572,2390,2392],{"className":2391},[653],"0625",[572,2394,1094],{"className":2395},[1093],[572,2397,2399],{"className":2398},[1005],[572,2400,2402],{"className":2401,"style":2314},[1009],[572,2403],{},[572,2405],{"className":2406},[1107,993],[572,2408],{"className":2409,"style":950},[743],[572,2411,907],{"className":2412},[954],[572,2414],{"className":2415,"style":950},[743],[572,2417,2419,2422,2425,2431],{"className":2418},[611],[572,2420],{"className":2421,"style":732},[615],[572,2423,637],{"className":2424},[653],[572,2426,2428],{"className":2427},[653],[572,2429,701],{"className":2430},[739],[572,2432,2434],{"className":2433},[653],"877604",[564,2436,2437,2438,2478,2479,1291],{},"Der genaue Wert ist ",[572,2439,2441,2456],{"className":2440},[575],[572,2442,2444],{"className":2443},[579],[581,2445,2446],{"xmlns":583},[585,2447,2448,2453],{},[588,2449,2450],{},[635,2451,2452],{},"0,877583",[599,2454,2455],{"encoding":601},"0{,}877583",[572,2457,2459],{"className":2458,"ariaHidden":607},[606],[572,2460,2462,2465,2468,2474],{"className":2461},[611],[572,2463],{"className":2464,"style":732},[615],[572,2466,637],{"className":2467},[653],[572,2469,2471],{"className":2470},[653],[572,2472,701],{"className":2473},[739],[572,2475,2477],{"className":2476},[653],"877583",". Der Fehler ist kleiner als das nächste Glied ",[572,2480,2482,2511],{"className":2481},[575],[572,2483,2485],{"className":2484},[579],[581,2486,2487],{"xmlns":583},[585,2488,2489,2508],{},[588,2490,2491,2503,2505],{},[913,2492,2493,2500],{},[916,2494,2495,2497],{},[635,2496,2097],{},[635,2498,2499],{},"6",[635,2501,2502],{},"720",[595,2504,907],{},[635,2506,2507],{},"0,000022",[599,2509,2510],{"encoding":601},"\\frac{0{,}5^6}{720} \\approx 0{,}000022",[572,2512,2514,2635],{"className":2513,"ariaHidden":607},[606],[572,2515,2517,2521,2626,2629,2632],{"className":2516},[611],[572,2518],{"className":2519,"style":2520},[615],"height:1.415em;vertical-align:-0.345em;",[572,2522,2524,2527,2623],{"className":2523},[653],[572,2525],{"className":2526},[992,993],[572,2528,2530],{"className":2529},[913],[572,2531,2533,2615],{"className":2532},[1000,1001],[572,2534,2536,2612],{"className":2535},[1005],[572,2537,2540,2554,2562],{"className":2538,"style":2539},[1009],"height:1.07em;",[572,2541,2542,2545],{"style":1013},[572,2543],{"className":2544,"style":1018},[1017],[572,2546,2548],{"className":2547},[1022,1023,1024,1025],[572,2549,2551],{"className":2550},[653,1025],[572,2552,2502],{"className":2553},[653,1025],[572,2555,2556,2559],{"style":1034},[572,2557],{"className":2558,"style":1018},[1017],[572,2560],{"className":2561,"style":1042},[1041],[572,2563,2565,2568],{"style":2564},"top:-3.4461em;",[572,2566],{"className":2567,"style":1018},[1017],[572,2569,2571],{"className":2570},[1022,1023,1024,1025],[572,2572,2574,2577,2583],{"className":2573},[653,1025],[572,2575,637],{"className":2576},[653,1025],[572,2578,2580],{"className":2579},[653,1025],[572,2581,701],{"className":2582},[739,1025],[572,2584,2586,2589],{"className":2585},[653,1025],[572,2587,2128],{"className":2588},[653,1025],[572,2590,2592],{"className":2591},[1064],[572,2593,2595],{"className":2594},[1000],[572,2596,2598],{"className":2597},[1005],[572,2599,2601],{"className":2600,"style":1074},[1009],[572,2602,2603,2606],{"style":1077},[572,2604],{"className":2605,"style":1081},[1017],[572,2607,2609],{"className":2608},[1022,1085,1086,1025],[572,2610,2499],{"className":2611},[653,1025],[572,2613,1094],{"className":2614},[1093],[572,2616,2618],{"className":2617},[1005],[572,2619,2621],{"className":2620,"style":1101},[1009],[572,2622],{},[572,2624],{"className":2625},[1107,993],[572,2627],{"className":2628,"style":950},[743],[572,2630,907],{"className":2631},[954],[572,2633],{"className":2634,"style":950},[743],[572,2636,2638,2641,2644,2650],{"className":2637},[611],[572,2639],{"className":2640,"style":732},[615],[572,2642,637],{"className":2643},[653],[572,2645,2647],{"className":2646},[653],[572,2648,701],{"className":2649},[739],[572,2651,2653],{"className":2652},[653],"000022",[564,2655,2006,2656,2718,2719,2935,2936,1291],{},[572,2657,2659,2678],{"className":2658},[575],[572,2660,2662],{"className":2661},[579],[581,2663,2664],{"xmlns":583},[585,2665,2666,2675],{},[588,2667,2668,2670,2672],{},[591,2669,832],{},[595,2671,1641],{},[635,2673,2674],{},"0,01",[599,2676,2677],{"encoding":601},"x = 0{,}01",[572,2679,2681,2699],{"className":2680,"ariaHidden":607},[606],[572,2682,2684,2687,2690,2693,2696],{"className":2683},[611],[572,2685],{"className":2686,"style":616},[615],[572,2688,832],{"className":2689},[653,847],[572,2691],{"className":2692,"style":950},[743],[572,2694,1641],{"className":2695},[954],[572,2697],{"className":2698,"style":950},[743],[572,2700,2702,2705,2708,2714],{"className":2701},[611],[572,2703],{"className":2704,"style":732},[615],[572,2706,637],{"className":2707},[653],[572,2709,2711],{"className":2710},[653],[572,2712,701],{"className":2713},[739],[572,2715,2717],{"className":2716},[653],"01"," ist ",[572,2720,2722,2759],{"className":2721},[575],[572,2723,2725],{"className":2724},[579],[581,2726,2727],{"xmlns":583},[585,2728,2729,2756],{},[588,2730,2731,2751,2753],{},[913,2732,2733,2745],{},[588,2734,2735,2737,2739,2741,2743],{},[635,2736,698],{},[595,2738,708],{},[591,2740,593],{},[595,2742,597],{},[635,2744,2674],{},[916,2746,2747,2749],{},[635,2748,2674],{},[635,2750,922],{},[595,2752,907],{},[635,2754,2755],{},"0,499996",[599,2757,2758],{"encoding":601},"\\frac{1 - \\cos 0{,}01}{0{,}01^2} \\approx 0{,}499996",[572,2760,2762,2916],{"className":2761,"ariaHidden":607},[606],[572,2763,2765,2769,2907,2910,2913],{"className":2764},[611],[572,2766],{"className":2767,"style":2768},[615],"height:1.3783em;vertical-align:-0.4811em;",[572,2770,2772,2775,2904],{"className":2771},[653],[572,2773],{"className":2774},[992,993],[572,2776,2778],{"className":2777},[913],[572,2779,2781,2895],{"className":2780},[1000,1001],[572,2782,2784,2892],{"className":2783},[1005],[572,2785,2788,2840,2848],{"className":2786,"style":2787},[1009],"height:0.8972em;",[572,2789,2790,2793],{"style":1013},[572,2791],{"className":2792,"style":1018},[1017],[572,2794,2796],{"className":2795},[1022,1023,1024,1025],[572,2797,2799,2802,2808,2811],{"className":2798},[653,1025],[572,2800,637],{"className":2801},[653,1025],[572,2803,2805],{"className":2804},[653,1025],[572,2806,701],{"className":2807},[739,1025],[572,2809,637],{"className":2810},[653,1025],[572,2812,2814,2817],{"className":2813},[653,1025],[572,2815,698],{"className":2816},[653,1025],[572,2818,2820],{"className":2819},[1064],[572,2821,2823],{"className":2822},[1000],[572,2824,2826],{"className":2825},[1005],[572,2827,2829],{"className":2828,"style":1397},[1009],[572,2830,2831,2834],{"style":1400},[572,2832],{"className":2833,"style":1081},[1017],[572,2835,2837],{"className":2836},[1022,1085,1086,1025],[572,2838,922],{"className":2839},[653,1025],[572,2841,2842,2845],{"style":1034},[572,2843],{"className":2844,"style":1018},[1017],[572,2846],{"className":2847,"style":1042},[1041],[572,2849,2850,2853],{"style":2564},[572,2851],{"className":2852,"style":1018},[1017],[572,2854,2856],{"className":2855},[1022,1023,1024,1025],[572,2857,2859,2862,2865,2877,2880,2883,2889],{"className":2858},[653,1025],[572,2860,698],{"className":2861},[653,1025],[572,2863,708],{"className":2864},[975,1025],[572,2866,2868,2871,2874],{"className":2867},[620,1025],[572,2869,1441],{"className":2870},[1025],[572,2872,1445],{"className":2873},[1025],[572,2875,1449],{"className":2876},[1025],[572,2878],{"className":2879,"style":1453},[743,1025],[572,2881,637],{"className":2882},[653,1025],[572,2884,2886],{"className":2885},[653,1025],[572,2887,701],{"className":2888},[739,1025],[572,2890,2717],{"className":2891},[653,1025],[572,2893,1094],{"className":2894},[1093],[572,2896,2898],{"className":2897},[1005],[572,2899,2902],{"className":2900,"style":2901},[1009],"height:0.4811em;",[572,2903],{},[572,2905],{"className":2906},[1107,993],[572,2908],{"className":2909,"style":950},[743],[572,2911,907],{"className":2912},[954],[572,2914],{"className":2915,"style":950},[743],[572,2917,2919,2922,2925,2931],{"className":2918},[611],[572,2920],{"className":2921,"style":732},[615],[572,2923,637],{"className":2924},[653],[572,2926,2928],{"className":2927},[653],[572,2929,701],{"className":2930},[739],[572,2932,2934],{"className":2933},[653],"499996",", in Übereinstimmung mit ",[572,2937,2939,2966],{"className":2938},[575],[572,2940,2942],{"className":2941},[579],[581,2943,2944],{"xmlns":583},[585,2945,2946,2963],{},[588,2947,2948,2954,2956],{},[913,2949,2950,2952],{},[635,2951,698],{},[635,2953,922],{},[595,2955,708],{},[913,2957,2958,2961],{},[635,2959,2960],{},"0,0001",[635,2962,1660],{},[599,2964,2965],{"encoding":601},"\\frac{1}{2} - \\frac{0{,}0001}{24}",[572,2967,2969,3052],{"className":2968,"ariaHidden":607},[606],[572,2970,2972,2975,3043,3046,3049],{"className":2971},[611],[572,2973],{"className":2974,"style":1348},[615],[572,2976,2978,2981,3040],{"className":2977},[653],[572,2979],{"className":2980},[992,993],[572,2982,2984],{"className":2983},[913],[572,2985,2987,3032],{"className":2986},[1000,1001],[572,2988,2990,3029],{"className":2989},[1005],[572,2991,2993,3007,3015],{"className":2992,"style":1367},[1009],[572,2994,2995,2998],{"style":1013},[572,2996],{"className":2997,"style":1018},[1017],[572,2999,3001],{"className":3000},[1022,1023,1024,1025],[572,3002,3004],{"className":3003},[653,1025],[572,3005,922],{"className":3006},[653,1025],[572,3008,3009,3012],{"style":1034},[572,3010],{"className":3011,"style":1018},[1017],[572,3013],{"className":3014,"style":1042},[1041],[572,3016,3017,3020],{"style":1045},[572,3018],{"className":3019,"style":1018},[1017],[572,3021,3023],{"className":3022},[1022,1023,1024,1025],[572,3024,3026],{"className":3025},[653,1025],[572,3027,698],{"className":3028},[653,1025],[572,3030,1094],{"className":3031},[1093],[572,3033,3035],{"className":3034},[1005],[572,3036,3038],{"className":3037,"style":1101},[1009],[572,3039],{},[572,3041],{"className":3042},[1107,993],[572,3044],{"className":3045,"style":971},[743],[572,3047,708],{"className":3048},[975],[572,3050],{"className":3051,"style":971},[743],[572,3053,3055,3059],{"className":3054},[611],[572,3056],{"className":3057,"style":3058},[615],"height:1.2422em;vertical-align:-0.345em;",[572,3060,3062,3065,3134],{"className":3061},[653],[572,3063],{"className":3064},[992,993],[572,3066,3068],{"className":3067},[913],[572,3069,3071,3126],{"className":3070},[1000,1001],[572,3072,3074,3123],{"className":3073},[1005],[572,3075,3077,3091,3099],{"className":3076,"style":2787},[1009],[572,3078,3079,3082],{"style":1013},[572,3080],{"className":3081,"style":1018},[1017],[572,3083,3085],{"className":3084},[1022,1023,1024,1025],[572,3086,3088],{"className":3087},[653,1025],[572,3089,1660],{"className":3090},[653,1025],[572,3092,3093,3096],{"style":1034},[572,3094],{"className":3095,"style":1018},[1017],[572,3097],{"className":3098,"style":1042},[1041],[572,3100,3101,3104],{"style":2564},[572,3102],{"className":3103,"style":1018},[1017],[572,3105,3107],{"className":3106},[1022,1023,1024,1025],[572,3108,3110,3113,3119],{"className":3109},[653,1025],[572,3111,637],{"className":3112},[653,1025],[572,3114,3116],{"className":3115},[653,1025],[572,3117,701],{"className":3118},[739,1025],[572,3120,3122],{"className":3121},[653,1025],"0001",[572,3124,1094],{"className":3125},[1093],[572,3127,3129],{"className":3128},[1005],[572,3130,3132],{"className":3131,"style":1101},[1009],[572,3133],{},[572,3135],{"className":3136},[1107,993],[559,3138,3140],{"id":3139},"typische-fehler","Typische Fehler",[882,3142,3143,3324,3521],{},[885,3144,3145,3146,3174,3175,3203,3204,3232,3233,3294,3295,3323],{},"Mit ",[572,3147,3149,3162],{"className":3148},[575],[572,3150,3152],{"className":3151},[579],[581,3153,3154],{"xmlns":583},[585,3155,3156,3160],{},[588,3157,3158],{},[591,3159,832],{},[599,3161,832],{"encoding":601},[572,3163,3165],{"className":3164,"ariaHidden":607},[606],[572,3166,3168,3171],{"className":3167},[611],[572,3169],{"className":3170,"style":616},[615],[572,3172,832],{"className":3173},[653,847]," statt mit ",[572,3176,3178,3191],{"className":3177},[575],[572,3179,3181],{"className":3180},[579],[581,3182,3183],{"xmlns":583},[585,3184,3185,3189],{},[588,3186,3187],{},[635,3188,698],{},[599,3190,698],{"encoding":601},[572,3192,3194],{"className":3193,"ariaHidden":607},[606],[572,3195,3197,3200],{"className":3196},[611],[572,3198],{"className":3199,"style":649},[615],[572,3201,698],{"className":3202},[653]," beginnen. Das konstante Glied ist ",[572,3205,3207,3220],{"className":3206},[575],[572,3208,3210],{"className":3209},[579],[581,3211,3212],{"xmlns":583},[585,3213,3214,3218],{},[588,3215,3216],{},[635,3217,698],{},[599,3219,698],{"encoding":601},[572,3221,3223],{"className":3222,"ariaHidden":607},[606],[572,3224,3226,3229],{"className":3225},[611],[572,3227],{"className":3228,"style":649},[615],[572,3230,698],{"className":3231},[653],", weil ",[572,3234,3236,3258],{"className":3235},[575],[572,3237,3239],{"className":3238},[579],[581,3240,3241],{"xmlns":583},[585,3242,3243,3255],{},[588,3244,3245,3247,3249,3251,3253],{},[591,3246,593],{},[595,3248,597],{},[635,3250,637],{},[595,3252,1641],{},[635,3254,698],{},[599,3256,3257],{"encoding":601},"\\cos 0 = 1",[572,3259,3261,3285],{"className":3260,"ariaHidden":607},[606],[572,3262,3264,3267,3270,3273,3276,3279,3282],{"className":3263},[611],[572,3265],{"className":3266,"style":649},[615],[572,3268,593],{"className":3269},[620],[572,3271],{"className":3272,"style":744},[743],[572,3274,637],{"className":3275},[653],[572,3277],{"className":3278,"style":950},[743],[572,3280,1641],{"className":3281},[954],[572,3283],{"className":3284,"style":950},[743],[572,3286,3288,3291],{"className":3287},[611],[572,3289],{"className":3290,"style":649},[615],[572,3292,698],{"className":3293},[653]," ist; mit ",[572,3296,3298,3311],{"className":3297},[575],[572,3299,3301],{"className":3300},[579],[581,3302,3303],{"xmlns":583},[585,3304,3305,3309],{},[588,3306,3307],{},[591,3308,832],{},[599,3310,832],{"encoding":601},[572,3312,3314],{"className":3313,"ariaHidden":607},[606],[572,3315,3317,3320],{"className":3316},[611],[572,3318],{"className":3319,"style":616},[615],[572,3321,832],{"className":3322},[653,847]," beginnt die Sinusreihe.",[885,3325,3326,3327,3390,3391,3450,3451,3486,3487,1291],{},"Ungerade Fakultäten verwenden: Zu ",[572,3328,3330,3349],{"className":3329},[575],[572,3331,3333],{"className":3332},[579],[581,3334,3335],{"xmlns":583},[585,3336,3337,3346],{},[588,3338,3339],{},[916,3340,3341,3343],{},[591,3342,832],{},[635,3344,3345],{},"4",[599,3347,3348],{"encoding":601},"x^4",[572,3350,3352],{"className":3351,"ariaHidden":607},[606],[572,3353,3355,3359],{"className":3354},[611],[572,3356],{"className":3357,"style":3358},[615],"height:0.8141em;",[572,3360,3362,3365],{"className":3361},[653],[572,3363,832],{"className":3364},[653,847],[572,3366,3368],{"className":3367},[1064],[572,3369,3371],{"className":3370},[1000],[572,3372,3374],{"className":3373},[1005],[572,3375,3377],{"className":3376,"style":3358},[1009],[572,3378,3380,3384],{"style":3379},"top:-3.063em;margin-right:0.05em;",[572,3381],{"className":3382,"style":3383},[1017],"height:2.7em;",[572,3385,3387],{"className":3386},[1022,1023,1024,1025],[572,3388,3345],{"className":3389},[653,1025]," gehört ",[572,3392,3394,3416],{"className":3393},[575],[572,3395,3397],{"className":3396},[579],[581,3398,3399],{"xmlns":583},[585,3400,3401,3413],{},[588,3402,3403,3405,3409,3411],{},[635,3404,3345],{},[595,3406,3408],{"stretchy":3407},"false","!",[595,3410,1641],{},[635,3412,1660],{},[599,3414,3415],{"encoding":601},"4! = 24",[572,3417,3419,3441],{"className":3418,"ariaHidden":607},[606],[572,3420,3422,3426,3429,3432,3435,3438],{"className":3421},[611],[572,3423],{"className":3424,"style":3425},[615],"height:0.6944em;",[572,3427,3345],{"className":3428},[653],[572,3430,3408],{"className":3431},[1107],[572,3433],{"className":3434,"style":950},[743],[572,3436,1641],{"className":3437},[954],[572,3439],{"className":3440,"style":950},[743],[572,3442,3444,3447],{"className":3443},[611],[572,3445],{"className":3446,"style":649},[615],[572,3448,1660],{"className":3449},[653],", nicht ",[572,3452,3454,3471],{"className":3453},[575],[572,3455,3457],{"className":3456},[579],[581,3458,3459],{"xmlns":583},[585,3460,3461,3468],{},[588,3462,3463,3466],{},[635,3464,3465],{},"3",[595,3467,3408],{"stretchy":3407},[599,3469,3470],{"encoding":601},"3!",[572,3472,3474],{"className":3473,"ariaHidden":607},[606],[572,3475,3477,3480,3483],{"className":3476},[611],[572,3478],{"className":3479,"style":3425},[615],[572,3481,3465],{"className":3482},[653],[572,3484,3408],{"className":3485},[1107]," oder ",[572,3488,3490,3506],{"className":3489},[575],[572,3491,3493],{"className":3492},[579],[581,3494,3495],{"xmlns":583},[585,3496,3497,3503],{},[588,3498,3499,3501],{},[635,3500,2128],{},[595,3502,3408],{"stretchy":3407},[599,3504,3505],{"encoding":601},"5!",[572,3507,3509],{"className":3508,"ariaHidden":607},[606],[572,3510,3512,3515,3518],{"className":3511},[611],[572,3513],{"className":3514,"style":3425},[615],[572,3516,2128],{"className":3517},[653],[572,3519,3408],{"className":3520},[1107],[885,3522,3523],{},"Den Winkel in Grad einsetzen. Die Reihe gilt nur im Bogenmaß.",{"title":3525,"searchDepth":3526,"depth":3526,"links":3527},"",2,[3528,3529,3530],{"id":561,"depth":3526,"text":562},{"id":2075,"depth":3526,"text":2076},{"id":3139,"depth":3526,"text":3140},[3532,3535,3538,3541,3544,3547,3550,3553],{"lhs":3533,"rhs":3534},"sum(map(0:10, f(n) = (-1)^n * x^(2*n)\u002F(2*n)!))","cos(x)",{"lhs":3536,"rhs":3537},"1 - 0.5^2\u002F2 + 0.5^4\u002F24","0.8776041666666666",{"lhs":3539,"rhs":3540},"round(1 - 0.5^2\u002F2 + 0.5^4\u002F24, 6)","0.877604",{"lhs":3542,"rhs":3543},"round(cos(0.5), 6)","0.877583",{"lhs":3545,"rhs":3546},"round(0.5^6\u002F720, 6)","0.000022",{"lhs":3548,"rhs":3549},"round((1 - cos(0.01))\u002F0.01^2, 6)","0.499996",{"lhs":3551,"rhs":3552},"1\u002F2 - 0.01^2\u002F24","0.49999583333333333",{"lhs":3554,"rhs":698},"cos(0)","x \\in \\mathbb{R} \\text{ im Bogenmaß}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x \\in \\mathbb{R}\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\">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:0.6889em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">im Bogenmaß\u003C\u002Fspan>",null,"md","cosine-series","\\cos x = \\sum_{n=0}^{\\infty} (-1)^n \\frac{x^{2n}}{(2n)!} = 1 - \\frac{x^2}{2!} + \\frac{x^4}{4!} - \\frac{x^6}{6!} + \\cdots","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>cos\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmunderover>\u003Cmo>∑\u003C\u002Fmo>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmunderover>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmfrac>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmrow>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>n\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>−\u003C\u002Fmo>\u003Cmfrac>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmrow>\u003Cmn>2\u003C\u002Fmn>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>+\u003C\u002Fmo>\u003Cmfrac>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>4\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmrow>\u003Cmn>4\u003C\u002Fmn>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>−\u003C\u002Fmo>\u003Cmfrac>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>6\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmrow>\u003Cmn>6\u003C\u002Fmn>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>+\u003C\u002Fmo>\u003Cmo>⋯\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\cos x = \\sum_{n=0}^{\\infty} (-1)^n \\frac{x^{2n}}{(2n)!} = 1 - \\frac{x^2}{2!} + \\frac{x^4}{4!} - \\frac{x^6}{6!} + \\cdots\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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">cos\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\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:2.9185em;vertical-align:-1.2671em;\">\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:-1.8829em;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>\u003Cspan class=\"mrel mtight\">=\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">0\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 mtight\">∞\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:1.2671em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">−\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7144em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:1.4911em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mclose\">)!\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:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.936em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\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:0.7278em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\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>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.1771em;vertical-align:-0.686em;\">\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:1.4911em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mclose\">!\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" 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