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",[573,1185,1187,1200],{"className":1186},[576],[573,1188,1190],{"className":1189},[580],[582,1191,1192],{"xmlns":584},[586,1193,1194,1198],{},[589,1195,1196],{},[1011,1197,1143],{},[603,1199,1143],{"encoding":605},[573,1201,1203],{"className":1202,"ariaHidden":611},[610],[573,1204,1206,1209],{"className":1205},[615],[573,1207],{"className":1208,"style":1054},[619],[573,1210,1143],{"className":1211},[633],[897,1213,1214,1246,1247,1313,1314,889],{},[573,1215,1217,1234],{"className":1216},[576],[573,1218,1220],{"className":1219},[580],[582,1221,1222],{"xmlns":584},[586,1223,1224,1231],{},[589,1225,1226,1229],{},[592,1227,1228],{},"tanh",[596,1230,598],{},[603,1232,1233],{"encoding":605},"\\tanh",[573,1235,1237],{"className":1236,"ariaHidden":611},[610],[573,1238,1240,1243],{"className":1239},[615],[573,1241],{"className":1242,"style":620},[619],[573,1244,1228],{"className":1245},[624]," ist ungerade, streng monoton wachsend und hat die Werte in ",[573,1248,1250,1279],{"className":1249},[576],[573,1251,1253],{"className":1252},[580],[582,1254,1255],{"xmlns":584},[586,1256,1257,1276],{},[589,1258,1259,1263,1266,1268,1271,1273],{},[596,1260,1262],{"stretchy":1261},"false","(",[596,1264,1265],{},"−",[1011,1267,1143],{},[596,1269,1270],{"separator":611},",",[1011,1272,1143],{},[596,1274,1275],{"stretchy":1261},")",[603,1277,1278],{"encoding":605},"(-1, 1)",[573,1280,1282],{"className":1281,"ariaHidden":611},[610],[573,1283,1285,1289,1293,1296,1299,1303,1306,1309],{"className":1284},[615],[573,1286],{"className":1287,"style":1288},[619],"height:1em;vertical-align:-0.25em;",[573,1290,1262],{"className":1291},[1292],"mopen",[573,1294,1265],{"className":1295},[633],[573,1297,1143],{"className":1298},[633],[573,1300,1270],{"className":1301},[1302],"mpunct",[573,1304],{"className":1305,"style":629},[628],[573,1307,1143],{"className":1308},[633],[573,1310,1275],{"className":1311},[1312],"mclose",", mit den Asymptoten ",[573,1315,1317,1339],{"className":1316},[576],[573,1318,1320],{"className":1319},[580],[582,1321,1322],{"xmlns":584},[586,1323,1324,1336],{},[589,1325,1326,1329,1331,1334],{},[592,1327,1328],{},"y",[596,1330,788],{},[596,1332,1333],{},"±",[1011,1335,1143],{},[603,1337,1338],{"encoding":605},"y = \\pm 1",[573,1340,1342,1362],{"className":1341,"ariaHidden":611},[610],[573,1343,1345,1349,1353,1356,1359],{"className":1344},[615],[573,1346],{"className":1347,"style":1348},[619],"height:0.625em;vertical-align:-0.1944em;",[573,1350,1328],{"className":1351,"style":1352},[633,634],"margin-right:0.0359em;",[573,1354],{"className":1355,"style":846},[628],[573,1357,788],{"className":1358},[850],[573,1360],{"className":1361,"style":846},[628],[573,1363,1365,1369,1372],{"className":1364},[615],[573,1366],{"className":1367,"style":1368},[619],"height:0.7278em;vertical-align:-0.0833em;",[573,1370,1333],{"className":1371},[633],[573,1373,1143],{"className":1374},[633],[565,1376,1377,1378,1451,1452,1455,1456,1593,1594,1668,1669,1838,1839,889],{},"Der Name kommt daher, dass ",[573,1379,1381,1412],{"className":1380},[576],[573,1382,1384],{"className":1383},[580],[582,1385,1386],{"xmlns":584},[586,1387,1388,1409],{},[589,1389,1390,1392,1394,1396,1399,1401,1403,1405,1407],{},[596,1391,1262],{"stretchy":1261},[592,1393,594],{},[596,1395,598],{},[592,1397,1398],{},"t",[596,1400,1270],{"separator":611},[592,1402,728],{},[596,1404,598],{},[592,1406,1398],{},[596,1408,1275],{"stretchy":1261},[603,1410,1411],{"encoding":605},"(\\cosh t, \\sinh t)",[573,1413,1415],{"className":1414,"ariaHidden":611},[610],[573,1416,1418,1421,1424,1427,1430,1433,1436,1439,1442,1445,1448],{"className":1417},[615],[573,1419],{"className":1420,"style":1288},[619],[573,1422,1262],{"className":1423},[1292],[573,1425,594],{"className":1426},[624],[573,1428],{"className":1429,"style":629},[628],[573,1431,1398],{"className":1432},[633,634],[573,1434,1270],{"className":1435},[1302],[573,1437],{"className":1438,"style":629},[628],[573,1440,728],{"className":1441},[624],[573,1443],{"className":1444,"style":629},[628],[573,1446,1398],{"className":1447},[633,634],[573,1449,1275],{"className":1450},[1312]," den rechten Ast der ",[569,1453,1454],{},"Hyperbel"," ",[573,1457,1459,1490],{"className":1458},[576],[573,1460,1462],{"className":1461},[580],[582,1463,1464],{"xmlns":584},[586,1465,1466,1487],{},[589,1467,1468,1475,1477,1483,1485],{},[653,1469,1470,1472],{},[592,1471,601],{},[1011,1473,1474],{},"2",[596,1476,1265],{},[653,1478,1479,1481],{},[592,1480,1328],{},[1011,1482,1474],{},[596,1484,788],{},[1011,1486,1143],{},[603,1488,1489],{"encoding":605},"x^2 - y^2 = 1",[573,1491,1493,1539,1584],{"className":1492,"ariaHidden":611},[610],[573,1494,1496,1500,1530,1533,1536],{"className":1495},[615],[573,1497],{"className":1498,"style":1499},[619],"height:0.8974em;vertical-align:-0.0833em;",[573,1501,1503,1506],{"className":1502},[633],[573,1504,601],{"className":1505},[633,634],[573,1507,1509],{"className":1508},[682],[573,1510,1512],{"className":1511},[686],[573,1513,1515],{"className":1514},[690],[573,1516,1519],{"className":1517,"style":1518},[694],"height:0.8141em;",[573,1520,1521,1524],{"style":697},[573,1522],{"className":1523,"style":702},[701],[573,1525,1527],{"className":1526},[706,707,708,709],[573,1528,1474],{"className":1529},[633,709],[573,1531],{"className":1532,"style":820},[628],[573,1534,1265],{"className":1535},[824],[573,1537],{"className":1538,"style":820},[628],[573,1540,1542,1546,1575,1578,1581],{"className":1541},[615],[573,1543],{"className":1544,"style":1545},[619],"height:1.0085em;vertical-align:-0.1944em;",[573,1547,1549,1552],{"className":1548},[633],[573,1550,1328],{"className":1551,"style":1352},[633,634],[573,1553,1555],{"className":1554},[682],[573,1556,1558],{"className":1557},[686],[573,1559,1561],{"className":1560},[690],[573,1562,1564],{"className":1563,"style":1518},[694],[573,1565,1566,1569],{"style":697},[573,1567],{"className":1568,"style":702},[701],[573,1570,1572],{"className":1571},[706,707,708,709],[573,1573,1474],{"className":1574},[633,709],[573,1576],{"className":1577,"style":846},[628],[573,1579,788],{"className":1580},[850],[573,1582],{"className":1583,"style":846},[628],[573,1585,1587,1590],{"className":1586},[615],[573,1588],{"className":1589,"style":1054},[619],[573,1591,1143],{"className":1592},[633]," durchläuft, so wie ",[573,1595,1597,1629],{"className":1596},[576],[573,1598,1600],{"className":1599},[580],[582,1601,1602],{"xmlns":584},[586,1603,1604,1626],{},[589,1605,1606,1608,1611,1613,1615,1617,1620,1622,1624],{},[596,1607,1262],{"stretchy":1261},[592,1609,1610],{},"cos",[596,1612,598],{},[592,1614,1398],{},[596,1616,1270],{"separator":611},[592,1618,1619],{},"sin",[596,1621,598],{},[592,1623,1398],{},[596,1625,1275],{"stretchy":1261},[603,1627,1628],{"encoding":605},"(\\cos t, \\sin t)",[573,1630,1632],{"className":1631,"ariaHidden":611},[610],[573,1633,1635,1638,1641,1644,1647,1650,1653,1656,1659,1662,1665],{"className":1634},[615],[573,1636],{"className":1637,"style":1288},[619],[573,1639,1262],{"className":1640},[1292],[573,1642,1610],{"className":1643},[624],[573,1645],{"className":1646,"style":629},[628],[573,1648,1398],{"className":1649},[633,634],[573,1651,1270],{"className":1652},[1302],[573,1654],{"className":1655,"style":629},[628],[573,1657,1619],{"className":1658},[624],[573,1660],{"className":1661,"style":629},[628],[573,1663,1398],{"className":1664},[633,634],[573,1666,1275],{"className":1667},[1312]," den Einheitskreis. Ein frei durchhängendes Seil hat die Form ",[573,1670,1672,1705],{"className":1671},[576],[573,1673,1675],{"className":1674},[580],[582,1676,1677],{"xmlns":584},[586,1678,1679,1702],{},[589,1680,1681,1683,1685,1688,1691,1693,1695],{},[592,1682,1328],{},[596,1684,788],{},[592,1686,1687],{},"c",[596,1689,1690],{},"⋅",[592,1692,594],{},[596,1694,598],{},[1696,1697,1698,1700],"mfrac",{},[592,1699,601],{},[592,1701,1687],{},[603,1703,1704],{"encoding":605},"y = c \\cdot \\cosh\\frac{x}{c}",[573,1706,1708,1726,1745],{"className":1707,"ariaHidden":611},[610],[573,1709,1711,1714,1717,1720,1723],{"className":1710},[615],[573,1712],{"className":1713,"style":1348},[619],[573,1715,1328],{"className":1716,"style":1352},[633,634],[573,1718],{"className":1719,"style":846},[628],[573,1721,788],{"className":1722},[850],[573,1724],{"className":1725,"style":846},[628],[573,1727,1729,1733,1736,1739,1742],{"className":1728},[615],[573,1730],{"className":1731,"style":1732},[619],"height:0.4445em;",[573,1734,1687],{"className":1735},[633,634],[573,1737],{"className":1738,"style":820},[628],[573,1740,1690],{"className":1741},[824],[573,1743],{"className":1744,"style":820},[628],[573,1746,1748,1752,1755,1758],{"className":1747},[615],[573,1749],{"className":1750,"style":1751},[619],"height:1.0404em;vertical-align:-0.345em;",[573,1753,594],{"className":1754},[624],[573,1756],{"className":1757,"style":629},[628],[573,1759,1761,1765,1835],{"className":1760},[633],[573,1762],{"className":1763},[1292,1764],"nulldelimiter",[573,1766,1768],{"className":1767},[1696],[573,1769,1772,1826],{"className":1770},[686,1771],"vlist-t2",[573,1773,1775,1821],{"className":1774},[690],[573,1776,1779,1795,1806],{"className":1777,"style":1778},[694],"height:0.6954em;",[573,1780,1782,1786],{"style":1781},"top:-2.655em;",[573,1783],{"className":1784,"style":1785},[701],"height:3em;",[573,1787,1789],{"className":1788},[706,707,708,709],[573,1790,1792],{"className":1791},[633,709],[573,1793,1687],{"className":1794},[633,634,709],[573,1796,1798,1801],{"style":1797},"top:-3.23em;",[573,1799],{"className":1800,"style":1785},[701],[573,1802],{"className":1803,"style":1805},[1804],"frac-line","border-bottom-width:0.04em;",[573,1807,1809,1812],{"style":1808},"top:-3.394em;",[573,1810],{"className":1811,"style":1785},[701],[573,1813,1815],{"className":1814},[706,707,708,709],[573,1816,1818],{"className":1817},[633,709],[573,1819,601],{"className":1820},[633,634,709],[573,1822,1825],{"className":1823},[1824],"vlist-s","​",[573,1827,1829],{"className":1828},[690],[573,1830,1833],{"className":1831,"style":1832},[694],"height:0.345em;",[573,1834],{},[573,1836],{"className":1837},[1312,1764],", die ",[569,1840,555],{},[565,1842,1843,1844,889],{},"Die Umkehrfunktionen heißen Areafunktionen, z.B. ",[573,1845,1847,1899],{"className":1846},[576],[573,1848,1850],{"className":1849},[580],[582,1851,1852],{"xmlns":584},[586,1853,1854,1896],{},[589,1855,1856,1860,1862,1864,1866,1869,1871],{},[592,1857,1859],{"mathvariant":1858},"normal","arsinh",[596,1861,598],{},[592,1863,601],{},[596,1865,788],{},[592,1867,1868],{},"ln",[596,1870,598],{},[589,1872,1873,1875,1877,1879,1894],{},[596,1874,1262],{"fence":611},[592,1876,601],{},[596,1878,779],{},[1880,1881,1882],"msqrt",{},[589,1883,1884,1890,1892],{},[653,1885,1886,1888],{},[592,1887,601],{},[1011,1889,1474],{},[596,1891,779],{},[1011,1893,1143],{},[596,1895,1275],{"fence":611},[603,1897,1898],{"encoding":605},"\\operatorname{arsinh} x = \\ln\\left(x + \\sqrt{x^2 + 1}\\right)",[573,1900,1902,1930],{"className":1901,"ariaHidden":611},[610],[573,1903,1905,1908,1915,1918,1921,1924,1927],{"className":1904},[615],[573,1906],{"className":1907,"style":620},[619],[573,1909,1911],{"className":1910},[624],[573,1912,1859],{"className":1913},[633,1914],"mathrm",[573,1916],{"className":1917,"style":629},[628],[573,1919,601],{"className":1920},[633,634],[573,1922],{"className":1923,"style":846},[628],[573,1925,788],{"className":1926},[850],[573,1928],{"className":1929,"style":846},[628],[573,1931,1933,1937,1940,1943],{"className":1932},[615],[573,1934],{"className":1935,"style":1936},[619],"height:1.2634em;vertical-align:-0.35em;",[573,1938,1868],{"className":1939},[624],[573,1941],{"className":1942,"style":629},[628],[573,1944,1947,1957,1960,1963,1966,1969,2073],{"className":1945},[1946],"minner",[573,1948,1952],{"className":1949,"style":1951},[1292,1950],"delimcenter","top:0em;",[573,1953,1262],{"className":1954},[1955,1956],"delimsizing","size1",[573,1958,601],{"className":1959},[633,634],[573,1961],{"className":1962,"style":820},[628],[573,1964,779],{"className":1965},[824],[573,1967],{"className":1968,"style":820},[628],[573,1970,1973],{"className":1971},[633,1972],"sqrt",[573,1974,1976,2064],{"className":1975},[686,1771],[573,1977,1979,2061],{"className":1978},[690],[573,1980,1983,2038],{"className":1981,"style":1982},[694],"height:0.9134em;",[573,1984,1988,1991],{"className":1985,"style":1987},[1986],"svg-align","top:-3em;",[573,1989],{"className":1990,"style":1785},[701],[573,1992,1995,2026,2029,2032,2035],{"className":1993,"style":1994},[633],"padding-left:0.833em;",[573,1996,1998,2001],{"className":1997},[633],[573,1999,601],{"className":2000},[633,634],[573,2002,2004],{"className":2003},[682],[573,2005,2007],{"className":2006},[686],[573,2008,2010],{"className":2009},[690],[573,2011,2014],{"className":2012,"style":2013},[694],"height:0.7401em;",[573,2015,2017,2020],{"style":2016},"top:-2.989em;margin-right:0.05em;",[573,2018],{"className":2019,"style":702},[701],[573,2021,2023],{"className":2022},[706,707,708,709],[573,2024,1474],{"className":2025},[633,709],[573,2027],{"className":2028,"style":820},[628],[573,2030,779],{"className":2031},[824],[573,2033],{"className":2034,"style":820},[628],[573,2036,1143],{"className":2037},[633],[573,2039,2041,2044],{"style":2040},"top:-2.8734em;",[573,2042],{"className":2043,"style":1785},[701],[573,2045,2049],{"className":2046,"style":2048},[2047],"hide-tail","min-width:0.853em;height:1.08em;",[2050,2051,2057],"svg",{"xmlns":2052,"width":2053,"height":2054,"viewBox":2055,"preserveAspectRatio":2056},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 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1 = \\frac{e - e^{-1}}{2} \\approx 1{,}1752,\\quad \\cosh 1 = \\frac{e + e^{-1}}{2} \\approx 1{,}5431,\\quad \\tanh 1 \\approx 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Mit der Areafunktion:",[573,2802,2804],{"className":2803},[2142],[573,2805,2807,2915],{"className":2806},[576],[573,2808,2810],{"className":2809},[580],[582,2811,2812],{"xmlns":584,"display":2151},[586,2813,2814,2912],{},[589,2815,2816,2818,2820,2822,2824,2833,2835,2837,2839,2873,2875,2877,2879,2904,2906,2908,2910],{},[592,2817,601],{},[596,2819,788],{},[592,2821,1859],{"mathvariant":1858},[596,2823,598],{},[2825,2826,2827],"mstyle",{"scriptlevel":1013,"displaystyle":1261},[1696,2828,2829,2831],{},[1011,2830,2690],{},[1011,2832,2693],{},[596,2834,788],{},[592,2836,1868],{},[596,2838,598],{},[589,2840,2841,2843,2851,2853,2871],{},[596,2842,1262],{"fence":611},[2825,2844,2845],{"scriptlevel":1013,"displaystyle":1261},[1696,2846,2847,2849],{},[1011,2848,2690],{},[1011,2850,2693],{},[596,2852,779],{},[1880,2854,2855],{},[589,2856,2857,2867,2869],{},[2825,2858,2859],{"scriptlevel":1013,"displaystyle":1261},[1696,2860,2861,2864],{},[1011,2862,2863],{},"9",[1011,2865,2866],{},"16",[596,2868,779],{},[1011,2870,1143],{},[596,2872,1275],{"fence":611},[596,2874,788],{},[592,2876,1868],{},[596,2878,598],{},[589,2880,2881,2883,2891,2893,2902],{},[596,2882,1262],{"fence":611},[2825,2884,2885],{"scriptlevel":1013,"displaystyle":1261},[1696,2886,2887,2889],{},[1011,2888,2690],{},[1011,2890,2693],{},[596,2892,779],{},[2825,2894,2895],{"scriptlevel":1013,"displaystyle":1261},[1696,2896,2897,2900],{},[1011,2898,2899],{},"5",[1011,2901,2693],{},[596,2903,1275],{"fence":611},[596,2905,788],{},[592,2907,1868],{},[596,2909,598],{},[1011,2911,1474],{},[603,2913,2914],{"encoding":605},"x = \\operatorname{arsinh} \\tfrac{3}{4} = \\ln\\left(\\tfrac{3}{4} + \\sqrt{\\tfrac{9}{16} + 1}\\right) = \\ln\\left(\\tfrac{3}{4} + \\tfrac{5}{4}\\right) = \\ln 2",[573,2916,2918,2936,3028,3276,3458],{"className":2917,"ariaHidden":611},[610],[573,2919,2921,2924,2927,2930,2933],{"className":2920},[615],[573,2922],{"className":2923,"style":2116},[619],[573,2925,601],{"className":2926},[633,634],[573,2928],{"className":2929,"style":846},[628],[573,2931,788],{"className":2932},[850],[573,2934],{"className":2935,"style":846},[628],[573,2937,2939,2942,2948,2951,3019,3022,3025],{"className":2938},[615],[573,2940],{"className":2941,"style":2730},[619],[573,2943,2945],{"className":2944},[624],[573,2946,1859],{"className":2947},[633,1914],[573,2949],{"className":2950,"style":629},[628],[573,2952,2954,2957,3016],{"className":2953},[633],[573,2955],{"className":2956},[1292,1764],[573,2958,2960],{"className":2959},[1696],[573,2961,2963,3008],{"className":2962},[686,1771],[573,2964,2966,3005],{"className":2965},[690],[573,2967,2969,2983,2991],{"className":2968,"style":2749},[694],[573,2970,2971,2974],{"style":1781},[573,2972],{"className":2973,"style":1785},[701],[573,2975,2977],{"className":2976},[706,707,708,709],[573,2978,2980],{"className":2979},[633,709],[573,2981,2693],{"className":2982},[633,709],[573,2984,2985,2988],{"style":1797},[573,2986],{"className":2987,"style":1785},[701],[573,2989],{"className":2990,"style":1805},[1804],[573,2992,2993,2996],{"style":1808},[573,2994],{"className":2995,"style":1785},[701],[573,2997,2999],{"className":2998},[706,707,708,709],[573,3000,3002],{"className":3001},[633,709],[573,3003,2690],{"className":3004},[633,709],[573,3006,1825],{"className":3007},[1824],[573,3009,3011],{"className":3010},[690],[573,3012,3014],{"className":3013,"style":1832},[694],[573,3015],{},[573,3017],{"className":3018},[1312,1764],[573,3020],{"className":3021,"style":846},[628],[573,3023,788],{"className":3024},[850],[573,3026],{"className":3027,"style":846},[628],[573,3029,3031,3035,3038,3041,3267,3270,3273],{"className":3030},[615],[573,3032],{"className":3033,"style":3034},[619],"height:2.4em;vertical-align:-0.95em;",[573,3036,1868],{"className":3037},[624],[573,3039],{"className":3040,"style":629},[628],[573,3042,3044,3050,3118,3121,3124,3127,3261],{"className":3043},[1946],[573,3045,3047],{"className":3046,"style":1951},[1292,1950],[573,3048,1262],{"className":3049},[1955,708],[573,3051,3053,3056,3115],{"className":3052},[633],[573,3054],{"className":3055},[1292,1764],[573,3057,3059],{"className":3058},[1696],[573,3060,3062,3107],{"className":3061},[686,1771],[573,3063,3065,3104],{"className":3064},[690],[573,3066,3068,3082,3090],{"className":3067,"style":2749},[694],[573,3069,3070,3073],{"style":1781},[573,3071],{"className":3072,"style":1785},[701],[573,3074,3076],{"className":3075},[706,707,708,709],[573,3077,3079],{"className":3078},[633,709],[573,3080,2693],{"className":3081},[633,709],[573,3083,3084,3087],{"style":1797},[573,3085],{"className":3086,"style":1785},[701],[573,3088],{"className":3089,"style":1805},[1804],[573,3091,3092,3095],{"style":1808},[573,3093],{"className":3094,"style":1785},[701],[573,3096,3098],{"className":3097},[706,707,708,709],[573,3099,3101],{"className":3100},[633,709],[573,3102,2690],{"className":3103},[633,709],[573,3105,1825],{"className":3106},[1824],[573,3108,3110],{"className":3109},[690],[573,3111,3113],{"className":3112,"style":1832},[694],[573,3114],{},[573,3116],{"className":3117},[1312,1764],[573,3119],{"className":3120,"style":820},[628],[573,3122,779],{"className":3123},[824],[573,3125],{"className":3126,"style":820},[628],[573,3128,3130],{"className":3129},[633,1972],[573,3131,3133,3252],{"className":3132},[686,1771],[573,3134,3136,3249],{"className":3135},[690],[573,3137,3140,3232],{"className":3138,"style":3139},[694],"height:1.2839em;",[573,3141,3144,3148],{"className":3142,"style":3143},[1986],"top:-3.8em;",[573,3145],{"className":3146,"style":3147},[701],"height:3.8em;",[573,3149,3152,3220,3223,3226,3229],{"className":3150,"style":3151},[633],"padding-left:1em;",[573,3153,3155,3158,3217],{"className":3154},[633],[573,3156],{"className":3157},[1292,1764],[573,3159,3161],{"className":3160},[1696],[573,3162,3164,3209],{"className":3163},[686,1771],[573,3165,3167,3206],{"className":3166},[690],[573,3168,3170,3184,3192],{"className":3169,"style":2749},[694],[573,3171,3172,3175],{"style":1781},[573,3173],{"className":3174,"style":1785},[701],[573,3176,3178],{"className":3177},[706,707,708,709],[573,3179,3181],{"className":3180},[633,709],[573,3182,2866],{"className":3183},[633,709],[573,3185,3186,3189],{"style":1797},[573,3187],{"className":3188,"style":1785},[701],[573,3190],{"className":3191,"style":1805},[1804],[573,3193,3194,3197],{"style":1808},[573,3195],{"className":3196,"style":1785},[701],[573,3198,3200],{"className":3199},[706,707,708,709],[573,3201,3203],{"className":3202},[633,709],[573,3204,2863],{"className":3205},[633,709],[573,3207,1825],{"className":3208},[1824],[573,3210,3212],{"className":3211},[690],[573,3213,3215],{"className":3214,"style":1832},[694],[573,3216],{},[573,3218],{"className":3219},[1312,1764],[573,3221],{"className":3222,"style":820},[628],[573,3224,779],{"className":3225},[824],[573,3227],{"className":3228,"style":820},[628],[573,3230,1143],{"className":3231},[633],[573,3233,3235,3238],{"style":3234},"top:-3.2439em;",[573,3236],{"className":3237,"style":3147},[701],[573,3239,3242],{"className":3240,"style":3241},[2047],"min-width:1.02em;height:1.88em;",[2050,3243,3246],{"xmlns":2052,"width":2053,"height":3244,"viewBox":3245,"preserveAspectRatio":2056},"1.88em","0 0 400000 1944",[2058,3247],{"d":3248},"M983 90\nl0 -0\nc4,-6.7,10,-10,18,-10 H400000v40\nH1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7\ns-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744\nc-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30\nc26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722\nc56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5\nc53.7,-170.3,84.5,-266.8,92.5,-289.5z\nM1001 80h400000v40h-400000z",[573,3250,1825],{"className":3251},[1824],[573,3253,3255],{"className":3254},[690],[573,3256,3259],{"className":3257,"style":3258},[694],"height:0.5561em;",[573,3260],{},[573,3262,3264],{"className":3263,"style":1951},[1312,1950],[573,3265,1275],{"className":3266},[1955,708],[573,3268],{"className":3269,"style":846},[628],[573,3271,788],{"className":3272},[850],[573,3274],{"className":3275,"style":846},[628],[573,3277,3279,3283,3286,3289,3449,3452,3455],{"className":3278},[615],[573,3280],{"className":3281,"style":3282},[619],"height:1.2em;vertical-align:-0.35em;",[573,3284,1868],{"className":3285},[624],[573,3287],{"className":3288,"style":629},[628],[573,3290,3292,3298,3366,3369,3372,3375,3443],{"className":3291},[1946],[573,3293,3295],{"className":3294,"style":1951},[1292,1950],[573,3296,1262],{"className":3297},[1955,1956],[573,3299,3301,3304,3363],{"className":3300},[633],[573,3302],{"className":3303},[1292,1764],[573,3305,3307],{"className":3306},[1696],[573,3308,3310,3355],{"className":3309},[686,1771],[573,3311,3313,3352],{"className":3312},[690],[573,3314,3316,3330,3338],{"className":3315,"style":2749},[694],[573,3317,3318,3321],{"style":1781},[573,3319],{"className":3320,"style":1785},[701],[573,3322,3324],{"className":3323},[706,707,708,709],[573,3325,3327],{"className":3326},[633,709],[573,3328,2693],{"className":3329},[633,709],[573,3331,3332,3335],{"style":1797},[573,3333],{"className":3334,"style":1785},[701],[573,3336],{"className":3337,"style":1805},[1804],[573,3339,3340,3343],{"style":1808},[573,3341],{"className":3342,"style":1785},[701],[573,3344,3346],{"className":3345},[706,707,708,709],[573,3347,3349],{"className":3348},[633,709],[573,3350,2690],{"className":3351},[633,709],[573,3353,1825],{"className":3354},[1824],[573,3356,3358],{"className":3357},[690],[573,3359,3361],{"className":3360,"style":1832},[694],[573,3362],{},[573,3364],{"className":3365},[1312,1764],[573,3367],{"className":3368,"style":820},[628],[573,3370,779],{"className":3371},[824],[573,3373],{"className":3374,"style":820},[628],[573,3376,3378,3381,3440],{"className":3377},[633],[573,3379],{"className":3380},[1292,1764],[573,3382,3384],{"className":3383},[1696],[573,3385,3387,3432],{"className":3386},[686,1771],[573,3388,3390,3429],{"className":3389},[690],[573,3391,3393,3407,3415],{"className":3392,"style":2749},[694],[573,3394,3395,3398],{"style":1781},[573,3396],{"className":3397,"style":1785},[701],[573,3399,3401],{"className":3400},[706,707,708,709],[573,3402,3404],{"className":3403},[633,709],[573,3405,2693],{"className":3406},[633,709],[573,3408,3409,3412],{"style":1797},[573,3410],{"className":3411,"style":1785},[701],[573,3413],{"className":3414,"style":1805},[1804],[573,3416,3417,3420],{"style":1808},[573,3418],{"className":3419,"style":1785},[701],[573,3421,3423],{"className":3422},[706,707,708,709],[573,3424,3426],{"className":3425},[633,709],[573,3427,2899],{"className":3428},[633,709],[573,3430,1825],{"className":3431},[1824],[573,3433,3435],{"className":3434},[690],[573,3436,3438],{"className":3437,"style":1832},[694],[573,3439],{},[573,3441],{"className":3442},[1312,1764],[573,3444,3446],{"className":3445,"style":1951},[1312,1950],[573,3447,1275],{"className":3448},[1955,1956],[573,3450],{"className":3451,"style":846},[628],[573,3453,788],{"className":3454},[850],[573,3456],{"className":3457,"style":846},[628],[573,3459,3461,3464,3467,3470],{"className":3460},[615],[573,3462],{"className":3463,"style":620},[619],[573,3465,1868],{"className":3466},[624],[573,3468],{"className":3469,"style":629},[628],[573,3471,1474],{"className":3472},[633],[560,3474,3476],{"id":3475},"typische-fehler","Typische Fehler",[894,3478,3479,3576,3805,4000],{},[897,3480,3481,3482,3512,3513,889],{},"Die Vorzeichen in den Definitionen vertauschen. Bei ",[573,3483,3485,3500],{"className":3484},[576],[573,3486,3488],{"className":3487},[580],[582,3489,3490],{"xmlns":584},[586,3491,3492,3498],{},[589,3493,3494,3496],{},[592,3495,594],{},[596,3497,598],{},[603,3499,1078],{"encoding":605},[573,3501,3503],{"className":3502,"ariaHidden":611},[610],[573,3504,3506,3509],{"className":3505},[615],[573,3507],{"className":3508,"style":620},[619],[573,3510,594],{"className":3511},[624]," steht das Plus, deshalb ist ",[573,3514,3516,3539],{"className":3515},[576],[573,3517,3519],{"className":3518},[580],[582,3520,3521],{"xmlns":584},[586,3522,3523,3536],{},[589,3524,3525,3527,3529,3531,3534],{},[592,3526,594],{},[596,3528,598],{},[592,3530,601],{},[596,3532,3533],{},"≥",[1011,3535,1143],{},[603,3537,3538],{"encoding":605},"\\cosh x \\geq 1",[573,3540,3542,3567],{"className":3541,"ariaHidden":611},[610],[573,3543,3545,3549,3552,3555,3558,3561,3564],{"className":3544},[615],[573,3546],{"className":3547,"style":3548},[619],"height:0.8304em;vertical-align:-0.136em;",[573,3550,594],{"className":3551},[624],[573,3553],{"className":3554,"style":629},[628],[573,3556,601],{"className":3557},[633,634],[573,3559],{"className":3560,"style":846},[628],[573,3562,3533],{"className":3563},[850],[573,3565],{"className":3566,"style":846},[628],[573,3568,3570,3573],{"className":3569},[615],[573,3571],{"className":3572,"style":1054},[619],[573,3574,1143],{"className":3575},[633],[897,3577,3578,3579,3739,3740,713,3770,3800,3801,3804],{},"Die Regeln der trigonometrischen Funktionen ungeprüft übertragen. Es gilt ",[573,3580,3582,3624],{"className":3581},[576],[573,3583,3585],{"className":3584},[580],[582,3586,3587],{"xmlns":584},[586,3588,3589,3621],{},[589,3590,3591,3601,3603,3605,3615,3617,3619],{},[653,3592,3593,3599],{},[589,3594,3595,3597],{},[592,3596,594],{},[596,3598,598],{},[1011,3600,1474],{},[592,3602,601],{},[596,3604,1265],{},[653,3606,3607,3613],{},[589,3608,3609,3611],{},[592,3610,728],{},[596,3612,598],{},[1011,3614,1474],{},[592,3616,601],{},[596,3618,788],{},[1011,3620,1143],{},[603,3622,3623],{"encoding":605},"\\cosh^2 x - \\sinh^2 x = 1",[573,3625,3627,3680,3730],{"className":3626,"ariaHidden":611},[610],[573,3628,3630,3634,3665,3668,3671,3674,3677],{"className":3629},[615],[573,3631],{"className":3632,"style":3633},[619],"height:0.9818em;vertical-align:-0.0833em;",[573,3635,3637,3640],{"className":3636},[624],[573,3638,594],{"className":3639},[624],[573,3641,3643],{"className":3642},[682],[573,3644,3646],{"className":3645},[686],[573,3647,3649],{"className":3648},[690],[573,3650,3653],{"className":3651,"style":3652},[694],"height:0.8984em;",[573,3654,3656,3659],{"style":3655},"top:-3.1473em;margin-right:0.05em;",[573,3657],{"className":3658,"style":702},[701],[573,3660,3662],{"className":3661},[706,707,708,709],[573,3663,1474],{"className":3664},[633,709],[573,3666],{"className":3667,"style":629},[628],[573,3669,601],{"className":3670},[633,634],[573,3672],{"className":3673,"style":820},[628],[573,3675,1265],{"className":3676},[824],[573,3678],{"className":3679,"style":820},[628],[573,3681,3683,3686,3715,3718,3721,3724,3727],{"className":3682},[615],[573,3684],{"className":3685,"style":3652},[619],[573,3687,3689,3692],{"className":3688},[624],[573,3690,728],{"className":3691},[624],[573,3693,3695],{"className":3694},[682],[573,3696,3698],{"className":3697},[686],[573,3699,3701],{"className":3700},[690],[573,3702,3704],{"className":3703,"style":3652},[694],[573,3705,3706,3709],{"style":3655},[573,3707],{"className":3708,"style":702},[701],[573,3710,3712],{"className":3711},[706,707,708,709],[573,3713,1474],{"className":3714},[633,709],[573,3716],{"className":3717,"style":629},[628],[573,3719,601],{"className":3720},[633,634],[573,3722],{"className":3723,"style":846},[628],[573,3725,788],{"className":3726},[850],[573,3728],{"className":3729,"style":846},[628],[573,3731,3733,3736],{"className":3732},[615],[573,3734],{"className":3735,"style":1054},[619],[573,3737,1143],{"className":3738},[633]," mit Minus, und ",[573,3741,3743,3758],{"className":3742},[576],[573,3744,3746],{"className":3745},[580],[582,3747,3748],{"xmlns":584},[586,3749,3750,3756],{},[589,3751,3752,3754],{},[592,3753,728],{},[596,3755,598],{},[603,3757,917],{"encoding":605},[573,3759,3761],{"className":3760,"ariaHidden":611},[610],[573,3762,3764,3767],{"className":3763},[615],[573,3765],{"className":3766,"style":620},[619],[573,3768,728],{"className":3769},[624],[573,3771,3773,3788],{"className":3772},[576],[573,3774,3776],{"className":3775},[580],[582,3777,3778],{"xmlns":584},[586,3779,3780,3786],{},[589,3781,3782,3784],{},[592,3783,594],{},[596,3785,598],{},[603,3787,1078],{"encoding":605},[573,3789,3791],{"className":3790,"ariaHidden":611},[610],[573,3792,3794,3797],{"className":3793},[615],[573,3795],{"className":3796,"style":620},[619],[573,3798,594],{"className":3799},[624]," sind ",[569,3802,3803],{},"nicht"," 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235.21 111 L 236.21 110.97 L 237.21 110.95 L 238.2 110.93 L 239.2 110.9\" class=\"fig-main fig-graph\" clip-path=\"url(#fig-hyperbolic-functions-clip)\"\u002F>\u003Ctext x=\"154.1\" y=\"46\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">cosh\u003C\u002Ftext>\u003Ctext x=\"80.5\" y=\"248.4\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">sinh\u003C\u002Ftext>\u003Ctext x=\"193.2\" y=\"138\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">tanh\u003C\u002Ftext>\u003C\u002Fsvg>","hyperbolic-functions","\\sinh x = \\frac{e^x - e^{-x}}{2},\\quad \\cosh x = \\frac{e^x + e^{-x}}{2},\\quad \\tanh x = \\frac{\\sinh x}{\\cosh x}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>sinh\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmsup>\u003Cmi>e\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>−\u003C\u002Fmo>\u003Cmsup>\u003Cmi>e\u003C\u002Fmi>\u003Cmrow>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"1em\"\u002F>\u003Cmi>cosh\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmsup>\u003Cmi>e\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmsup>\u003Cmi>e\u003C\u002Fmi>\u003Cmrow>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"1em\"\u002F>\u003Cmi>tanh\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>sinh\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>cosh\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\sinh x = \\frac{e^x - e^{-x}}{2},\\quad \\cosh x = \\frac{e^x + e^{-x}}{2},\\quad \\tanh x = \\frac{\\sinh x}{\\cosh x}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">sinh\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:2.1343em;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:1.4483em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\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\">e\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6644em;\">\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 mathnormal mtight\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">e\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7713em;\">\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\">−\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">x\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:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:1em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">cosh\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:2.1343em;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:1.4483em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\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\">e\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6644em;\">\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 mathnormal mtight\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">e\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7713em;\">\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\">−\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal 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