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dann hat ",[572,1126,1128,1141],{"className":1127},[575],[572,1129,1131],{"className":1130},[579],[581,1132,1133],{"xmlns":583},[585,1134,1135,1139],{},[588,1136,1137],{},[591,1138,633],{},[595,1140,633],{"encoding":597},[572,1142,1144],{"className":1143,"ariaHidden":602},[601],[572,1145,1147,1150],{"className":1146},[606],[572,1148],{"className":1149,"style":747},[610],[572,1151,633],{"className":1152,"style":661},[615,616]," in ",[572,1155,1157,1180],{"className":1156},[575],[572,1158,1160],{"className":1159},[579],[581,1161,1162],{"xmlns":583},[585,1163,1164,1177],{},[588,1165,1166,1168,1170,1173,1175],{},[635,1167,638],{"stretchy":637},[591,1169,641],{},[635,1171,1172],{"separator":602},",",[591,1174,692],{},[635,1176,644],{"stretchy":637},[595,1178,1179],{"encoding":597},"(a, b)",[572,1181,1183],{"className":1182,"ariaHidden":602},[601],[572,1184,1186,1189,1192,1195,1199,1203,1206],{"className":1185},[606],[572,1187],{"className":1188,"style":657},[610],[572,1190,638],{"className":1191},[665],[572,1193,641],{"className":1194},[615,616],[572,1196,1172],{"className":1197},[1198],"mpunct",[572,1200],{"className":1201,"style":1202},[811],"margin-right:0.1667em;",[572,1204,692],{"className":1205},[615,616],[572,1207,644],{"className":1208},[672]," eine Nullstelle.",[564,1211,1212,1213,1216,1217,1220],{},"Der Satz sichert nur die ",[568,1214,1215],{},"Existenz",". Er sagt nicht, wo die Stelle liegt und wie viele es gibt. Eine Näherung liefert das ",[568,1218,1219],{},"Bisektionsverfahren",", das den Vorzeichenwechsel immer weiter einschachtelt.",[564,1222,1223],{},"Beide Voraussetzungen sind nötig: Ohne Stetigkeit oder auf einem zerrissenen Definitionsbereich kann der Wert übersprungen werden.",[559,1225,1227],{"id":1226},"beispiele","Beispiele",[564,1229,1230,1391,1392,1446,1447,673,1541,1630,1631,1659,1660,1712,1713,1777],{},[572,1231,1233,1276],{"className":1232},[575],[572,1234,1236],{"className":1235},[579],[581,1237,1238],{"xmlns":583},[585,1239,1240,1273],{},[588,1241,1242,1244,1246,1249,1251,1254,1262,1265,1267,1270],{},[591,1243,633],{},[635,1245,638],{"stretchy":637},[591,1247,1248],{},"x",[635,1250,644],{"stretchy":637},[635,1252,1253],{},"=",[1255,1256,1257,1259],"msup",{},[591,1258,1248],{},[1049,1260,1261],{},"3",[635,1263,1264],{},"+",[591,1266,1248],{},[635,1268,1269],{},"−",[1049,1271,1272],{},"1",[595,1274,1275],{"encoding":597},"f(x) = x^3 + x - 1",[572,1277,1279,1306,1363,1382],{"className":1278,"ariaHidden":602},[601],[572,1280,1282,1285,1288,1291,1294,1297,1300,1303],{"className":1281},[606],[572,1283],{"className":1284,"style":657},[610],[572,1286,633],{"className":1287,"style":661},[615,616],[572,1289,638],{"className":1290},[665],[572,1292,1248],{"className":1293},[615,616],[572,1295,644],{"className":1296},[672],[572,1298],{"className":1299,"style":812},[811],[572,1301,1253],{"className":1302},[816],[572,1304],{"className":1305,"style":812},[811],[572,1307,1309,1313,1354,1357,1360],{"className":1308},[606],[572,1310],{"className":1311,"style":1312},[610],"height:0.8974em;vertical-align:-0.0833em;",[572,1314,1316,1319],{"className":1315},[615],[572,1317,1248],{"className":1318},[615,616],[572,1320,1323],{"className":1321},[1322],"msupsub",[572,1324,1327],{"className":1325},[1326],"vlist-t",[572,1328,1331],{"className":1329},[1330],"vlist-r",[572,1332,1336],{"className":1333,"style":1335},[1334],"vlist","height:0.8141em;",[572,1337,1339,1344],{"style":1338},"top:-3.063em;margin-right:0.05em;",[572,1340],{"className":1341,"style":1343},[1342],"pstrut","height:2.7em;",[572,1345,1351],{"className":1346},[1347,1348,1349,1350],"sizing","reset-size6","size3","mtight",[572,1352,1261],{"className":1353},[615,1350],[572,1355],{"className":1356,"style":1079},[811],[572,1358,1264],{"className":1359},[1083],[572,1361],{"className":1362,"style":1079},[811],[572,1364,1366,1370,1373,1376,1379],{"className":1365},[606],[572,1367],{"className":1368,"style":1369},[610],"height:0.6667em;vertical-align:-0.0833em;",[572,1371,1248],{"className":1372},[615,616],[572,1374],{"className":1375,"style":1079},[811],[572,1377,1269],{"className":1378},[1083],[572,1380],{"className":1381,"style":1079},[811],[572,1383,1385,1388],{"className":1384},[606],[572,1386],{"className":1387,"style":1120},[610],[572,1389,1272],{"className":1390},[615]," auf ",[572,1393,1395,1419],{"className":1394},[575],[572,1396,1398],{"className":1397},[579],[581,1399,1400],{"xmlns":583},[585,1401,1402,1416],{},[588,1403,1404,1407,1409,1411,1413],{},[635,1405,1406],{"stretchy":637},"[",[1049,1408,1051],{},[635,1410,1172],{"separator":602},[1049,1412,1272],{},[635,1414,1415],{"stretchy":637},"]",[595,1417,1418],{"encoding":597},"[0, 1]",[572,1420,1422],{"className":1421,"ariaHidden":602},[601],[572,1423,1425,1428,1431,1434,1437,1440,1443],{"className":1424},[606],[572,1426],{"className":1427,"style":657},[610],[572,1429,1406],{"className":1430},[665],[572,1432,1051],{"className":1433},[615],[572,1435,1172],{"className":1436},[1198],[572,1438],{"className":1439,"style":1202},[811],[572,1441,1272],{"className":1442},[615],[572,1444,1415],{"className":1445},[672],": Es ist ",[572,1448,1450,1480],{"className":1449},[575],[572,1451,1453],{"className":1452},[579],[581,1454,1455],{"xmlns":583},[585,1456,1457,1477],{},[588,1458,1459,1461,1463,1465,1467,1469,1471,1473,1475],{},[591,1460,633],{},[635,1462,638],{"stretchy":637},[1049,1464,1051],{},[635,1466,644],{"stretchy":637},[635,1468,1253],{},[635,1470,1269],{},[1049,1472,1272],{},[635,1474,775],{},[1049,1476,1051],{},[595,1478,1479],{"encoding":597},"f(0) = -1 \u003C 0",[572,1481,1483,1510,1532],{"className":1482,"ariaHidden":602},[601],[572,1484,1486,1489,1492,1495,1498,1501,1504,1507],{"className":1485},[606],[572,1487],{"className":1488,"style":657},[610],[572,1490,633],{"className":1491,"style":661},[615,616],[572,1493,638],{"className":1494},[665],[572,1496,1051],{"className":1497},[615],[572,1499,644],{"className":1500},[672],[572,1502],{"className":1503,"style":812},[811],[572,1505,1253],{"className":1506},[816],[572,1508],{"className":1509,"style":812},[811],[572,1511,1513,1517,1520,1523,1526,1529],{"className":1512},[606],[572,1514],{"className":1515,"style":1516},[610],"height:0.7278em;vertical-align:-0.0833em;",[572,1518,1269],{"className":1519},[615],[572,1521,1272],{"className":1522},[615],[572,1524],{"className":1525,"style":812},[811],[572,1527,775],{"className":1528},[816],[572,1530],{"className":1531,"style":812},[811],[572,1533,1535,1538],{"className":1534},[606],[572,1536],{"className":1537,"style":1120},[610],[572,1539,1051],{"className":1540},[615],[572,1542,1544,1572],{"className":1543},[575],[572,1545,1547],{"className":1546},[579],[581,1548,1549],{"xmlns":583},[585,1550,1551,1569],{},[588,1552,1553,1555,1557,1559,1561,1563,1565,1567],{},[591,1554,633],{},[635,1556,638],{"stretchy":637},[1049,1558,1272],{},[635,1560,644],{"stretchy":637},[635,1562,1253],{},[1049,1564,1272],{},[635,1566,861],{},[1049,1568,1051],{},[595,1570,1571],{"encoding":597},"f(1) = 1 > 0",[572,1573,1575,1602,1621],{"className":1574,"ariaHidden":602},[601],[572,1576,1578,1581,1584,1587,1590,1593,1596,1599],{"className":1577},[606],[572,1579],{"className":1580,"style":657},[610],[572,1582,633],{"className":1583,"style":661},[615,616],[572,1585,638],{"className":1586},[665],[572,1588,1272],{"className":1589},[615],[572,1591,644],{"className":1592},[672],[572,1594],{"className":1595,"style":812},[811],[572,1597,1253],{"className":1598},[816],[572,1600],{"className":1601,"style":812},[811],[572,1603,1605,1609,1612,1615,1618],{"className":1604},[606],[572,1606],{"className":1607,"style":1608},[610],"height:0.6835em;vertical-align:-0.0391em;",[572,1610,1272],{"className":1611},[615],[572,1613],{"className":1614,"style":812},[811],[572,1616,861],{"className":1617},[816],[572,1619],{"className":1620,"style":812},[811],[572,1622,1624,1627],{"className":1623},[606],[572,1625],{"className":1626,"style":1120},[610],[572,1628,1051],{"className":1629},[615],". Als Polynom ist ",[572,1632,1634,1647],{"className":1633},[575],[572,1635,1637],{"className":1636},[579],[581,1638,1639],{"xmlns":583},[585,1640,1641,1645],{},[588,1642,1643],{},[591,1644,633],{},[595,1646,633],{"encoding":597},[572,1648,1650],{"className":1649,"ariaHidden":602},[601],[572,1651,1653,1656],{"className":1652},[606],[572,1654],{"className":1655,"style":747},[610],[572,1657,633],{"className":1658,"style":661},[615,616]," stetig, also gibt es eine Nullstelle in ",[572,1661,1663,1685],{"className":1662},[575],[572,1664,1666],{"className":1665},[579],[581,1667,1668],{"xmlns":583},[585,1669,1670,1682],{},[588,1671,1672,1674,1676,1678,1680],{},[635,1673,638],{"stretchy":637},[1049,1675,1051],{},[635,1677,1172],{"separator":602},[1049,1679,1272],{},[635,1681,644],{"stretchy":637},[595,1683,1684],{"encoding":597},"(0, 1)",[572,1686,1688],{"className":1687,"ariaHidden":602},[601],[572,1689,1691,1694,1697,1700,1703,1706,1709],{"className":1690},[606],[572,1692],{"className":1693,"style":657},[610],[572,1695,638],{"className":1696},[665],[572,1698,1051],{"className":1699},[615],[572,1701,1172],{"className":1702},[1198],[572,1704],{"className":1705,"style":1202},[811],[572,1707,1272],{"className":1708},[615],[572,1710,644],{"className":1711},[672],". Bisektion liefert ",[572,1714,1716,1736],{"className":1715},[575],[572,1717,1719],{"className":1718},[579],[581,1720,1721],{"xmlns":583},[585,1722,1723,1733],{},[588,1724,1725,1727,1730],{},[591,1726,734],{},[635,1728,1729],{},"≈",[1049,1731,1732],{},"0,6823",[595,1734,1735],{"encoding":597},"\\xi \\approx 0{,}6823",[572,1737,1739,1757],{"className":1738,"ariaHidden":602},[601],[572,1740,1742,1745,1748,1751,1754],{"className":1741},[606],[572,1743],{"className":1744,"style":747},[610],[572,1746,734],{"className":1747,"style":751},[615,616],[572,1749],{"className":1750,"style":812},[811],[572,1752,1729],{"className":1753},[816],[572,1755],{"className":1756,"style":812},[811],[572,1758,1760,1764,1767,1773],{"className":1759},[606],[572,1761],{"className":1762,"style":1763},[610],"height:0.8389em;vertical-align:-0.1944em;",[572,1765,1051],{"className":1766},[615],[572,1768,1770],{"className":1769},[615],[572,1771,1172],{"className":1772},[1198],[572,1774,1776],{"className":1775},[615],"6823",".",[564,1779,1780,1781,1846,1847,1998,1999,2098,2099,673,2187,2433,2434,1777],{},"Die Gleichung ",[572,1782,1784,1808],{"className":1783},[575],[572,1785,1787],{"className":1786},[579],[581,1788,1789],{"xmlns":583},[585,1790,1791,1805],{},[588,1792,1793,1796,1799,1801,1803],{},[591,1794,1795],{},"cos",[635,1797,1798],{},"⁡",[591,1800,1248],{},[635,1802,1253],{},[591,1804,1248],{},[595,1806,1807],{"encoding":597},"\\cos x = x",[572,1809,1811,1837],{"className":1810,"ariaHidden":602},[601],[572,1812,1814,1818,1822,1825,1828,1831,1834],{"className":1813},[606],[572,1815],{"className":1816,"style":1817},[610],"height:0.4306em;",[572,1819,1795],{"className":1820},[1821],"mop",[572,1823],{"className":1824,"style":1202},[811],[572,1826,1248],{"className":1827},[615,616],[572,1829],{"className":1830,"style":812},[811],[572,1832,1253],{"className":1833},[816],[572,1835],{"className":1836,"style":812},[811],[572,1838,1840,1843],{"className":1839},[606],[572,1841],{"className":1842,"style":1817},[610],[572,1844,1248],{"className":1845},[615,616]," hat eine Lösung in ",[572,1848,1850,1879],{"className":1849},[575],[572,1851,1853],{"className":1852},[579],[581,1854,1855],{"xmlns":583},[585,1856,1857,1876],{},[588,1858,1859,1861,1863,1865,1874],{},[635,1860,1406],{"fence":602},[1049,1862,1051],{},[635,1864,1172],{"separator":602},[1866,1867,1868,1871],"mfrac",{},[591,1869,1870],{},"π",[1049,1872,1873],{},"2",[635,1875,1415],{"fence":602},[595,1877,1878],{"encoding":597},"\\left[0, \\frac{\\pi}{2}\\right]",[572,1880,1882],{"className":1881,"ariaHidden":602},[601],[572,1883,1885,1889],{"className":1884},[606],[572,1886],{"className":1887,"style":1888},[610],"height:1.2em;vertical-align:-0.35em;",[572,1890,1893,1903,1906,1909,1912,1992],{"className":1891},[1892],"minner",[572,1894,1898],{"className":1895,"style":1897},[665,1896],"delimcenter","top:0em;",[572,1899,1406],{"className":1900},[1901,1902],"delimsizing","size1",[572,1904,1051],{"className":1905},[615],[572,1907,1172],{"className":1908},[1198],[572,1910],{"className":1911,"style":1202},[811],[572,1913,1915,1919,1989],{"className":1914},[615],[572,1916],{"className":1917},[665,1918],"nulldelimiter",[572,1920,1922],{"className":1921},[1866],[572,1923,1926,1980],{"className":1924},[1326,1925],"vlist-t2",[572,1927,1929,1975],{"className":1928},[1330],[572,1930,1933,1949,1960],{"className":1931,"style":1932},[1334],"height:0.6954em;",[572,1934,1936,1940],{"style":1935},"top:-2.655em;",[572,1937],{"className":1938,"style":1939},[1342],"height:3em;",[572,1941,1943],{"className":1942},[1347,1348,1349,1350],[572,1944,1946],{"className":1945},[615,1350],[572,1947,1873],{"className":1948},[615,1350],[572,1950,1952,1955],{"style":1951},"top:-3.23em;",[572,1953],{"className":1954,"style":1939},[1342],[572,1956],{"className":1957,"style":1959},[1958],"frac-line","border-bottom-width:0.04em;",[572,1961,1963,1966],{"style":1962},"top:-3.394em;",[572,1964],{"className":1965,"style":1939},[1342],[572,1967,1969],{"className":1968},[1347,1348,1349,1350],[572,1970,1972],{"className":1971},[615,1350],[572,1973,1870],{"className":1974,"style":617},[615,616,1350],[572,1976,1979],{"className":1977},[1978],"vlist-s","​",[572,1981,1983],{"className":1982},[1330],[572,1984,1987],{"className":1985,"style":1986},[1334],"height:0.345em;",[572,1988],{},[572,1990],{"className":1991},[672,1918],[572,1993,1995],{"className":1994,"style":1897},[672,1896],[572,1996,1415],{"className":1997},[1901,1902],": Für ",[572,2000,2002,2035],{"className":2001},[575],[572,2003,2005],{"className":2004},[579],[581,2006,2007],{"xmlns":583},[585,2008,2009,2032],{},[588,2010,2011,2014,2016,2018,2020,2022,2024,2026,2028,2030],{},[591,2012,2013],{},"g",[635,2015,638],{"stretchy":637},[591,2017,1248],{},[635,2019,644],{"stretchy":637},[635,2021,1253],{},[591,2023,1795],{},[635,2025,1798],{},[591,2027,1248],{},[635,2029,1269],{},[591,2031,1248],{},[595,2033,2034],{"encoding":597},"g(x) = \\cos x - x",[572,2036,2038,2065,2089],{"className":2037,"ariaHidden":602},[601],[572,2039,2041,2044,2047,2050,2053,2056,2059,2062],{"className":2040},[606],[572,2042],{"className":2043,"style":657},[610],[572,2045,2013],{"className":2046,"style":617},[615,616],[572,2048,638],{"className":2049},[665],[572,2051,1248],{"className":2052},[615,616],[572,2054,644],{"className":2055},[672],[572,2057],{"className":2058,"style":812},[811],[572,2060,1253],{"className":2061},[816],[572,2063],{"className":2064,"style":812},[811],[572,2066,2068,2071,2074,2077,2080,2083,2086],{"className":2067},[606],[572,2069],{"className":2070,"style":1369},[610],[572,2072,1795],{"className":2073},[1821],[572,2075],{"className":2076,"style":1202},[811],[572,2078,1248],{"className":2079},[615,616],[572,2081],{"className":2082,"style":1079},[811],[572,2084,1269],{"className":2085},[1083],[572,2087],{"className":2088,"style":1079},[811],[572,2090,2092,2095],{"className":2091},[606],[572,2093],{"className":2094,"style":1817},[610],[572,2096,1248],{"className":2097},[615,616]," ist ",[572,2100,2102,2130],{"className":2101},[575],[572,2103,2105],{"className":2104},[579],[581,2106,2107],{"xmlns":583},[585,2108,2109,2127],{},[588,2110,2111,2113,2115,2117,2119,2121,2123,2125],{},[591,2112,2013],{},[635,2114,638],{"stretchy":637},[1049,2116,1051],{},[635,2118,644],{"stretchy":637},[635,2120,1253],{},[1049,2122,1272],{},[635,2124,861],{},[1049,2126,1051],{},[595,2128,2129],{"encoding":597},"g(0) = 1 > 0",[572,2131,2133,2160,2178],{"className":2132,"ariaHidden":602},[601],[572,2134,2136,2139,2142,2145,2148,2151,2154,2157],{"className":2135},[606],[572,2137],{"className":2138,"style":657},[610],[572,2140,2013],{"className":2141,"style":617},[615,616],[572,2143,638],{"className":2144},[665],[572,2146,1051],{"className":2147},[615],[572,2149,644],{"className":2150},[672],[572,2152],{"className":2153,"style":812},[811],[572,2155,1253],{"className":2156},[816],[572,2158],{"className":2159,"style":812},[811],[572,2161,2163,2166,2169,2172,2175],{"className":2162},[606],[572,2164],{"className":2165,"style":1608},[610],[572,2167,1272],{"className":2168},[615],[572,2170],{"className":2171,"style":812},[811],[572,2173,861],{"className":2174},[816],[572,2176],{"className":2177,"style":812},[811],[572,2179,2181,2184],{"className":2180},[606],[572,2182],{"className":2183,"style":1120},[610],[572,2185,1051],{"className":2186},[615],[572,2188,2190,2230],{"className":2189},[575],[572,2191,2193],{"className":2192},[579],[581,2194,2195],{"xmlns":583},[585,2196,2197,2227],{},[588,2198,2199,2201,2213,2215,2217,2223,2225],{},[591,2200,2013],{},[588,2202,2203,2205,2211],{},[635,2204,638],{"fence":602},[1866,2206,2207,2209],{},[591,2208,1870],{},[1049,2210,1873],{},[635,2212,644],{"fence":602},[635,2214,1253],{},[635,2216,1269],{},[1866,2218,2219,2221],{},[591,2220,1870],{},[1049,2222,1873],{},[635,2224,775],{},[1049,2226,1051],{},[595,2228,2229],{"encoding":597},"g\\left(\\frac{\\pi}{2}\\right) = -\\frac{\\pi}{2} \u003C 0",[572,2231,2233,2337,2424],{"className":2232,"ariaHidden":602},[601],[572,2234,2236,2239,2242,2245,2328,2331,2334],{"className":2235},[606],[572,2237],{"className":2238,"style":1888},[610],[572,2240,2013],{"className":2241,"style":617},[615,616],[572,2243],{"className":2244,"style":1202},[811],[572,2246,2248,2254,2322],{"className":2247},[1892],[572,2249,2251],{"className":2250,"style":1897},[665,1896],[572,2252,638],{"className":2253},[1901,1902],[572,2255,2257,2260,2319],{"className":2256},[615],[572,2258],{"className":2259},[665,1918],[572,2261,2263],{"className":2262},[1866],[572,2264,2266,2311],{"className":2265},[1326,1925],[572,2267,2269,2308],{"className":2268},[1330],[572,2270,2272,2286,2294],{"className":2271,"style":1932},[1334],[572,2273,2274,2277],{"style":1935},[572,2275],{"className":2276,"style":1939},[1342],[572,2278,2280],{"className":2279},[1347,1348,1349,1350],[572,2281,2283],{"className":2282},[615,1350],[572,2284,1873],{"className":2285},[615,1350],[572,2287,2288,2291],{"style":1951},[572,2289],{"className":2290,"style":1939},[1342],[572,2292],{"className":2293,"style":1959},[1958],[572,2295,2296,2299],{"style":1962},[572,2297],{"className":2298,"style":1939},[1342],[572,2300,2302],{"className":2301},[1347,1348,1349,1350],[572,2303,2305],{"className":2304},[615,1350],[572,2306,1870],{"className":2307,"style":617},[615,616,1350],[572,2309,1979],{"className":2310},[1978],[572,2312,2314],{"className":2313},[1330],[572,2315,2317],{"className":2316,"style":1986},[1334],[572,2318],{},[572,2320],{"className":2321},[672,1918],[572,2323,2325],{"className":2324,"style":1897},[672,1896],[572,2326,644],{"className":2327},[1901,1902],[572,2329],{"className":2330,"style":812},[811],[572,2332,1253],{"className":2333},[816],[572,2335],{"className":2336,"style":812},[811],[572,2338,2340,2344,2347,2415,2418,2421],{"className":2339},[606],[572,2341],{"className":2342,"style":2343},[610],"height:1.0404em;vertical-align:-0.345em;",[572,2345,1269],{"className":2346},[615],[572,2348,2350,2353,2412],{"className":2349},[615],[572,2351],{"className":2352},[665,1918],[572,2354,2356],{"className":2355},[1866],[572,2357,2359,2404],{"className":2358},[1326,1925],[572,2360,2362,2401],{"className":2361},[1330],[572,2363,2365,2379,2387],{"className":2364,"style":1932},[1334],[572,2366,2367,2370],{"style":1935},[572,2368],{"className":2369,"style":1939},[1342],[572,2371,2373],{"className":2372},[1347,1348,1349,1350],[572,2374,2376],{"className":2375},[615,1350],[572,2377,1873],{"className":2378},[615,1350],[572,2380,2381,2384],{"style":1951},[572,2382],{"className":2383,"style":1939},[1342],[572,2385],{"className":2386,"style":1959},[1958],[572,2388,2389,2392],{"style":1962},[572,2390],{"className":2391,"style":1939},[1342],[572,2393,2395],{"className":2394},[1347,1348,1349,1350],[572,2396,2398],{"className":2397},[615,1350],[572,2399,1870],{"className":2400,"style":617},[615,616,1350],[572,2402,1979],{"className":2403},[1978],[572,2405,2407],{"className":2406},[1330],[572,2408,2410],{"className":2409,"style":1986},[1334],[572,2411],{},[572,2413],{"className":2414},[672,1918],[572,2416],{"className":2417,"style":812},[811],[572,2419,775],{"className":2420},[816],[572,2422],{"className":2423,"style":812},[811],[572,2425,2427,2430],{"className":2426},[606],[572,2428],{"className":2429,"style":1120},[610],[572,2431,1051],{"className":2432},[615],". Die Lösung liegt bei ",[572,2435,2437,2456],{"className":2436},[575],[572,2438,2440],{"className":2439},[579],[581,2441,2442],{"xmlns":583},[585,2443,2444,2453],{},[588,2445,2446,2448,2450],{},[591,2447,734],{},[635,2449,1729],{},[1049,2451,2452],{},"0,7391",[595,2454,2455],{"encoding":597},"\\xi \\approx 0{,}7391",[572,2457,2459,2477],{"className":2458,"ariaHidden":602},[601],[572,2460,2462,2465,2468,2471,2474],{"className":2461},[606],[572,2463],{"className":2464,"style":747},[610],[572,2466,734],{"className":2467,"style":751},[615,616],[572,2469],{"className":2470,"style":812},[811],[572,2472,1729],{"className":2473},[816],[572,2475],{"className":2476,"style":812},[811],[572,2478,2480,2483,2486,2492],{"className":2479},[606],[572,2481],{"className":2482,"style":1763},[610],[572,2484,1051],{"className":2485},[615],[572,2487,2489],{"className":2488},[615],[572,2490,1172],{"className":2491},[1198],[572,2493,2495],{"className":2494},[615],"7391",[564,2497,2498,2499,2502,2503,673,2562,2613],{},"Jedes Polynom mit ",[568,2500,2501],{},"ungeradem"," Grad hat mindestens eine reelle Nullstelle, denn für ",[572,2504,2506,2529],{"className":2505},[575],[572,2507,2509],{"className":2508},[579],[581,2510,2511],{"xmlns":583},[585,2512,2513,2526],{},[588,2514,2515,2517,2520,2522],{},[591,2516,1248],{},[635,2518,2519],{},"→",[635,2521,1269],{},[591,2523,2525],{"mathvariant":2524},"normal","∞",[595,2527,2528],{"encoding":597},"x \\to -\\infty",[572,2530,2532,2550],{"className":2531,"ariaHidden":602},[601],[572,2533,2535,2538,2541,2544,2547],{"className":2534},[606],[572,2536],{"className":2537,"style":1817},[610],[572,2539,1248],{"className":2540},[615,616],[572,2542],{"className":2543,"style":812},[811],[572,2545,2519],{"className":2546},[816],[572,2548],{"className":2549,"style":812},[811],[572,2551,2553,2556,2559],{"className":2552},[606],[572,2554],{"className":2555,"style":1369},[610],[572,2557,1269],{"className":2558},[615],[572,2560,2525],{"className":2561},[615],[572,2563,2565,2583],{"className":2564},[575],[572,2566,2568],{"className":2567},[579],[581,2569,2570],{"xmlns":583},[585,2571,2572,2580],{},[588,2573,2574,2576,2578],{},[591,2575,1248],{},[635,2577,2519],{},[591,2579,2525],{"mathvariant":2524},[595,2581,2582],{"encoding":597},"x \\to \\infty",[572,2584,2586,2604],{"className":2585,"ariaHidden":602},[601],[572,2587,2589,2592,2595,2598,2601],{"className":2588},[606],[572,2590],{"className":2591,"style":1817},[610],[572,2593,1248],{"className":2594},[615,616],[572,2596],{"className":2597,"style":812},[811],[572,2599,2519],{"className":2600},[816],[572,2602],{"className":2603,"style":812},[811],[572,2605,2607,2610],{"className":2606},[606],[572,2608],{"className":2609,"style":1817},[610],[572,2611,2525],{"className":2612},[615]," gehen die Werte in entgegengesetzte Richtungen.",[559,2615,2617],{"id":2616},"typische-fehler","Typische Fehler",[2619,2620,2621,2963,3320],"ul",{},[2622,2623,2624,2625,2762,2763,673,2839,2905,2906,2098,2934,2962],"li",{},"Den Satz auf unstetige Funktionen anwenden. ",[572,2626,2628,2656],{"className":2627},[575],[572,2629,2631],{"className":2630},[579],[581,2632,2633],{"xmlns":583},[585,2634,2635,2653],{},[588,2636,2637,2639,2641,2643,2645,2647],{},[591,2638,633],{},[635,2640,638],{"stretchy":637},[591,2642,1248],{},[635,2644,644],{"stretchy":637},[635,2646,1253],{},[1866,2648,2649,2651],{},[1049,2650,1272],{},[591,2652,1248],{},[595,2654,2655],{"encoding":597},"f(x) = \\frac{1}{x}",[572,2657,2659,2686],{"className":2658,"ariaHidden":602},[601],[572,2660,2662,2665,2668,2671,2674,2677,2680,2683],{"className":2661},[606],[572,2663],{"className":2664,"style":657},[610],[572,2666,633],{"className":2667,"style":661},[615,616],[572,2669,638],{"className":2670},[665],[572,2672,1248],{"className":2673},[615,616],[572,2675,644],{"className":2676},[672],[572,2678],{"className":2679,"style":812},[811],[572,2681,1253],{"className":2682},[816],[572,2684],{"className":2685,"style":812},[811],[572,2687,2689,2693],{"className":2688},[606],[572,2690],{"className":2691,"style":2692},[610],"height:1.1901em;vertical-align:-0.345em;",[572,2694,2696,2699,2759],{"className":2695},[615],[572,2697],{"className":2698},[665,1918],[572,2700,2702],{"className":2701},[1866],[572,2703,2705,2751],{"className":2704},[1326,1925],[572,2706,2708,2748],{"className":2707},[1330],[572,2709,2712,2726,2734],{"className":2710,"style":2711},[1334],"height:0.8451em;",[572,2713,2714,2717],{"style":1935},[572,2715],{"className":2716,"style":1939},[1342],[572,2718,2720],{"className":2719},[1347,1348,1349,1350],[572,2721,2723],{"className":2722},[615,1350],[572,2724,1248],{"className":2725},[615,616,1350],[572,2727,2728,2731],{"style":1951},[572,2729],{"className":2730,"style":1939},[1342],[572,2732],{"className":2733,"style":1959},[1958],[572,2735,2736,2739],{"style":1962},[572,2737],{"className":2738,"style":1939},[1342],[572,2740,2742],{"className":2741},[1347,1348,1349,1350],[572,2743,2745],{"className":2744},[615,1350],[572,2746,1272],{"className":2747},[615,1350],[572,2749,1979],{"className":2750},[1978],[572,2752,2754],{"className":2753},[1330],[572,2755,2757],{"className":2756,"style":1986},[1334],[572,2758],{},[572,2760],{"className":2761},[672,1918]," hat ",[572,2764,2766,2794],{"className":2765},[575],[572,2767,2769],{"className":2768},[579],[581,2770,2771],{"xmlns":583},[585,2772,2773,2791],{},[588,2774,2775,2777,2779,2781,2783,2785,2787,2789],{},[591,2776,633],{},[635,2778,638],{"stretchy":637},[635,2780,1269],{},[1049,2782,1272],{},[635,2784,644],{"stretchy":637},[635,2786,1253],{},[635,2788,1269],{},[1049,2790,1272],{},[595,2792,2793],{"encoding":597},"f(-1) = -1",[572,2795,2797,2827],{"className":2796,"ariaHidden":602},[601],[572,2798,2800,2803,2806,2809,2812,2815,2818,2821,2824],{"className":2799},[606],[572,2801],{"className":2802,"style":657},[610],[572,2804,633],{"className":2805,"style":661},[615,616],[572,2807,638],{"className":2808},[665],[572,2810,1269],{"className":2811},[615],[572,2813,1272],{"className":2814},[615],[572,2816,644],{"className":2817},[672],[572,2819],{"className":2820,"style":812},[811],[572,2822,1253],{"className":2823},[816],[572,2825],{"className":2826,"style":812},[811],[572,2828,2830,2833,2836],{"className":2829},[606],[572,2831],{"className":2832,"style":1516},[610],[572,2834,1269],{"className":2835},[615],[572,2837,1272],{"className":2838},[615],[572,2840,2842,2866],{"className":2841},[575],[572,2843,2845],{"className":2844},[579],[581,2846,2847],{"xmlns":583},[585,2848,2849,2863],{},[588,2850,2851,2853,2855,2857,2859,2861],{},[591,2852,633],{},[635,2854,638],{"stretchy":637},[1049,2856,1272],{},[635,2858,644],{"stretchy":637},[635,2860,1253],{},[1049,2862,1272],{},[595,2864,2865],{"encoding":597},"f(1) = 1",[572,2867,2869,2896],{"className":2868,"ariaHidden":602},[601],[572,2870,2872,2875,2878,2881,2884,2887,2890,2893],{"className":2871},[606],[572,2873],{"className":2874,"style":657},[610],[572,2876,633],{"className":2877,"style":661},[615,616],[572,2879,638],{"className":2880},[665],[572,2882,1272],{"className":2883},[615],[572,2885,644],{"className":2886},[672],[572,2888],{"className":2889,"style":812},[811],[572,2891,1253],{"className":2892},[816],[572,2894],{"className":2895,"style":812},[811],[572,2897,2899,2902],{"className":2898},[606],[572,2900],{"className":2901,"style":1120},[610],[572,2903,1272],{"className":2904},[615],", aber keine Nullstelle. Bei ",[572,2907,2909,2922],{"className":2908},[575],[572,2910,2912],{"className":2911},[579],[581,2913,2914],{"xmlns":583},[585,2915,2916,2920],{},[588,2917,2918],{},[1049,2919,1051],{},[595,2921,1051],{"encoding":597},[572,2923,2925],{"className":2924,"ariaHidden":602},[601],[572,2926,2928,2931],{"className":2927},[606],[572,2929],{"className":2930,"style":1120},[610],[572,2932,1051],{"className":2933},[615],[572,2935,2937,2950],{"className":2936},[575],[572,2938,2940],{"className":2939},[579],[581,2941,2942],{"xmlns":583},[585,2943,2944,2948],{},[588,2945,2946],{},[591,2947,633],{},[595,2949,633],{"encoding":597},[572,2951,2953],{"className":2952,"ariaHidden":602},[601],[572,2954,2956,2959],{"className":2955},[606],[572,2957],{"className":2958,"style":747},[610],[572,2960,633],{"className":2961,"style":661},[615,616]," nicht definiert.",[2622,2964,2965,2966,2762,3154,3273,3274,1777],{},"Aus gleichen Vorzeichen auf „keine Nullstelle“ schließen. ",[572,2967,2969,3006],{"className":2968},[575],[572,2970,2972],{"className":2971},[579],[581,2973,2974],{"xmlns":583},[585,2975,2976,3003],{},[588,2977,2978,2980,2982,2984,2986,2988,2994,2996],{},[591,2979,633],{},[635,2981,638],{"stretchy":637},[591,2983,1248],{},[635,2985,644],{"stretchy":637},[635,2987,1253],{},[1255,2989,2990,2992],{},[591,2991,1248],{},[1049,2993,1873],{},[635,2995,1269],{},[1866,2997,2998,3000],{},[1049,2999,1272],{},[1049,3001,3002],{},"4",[595,3004,3005],{"encoding":597},"f(x) = x^2 - \\frac{1}{4}",[572,3007,3009,3036,3080],{"className":3008,"ariaHidden":602},[601],[572,3010,3012,3015,3018,3021,3024,3027,3030,3033],{"className":3011},[606],[572,3013],{"className":3014,"style":657},[610],[572,3016,633],{"className":3017,"style":661},[615,616],[572,3019,638],{"className":3020},[665],[572,3022,1248],{"className":3023},[615,616],[572,3025,644],{"className":3026},[672],[572,3028],{"className":3029,"style":812},[811],[572,3031,1253],{"className":3032},[816],[572,3034],{"className":3035,"style":812},[811],[572,3037,3039,3042,3071,3074,3077],{"className":3038},[606],[572,3040],{"className":3041,"style":1312},[610],[572,3043,3045,3048],{"className":3044},[615],[572,3046,1248],{"className":3047},[615,616],[572,3049,3051],{"className":3050},[1322],[572,3052,3054],{"className":3053},[1326],[572,3055,3057],{"className":3056},[1330],[572,3058,3060],{"className":3059,"style":1335},[1334],[572,3061,3062,3065],{"style":1338},[572,3063],{"className":3064,"style":1343},[1342],[572,3066,3068],{"className":3067},[1347,1348,1349,1350],[572,3069,1873],{"className":3070},[615,1350],[572,3072],{"className":3073,"style":1079},[811],[572,3075,1269],{"className":3076},[1083],[572,3078],{"className":3079,"style":1079},[811],[572,3081,3083,3086],{"className":3082},[606],[572,3084],{"className":3085,"style":2692},[610],[572,3087,3089,3092,3151],{"className":3088},[615],[572,3090],{"className":3091},[665,1918],[572,3093,3095],{"className":3094},[1866],[572,3096,3098,3143],{"className":3097},[1326,1925],[572,3099,3101,3140],{"className":3100},[1330],[572,3102,3104,3118,3126],{"className":3103,"style":2711},[1334],[572,3105,3106,3109],{"style":1935},[572,3107],{"className":3108,"style":1939},[1342],[572,3110,3112],{"className":3111},[1347,1348,1349,1350],[572,3113,3115],{"className":3114},[615,1350],[572,3116,3002],{"className":3117},[615,1350],[572,3119,3120,3123],{"style":1951},[572,3121],{"className":3122,"style":1939},[1342],[572,3124],{"className":3125,"style":1959},[1958],[572,3127,3128,3131],{"style":1962},[572,3129],{"className":3130,"style":1939},[1342],[572,3132,3134],{"className":3133},[1347,1348,1349,1350],[572,3135,3137],{"className":3136},[615,1350],[572,3138,1272],{"className":3139},[615,1350],[572,3141,1979],{"className":3142},[1978],[572,3144,3146],{"className":3145},[1330],[572,3147,3149],{"className":3148,"style":1986},[1334],[572,3150],{},[572,3152],{"className":3153},[672,1918],[572,3155,3157,3194],{"className":3156},[575],[572,3158,3160],{"className":3159},[579],[581,3161,3162],{"xmlns":583},[585,3163,3164,3191],{},[588,3165,3166,3168,3170,3172,3174,3176,3178,3180,3182,3184,3186,3188],{},[591,3167,633],{},[635,3169,638],{"stretchy":637},[635,3171,1269],{},[1049,3173,1272],{},[635,3175,644],{"stretchy":637},[635,3177,1253],{},[591,3179,633],{},[635,3181,638],{"stretchy":637},[1049,3183,1272],{},[635,3185,644],{"stretchy":637},[635,3187,1253],{},[1049,3189,3190],{},"0,75",[595,3192,3193],{"encoding":597},"f(-1) = f(1) = 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