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stetig genau dann, wenn für jede Folge ",[568,1092,1094,1122],{"className":1093},[571],[568,1095,1097],{"className":1096},[575],[577,1098,1099],{"xmlns":579},[581,1100,1101,1119],{},[584,1102,1103,1110,1113],{},[587,1104,1105,1107],{},[590,1106,592],{},[590,1108,1109],{},"n",[696,1111,1112],{},"→",[587,1114,1115,1117],{},[590,1116,592],{},[594,1118,596],{},[598,1120,1121],{"encoding":600},"x_n \\to x_0",[568,1123,1125,1184],{"className":1124,"ariaHidden":606},[605],[568,1126,1128,1131,1172,1177,1181],{"className":1127},[610],[568,1129],{"className":1130,"style":615},[614],[568,1132,1134,1137],{"className":1133},[619],[568,1135,592],{"className":1136},[619,623],[568,1138,1140],{"className":1139},[627],[568,1141,1143,1164],{"className":1142},[631,632],[568,1144,1146,1161],{"className":1145},[636],[568,1147,1150],{"className":1148,"style":1149},[640],"height:0.1514em;",[568,1151,1152,1155],{"style":644},[568,1153],{"className":1154,"style":649},[648],[568,1156,1158],{"className":1157},[653,654,655,656],[568,1159,1109],{"className":1160},[619,623,656],[568,1162,664],{"className":1163},[663],[568,1165,1167],{"className":1166},[636],[568,1168,1170],{"className":1169,"style":671},[640],[568,1171],{},[568,1173],{"className":1174,"style":1176},[1175],"mspace","margin-right:0.2778em;",[568,1178,1112],{"className":1179},[1180],"mrel",[568,1182],{"className":1183,"style":1176},[1175],[568,1185,1187,1190],{"className":1186},[610],[568,1188],{"className":1189,"style":615},[614],[568,1191,1193,1196],{"className":1192},[619],[568,1194,592],{"className":1195},[619,623],[568,1197,1199],{"className":1198},[627],[568,1200,1202,1222],{"className":1201},[631,632],[568,1203,1205,1219],{"className":1204},[636],[568,1206,1208],{"className":1207,"style":641},[640],[568,1209,1210,1213],{"style":644},[568,1211],{"className":1212,"style":649},[648],[568,1214,1216],{"className":1215},[653,654,655,656],[568,1217,596],{"className":1218},[619,656],[568,1220,664],{"className":1221},[663],[568,1223,1225],{"className":1224},[636],[568,1226,1228],{"className":1227,"style":671},[640],[568,1229],{}," in ",[568,1232,1234,1248],{"className":1233},[571],[568,1235,1237],{"className":1236},[575],[577,1238,1239],{"xmlns":579},[581,1240,1241,1246],{},[584,1242,1243],{},[590,1244,1245],{},"D",[598,1247,1245],{"encoding":600},[568,1249,1251],{"className":1250,"ariaHidden":606},[605],[568,1252,1254,1258],{"className":1253},[610],[568,1255],{"className":1256,"style":1257},[614],"height:0.6833em;",[568,1259,1245],{"className":1260,"style":1261},[619,623],"margin-right:0.0278em;"," auch ",[568,1264,1266,1304],{"className":1265},[571],[568,1267,1269],{"className":1268},[575],[577,1270,1271],{"xmlns":579},[581,1272,1273,1301],{},[584,1274,1275,1277,1279,1285,1287,1289,1291,1293,1299],{},[590,1276,694],{},[696,1278,699],{"stretchy":698},[587,1280,1281,1283],{},[590,1282,592],{},[590,1284,1109],{},[696,1286,704],{"stretchy":698},[696,1288,1112],{},[590,1290,694],{},[696,1292,699],{"stretchy":698},[587,1294,1295,1297],{},[590,1296,592],{},[594,1298,596],{},[696,1300,704],{"stretchy":698},[598,1302,1303],{"encoding":600},"f(x_n) \\to f(x_0)",[568,1305,1307,1371],{"className":1306,"ariaHidden":606},[605],[568,1308,1310,1313,1316,1319,1359,1362,1365,1368],{"className":1309},[610],[568,1311],{"className":1312,"style":717},[614],[568,1314,694],{"className":1315,"style":721},[619,623],[568,1317,699],{"className":1318},[725],[568,1320,1322,1325],{"className":1321},[619],[568,1323,592],{"className":1324},[619,623],[568,1326,1328],{"className":1327},[627],[568,1329,1331,1351],{"className":1330},[631,632],[568,1332,1334,1348],{"className":1333},[636],[568,1335,1337],{"className":1336,"style":1149},[640],[568,1338,1339,1342],{"style":644},[568,1340],{"className":1341,"style":649},[648],[568,1343,1345],{"className":1344},[653,654,655,656],[568,1346,1109],{"className":1347},[619,623,656],[568,1349,664],{"className":1350},[663],[568,1352,1354],{"className":1353},[636],[568,1355,1357],{"className":1356,"style":671},[640],[568,1358],{},[568,1360,704],{"className":1361},[732],[568,1363],{"className":1364,"style":1176},[1175],[568,1366,1112],{"className":1367},[1180],[568,1369],{"className":1370,"style":1176},[1175],[568,1372,1374,1377,1380,1383,1423],{"className":1373},[610],[568,1375],{"className":1376,"style":717},[614],[568,1378,694],{"className":1379,"style":721},[619,623],[568,1381,699],{"className":1382},[725],[568,1384,1386,1389],{"className":1385},[619],[568,1387,592],{"className":1388},[619,623],[568,1390,1392],{"className":1391},[627],[568,1393,1395,1415],{"className":1394},[631,632],[568,1396,1398,1412],{"className":1397},[636],[568,1399,1401],{"className":1400,"style":641},[640],[568,1402,1403,1406],{"style":644},[568,1404],{"className":1405,"style":649},[648],[568,1407,1409],{"className":1408},[653,654,655,656],[568,1410,596],{"className":1411},[619,656],[568,1413,664],{"className":1414},[663],[568,1416,1418],{"className":1417},[636],[568,1419,1421],{"className":1420,"style":671},[640],[568,1422],{},[568,1424,704],{"className":1425},[732]," gilt. Damit zeigt man Unstetigkeit oft leichter, weil eine einzige passende Folge genügt.",[564,1428,1429,1457,1458,1486,1487,1515,1516,1603,1604,1639,1640,1639,1672,1735,1736,1768],{},[568,1430,1432,1445],{"className":1431},[571],[568,1433,1435],{"className":1434},[575],[577,1436,1437],{"xmlns":579},[581,1438,1439,1443],{},[584,1440,1441],{},[590,1442,694],{},[598,1444,694],{"encoding":600},[568,1446,1448],{"className":1447,"ariaHidden":606},[605],[568,1449,1451,1454],{"className":1450},[610],[568,1452],{"className":1453,"style":1016},[614],[568,1455,694],{"className":1456,"style":721},[619,623]," heißt stetig auf ",[568,1459,1461,1474],{"className":1460},[571],[568,1462,1464],{"className":1463},[575],[577,1465,1466],{"xmlns":579},[581,1467,1468,1472],{},[584,1469,1470],{},[590,1471,1245],{},[598,1473,1245],{"encoding":600},[568,1475,1477],{"className":1476,"ariaHidden":606},[605],[568,1478,1480,1483],{"className":1479},[610],[568,1481],{"className":1482,"style":1257},[614],[568,1484,1245],{"className":1485,"style":1261},[619,623],", wenn sie an jeder Stelle von ",[568,1488,1490,1503],{"className":1489},[571],[568,1491,1493],{"className":1492},[575],[577,1494,1495],{"xmlns":579},[581,1496,1497,1501],{},[584,1498,1499],{},[590,1500,1245],{},[598,1502,1245],{"encoding":600},[568,1504,1506],{"className":1505,"ariaHidden":606},[605],[568,1507,1509,1512],{"className":1508},[610],[568,1510],{"className":1511,"style":1257},[614],[568,1513,1245],{"className":1514,"style":1261},[619,623]," stetig ist. Summen, Produkte, Quotienten (mit Nenner ",[568,1517,1519,1537],{"className":1518},[571],[568,1520,1522],{"className":1521},[575],[577,1523,1524],{"xmlns":579},[581,1525,1526,1534],{},[584,1527,1528,1532],{},[696,1529,1531],{"mathvariant":1530},"normal","≠",[594,1533,596],{},[598,1535,1536],{"encoding":600},"\\neq 0",[568,1538,1540,1593],{"className":1539,"ariaHidden":606},[605],[568,1541,1543,1546,1590],{"className":1542},[610],[568,1544],{"className":1545,"style":1016},[614],[568,1547,1549,1582,1586],{"className":1548},[1180],[568,1550,1552],{"className":1551},[1180],[568,1553,1556],{"className":1554},[619,1555],"vbox",[568,1557,1560],{"className":1558},[1559],"thinbox",[568,1561,1564,1567,1578],{"className":1562},[1563],"rlap",[568,1565],{"className":1566,"style":1016},[614],[568,1568,1571],{"className":1569},[1570],"inner",[568,1572,1574],{"className":1573},[619],[568,1575,1577],{"className":1576},[1180],"",[568,1579],{"className":1580},[1581],"fix",[568,1583],{"className":1584},[1175,1585],"nobreak",[568,1587,1589],{"className":1588},[1180],"=",[568,1591],{"className":1592,"style":1176},[1175],[568,1594,1596,1600],{"className":1595},[610],[568,1597],{"className":1598,"style":1599},[614],"height:0.6444em;",[568,1601,596],{"className":1602},[619],") und Verkettungen stetiger Funktionen sind wieder stetig. Polynome, ",[568,1605,1607,1625],{"className":1606},[571],[568,1608,1610],{"className":1609},[575],[577,1611,1612],{"xmlns":579},[581,1613,1614,1622],{},[584,1615,1616,1619],{},[590,1617,1618],{},"sin",[696,1620,1621],{},"⁡",[598,1623,1624],{"encoding":600},"\\sin",[568,1626,1628],{"className":1627,"ariaHidden":606},[605],[568,1629,1631,1635],{"className":1630},[610],[568,1632],{"className":1633,"style":1634},[614],"height:0.6679em;",[568,1636,1618],{"className":1637},[1638],"mop",", ",[568,1641,1643,1660],{"className":1642},[571],[568,1644,1646],{"className":1645},[575],[577,1647,1648],{"xmlns":579},[581,1649,1650,1657],{},[584,1651,1652,1655],{},[590,1653,1654],{},"cos",[696,1656,1621],{},[598,1658,1659],{"encoding":600},"\\cos",[568,1661,1663],{"className":1662,"ariaHidden":606},[605],[568,1664,1666,1669],{"className":1665},[610],[568,1667],{"className":1668,"style":845},[614],[568,1670,1654],{"className":1671},[1638],[568,1673,1675,1695],{"className":1674},[571],[568,1676,1678],{"className":1677},[575],[577,1679,1680],{"xmlns":579},[581,1681,1682,1692],{},[584,1683,1684],{},[1685,1686,1687,1690],"msup",{},[590,1688,1689],{},"e",[590,1691,592],{},[598,1693,1694],{"encoding":600},"e^x",[568,1696,1698],{"className":1697,"ariaHidden":606},[605],[568,1699,1701,1705],{"className":1700},[610],[568,1702],{"className":1703,"style":1704},[614],"height:0.6644em;",[568,1706,1708,1711],{"className":1707},[619],[568,1709,1689],{"className":1710},[619,623],[568,1712,1714],{"className":1713},[627],[568,1715,1717],{"className":1716},[631],[568,1718,1720],{"className":1719},[636],[568,1721,1723],{"className":1722,"style":1704},[640],[568,1724,1726,1729],{"style":1725},"top:-3.063em;margin-right:0.05em;",[568,1727],{"className":1728,"style":649},[648],[568,1730,1732],{"className":1731},[653,654,655,656],[568,1733,592],{"className":1734},[619,623,656]," und ",[568,1737,1739,1756],{"className":1738},[571],[568,1740,1742],{"className":1741},[575],[577,1743,1744],{"xmlns":579},[581,1745,1746,1753],{},[584,1747,1748,1751],{},[590,1749,1750],{},"ln",[696,1752,1621],{},[598,1754,1755],{"encoding":600},"\\ln",[568,1757,1759],{"className":1758,"ariaHidden":606},[605],[568,1760,1762,1765],{"className":1761},[610],[568,1763],{"className":1764,"style":978},[614],[568,1766,1750],{"className":1767},[1638]," sind auf ihrem Definitionsbereich stetig.",[559,1770,1772],{"id":1771},"beispiele","Beispiele",[564,1774,1775,1874,1875,2117,2118,2249,2250,2375,2376,2557],{},[568,1776,1778,1811],{"className":1777},[571],[568,1779,1781],{"className":1780},[575],[577,1782,1783],{"xmlns":579},[581,1784,1785,1808],{},[584,1786,1787,1789,1791,1793,1795,1797,1800,1802,1805],{},[590,1788,694],{},[696,1790,699],{"stretchy":698},[590,1792,592],{},[696,1794,704],{"stretchy":698},[696,1796,1589],{},[594,1798,1799],{},"3",[590,1801,592],{},[696,1803,1804],{},"+",[594,1806,1807],{},"1",[598,1809,1810],{"encoding":600},"f(x) = 3x + 1",[568,1812,1814,1841,1865],{"className":1813,"ariaHidden":606},[605],[568,1815,1817,1820,1823,1826,1829,1832,1835,1838],{"className":1816},[610],[568,1818],{"className":1819,"style":717},[614],[568,1821,694],{"className":1822,"style":721},[619,623],[568,1824,699],{"className":1825},[725],[568,1827,592],{"className":1828},[619,623],[568,1830,704],{"className":1831},[732],[568,1833],{"className":1834,"style":1176},[1175],[568,1836,1589],{"className":1837},[1180],[568,1839],{"className":1840,"style":1176},[1175],[568,1842,1844,1848,1851,1854,1858,1862],{"className":1843},[610],[568,1845],{"className":1846,"style":1847},[614],"height:0.7278em;vertical-align:-0.0833em;",[568,1849,1799],{"className":1850},[619],[568,1852,592],{"className":1853},[619,623],[568,1855],{"className":1856,"style":1857},[1175],"margin-right:0.2222em;",[568,1859,1804],{"className":1860},[1861],"mbin",[568,1863],{"className":1864,"style":1857},[1175],[568,1866,1868,1871],{"className":1867},[610],[568,1869],{"className":1870,"style":1599},[614],[568,1872,1807],{"className":1873},[619]," ist überall stetig. Es gilt ",[568,1876,1878,1940],{"className":1877},[571],[568,1879,1881],{"className":1880},[575],[577,1882,1883],{"xmlns":579},[581,1884,1885,1937],{},[584,1886,1887,1890,1892,1894,1896,1898,1901,1903,1905,1911,1913,1915,1917,1919,1923,1925,1927,1929,1935],{},[590,1888,1889],{"mathvariant":1530},"∣",[590,1891,694],{},[696,1893,699],{"stretchy":698},[590,1895,592],{},[696,1897,704],{"stretchy":698},[696,1899,1900],{},"−",[590,1902,694],{},[696,1904,699],{"stretchy":698},[587,1906,1907,1909],{},[590,1908,592],{},[594,1910,596],{},[696,1912,704],{"stretchy":698},[590,1914,1889],{"mathvariant":1530},[696,1916,1589],{},[594,1918,1799],{},[1920,1921,1922],"mtext",{}," ",[590,1924,1889],{"mathvariant":1530},[590,1926,592],{},[696,1928,1900],{},[587,1930,1931,1933],{},[590,1932,592],{},[594,1934,596],{},[590,1936,1889],{"mathvariant":1530},[598,1938,1939],{"encoding":600},"|f(x) - f(x_0)| = 3\\,|x - x_0|",[568,1941,1943,1973,2040,2068],{"className":1942,"ariaHidden":606},[605],[568,1944,1946,1949,1952,1955,1958,1961,1964,1967,1970],{"className":1945},[610],[568,1947],{"className":1948,"style":717},[614],[568,1950,1889],{"className":1951},[619],[568,1953,694],{"className":1954,"style":721},[619,623],[568,1956,699],{"className":1957},[725],[568,1959,592],{"className":1960},[619,623],[568,1962,704],{"className":1963},[732],[568,1965],{"className":1966,"style":1857},[1175],[568,1968,1900],{"className":1969},[1861],[568,1971],{"className":1972,"style":1857},[1175],[568,1974,1976,1979,1982,1985,2025,2028,2031,2034,2037],{"className":1975},[610],[568,1977],{"className":1978,"style":717},[614],[568,1980,694],{"className":1981,"style":721},[619,623],[568,1983,699],{"className":1984},[725],[568,1986,1988,1991],{"className":1987},[619],[568,1989,592],{"className":1990},[619,623],[568,1992,1994],{"className":1993},[627],[568,1995,1997,2017],{"className":1996},[631,632],[568,1998,2000,2014],{"className":1999},[636],[568,2001,2003],{"className":2002,"style":641},[640],[568,2004,2005,2008],{"style":644},[568,2006],{"className":2007,"style":649},[648],[568,2009,2011],{"className":2010},[653,654,655,656],[568,2012,596],{"className":2013},[619,656],[568,2015,664],{"className":2016},[663],[568,2018,2020],{"className":2019},[636],[568,2021,2023],{"className":2022,"style":671},[640],[568,2024],{},[568,2026,704],{"className":2027},[732],[568,2029,1889],{"className":2030},[619],[568,2032],{"className":2033,"style":1176},[1175],[568,2035,1589],{"className":2036},[1180],[568,2038],{"className":2039,"style":1176},[1175],[568,2041,2043,2046,2049,2053,2056,2059,2062,2065],{"className":2042},[610],[568,2044],{"className":2045,"style":717},[614],[568,2047,1799],{"className":2048},[619],[568,2050],{"className":2051,"style":2052},[1175],"margin-right:0.1667em;",[568,2054,1889],{"className":2055},[619],[568,2057,592],{"className":2058},[619,623],[568,2060],{"className":2061,"style":1857},[1175],[568,2063,1900],{"className":2064},[1861],[568,2066],{"className":2067,"style":1857},[1175],[568,2069,2071,2074,2114],{"className":2070},[610],[568,2072],{"className":2073,"style":717},[614],[568,2075,2077,2080],{"className":2076},[619],[568,2078,592],{"className":2079},[619,623],[568,2081,2083],{"className":2082},[627],[568,2084,2086,2106],{"className":2085},[631,632],[568,2087,2089,2103],{"className":2088},[636],[568,2090,2092],{"className":2091,"style":641},[640],[568,2093,2094,2097],{"style":644},[568,2095],{"className":2096,"style":649},[648],[568,2098,2100],{"className":2099},[653,654,655,656],[568,2101,596],{"className":2102},[619,656],[568,2104,664],{"className":2105},[663],[568,2107,2109],{"className":2108},[636],[568,2110,2112],{"className":2111,"style":671},[640],[568,2113],{},[568,2115,1889],{"className":2116},[619],". Mit ",[568,2119,2121,2144],{"className":2120},[571],[568,2122,2124],{"className":2123},[575],[577,2125,2126],{"xmlns":579},[581,2127,2128,2141],{},[584,2129,2130,2132,2134],{},[590,2131,965],{},[696,2133,1589],{},[2135,2136,2137,2139],"mfrac",{},[590,2138,934],{},[594,2140,1799],{},[598,2142,2143],{"encoding":600},"\\delta = 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\\delta",[568,2285,2287,2308,2366],{"className":2286,"ariaHidden":606},[605],[568,2288,2290,2293,2296,2299,2302,2305],{"className":2289},[610],[568,2291],{"className":2292,"style":717},[614],[568,2294,1889],{"className":2295},[619],[568,2297,592],{"className":2298},[619,623],[568,2300],{"className":2301,"style":1857},[1175],[568,2303,1900],{"className":2304},[1861],[568,2306],{"className":2307,"style":1857},[1175],[568,2309,2311,2314,2354,2357,2360,2363],{"className":2310},[610],[568,2312],{"className":2313,"style":717},[614],[568,2315,2317,2320],{"className":2316},[619],[568,2318,592],{"className":2319},[619,623],[568,2321,2323],{"className":2322},[627],[568,2324,2326,2346],{"className":2325},[631,632],[568,2327,2329,2343],{"className":2328},[636],[568,2330,2332],{"className":2331,"style":641},[640],[568,2333,2334,2337],{"style":644},[568,2335],{"className":2336,"style":649},[648],[568,2338,2340],{"className":2339},[653,654,655,656],[568,2341,596],{"className":2342},[619,656],[568,2344,664],{"className":2345},[663],[568,2347,2349],{"className":2348},[636],[568,2350,2352],{"className":2351,"style":671},[640],[568,2353],{},[568,2355,1889],{"className":2356},[619],[568,2358],{"className":2359,"style":1176},[1175],[568,2361,2278],{"className":2362},[1180],[568,2364],{"className":2365,"style":1176},[1175],[568,2367,2369,2372],{"className":2368},[610],[568,2370],{"className":2371,"style":978},[614],[568,2373,965],{"className":2374,"style":982},[619,623]," sofort ",[568,2377,2379,2427],{"className":2378},[571],[568,2380,2382],{"className":2381},[575],[577,2383,2384],{"xmlns":579},[581,2385,2386,2424],{},[584,2387,2388,2390,2392,2394,2396,2398,2400,2402,2404,2410,2412,2414,2416,2418,2420,2422],{},[590,2389,1889],{"mathvariant":1530},[590,2391,694],{},[696,2393,699],{"stretchy":698},[590,2395,592],{},[696,2397,704],{"stretchy":698},[696,2399,1900],{},[590,2401,694],{},[696,2403,699],{"stretchy":698},[587,2405,2406,2408],{},[590,2407,592],{},[594,2409,596],{},[696,2411,704],{"stretchy":698},[590,2413,1889],{"mathvariant":1530},[696,2415,2278],{},[594,2417,1799],{},[590,2419,965],{},[696,2421,1589],{},[590,2423,934],{},[598,2425,2426],{"encoding":600},"|f(x) - f(x_0)| \u003C 3\\delta = 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= 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stetig. Man zerlegt ",[568,2752,2754,2806],{"className":2753},[571],[568,2755,2757],{"className":2756},[575],[577,2758,2759],{"xmlns":579},[581,2760,2761,2803],{},[584,2762,2763,2765,2771,2773,2776,2778,2780,2782,2784,2786,2788,2790,2793,2795,2797,2799,2801],{},[590,2764,1889],{"mathvariant":1530},[1685,2766,2767,2769],{},[590,2768,592],{},[594,2770,2588],{},[696,2772,1900],{},[594,2774,2775],{},"4",[590,2777,1889],{"mathvariant":1530},[696,2779,1589],{},[590,2781,1889],{"mathvariant":1530},[590,2783,592],{},[696,2785,1900],{},[594,2787,2588],{},[590,2789,1889],{"mathvariant":1530},[696,2791,2792],{},"⋅",[590,2794,1889],{"mathvariant":1530},[590,2796,592],{},[696,2798,1804],{},[594,2800,2588],{},[590,2802,1889],{"mathvariant":1530},[598,2804,2805],{"encoding":600},"|x^2 - 4| = |x - 2| \\cdot |x + 2|",[568,2807,2809,2857,2876,2897,2916,2937],{"className":2808,"ariaHidden":606},[605],[568,2810,2812,2816,2819,2848,2851,2854],{"className":2811},[610],[568,2813],{"className":2814,"style":2815},[614],"height:1.0641em;vertical-align:-0.25em;",[568,2817,1889],{"className":2818},[619],[568,2820,2822,2825],{"className":2821},[619],[568,2823,592],{"className":2824},[619,623],[568,2826,2828],{"className":2827},[627],[568,2829,2831],{"className":2830},[631],[568,2832,2834],{"className":2833},[636],[568,2835,2837],{"className":2836,"style":2628},[640],[568,2838,2839,2842],{"style":1725},[568,2840],{"className":2841,"style":649},[648],[568,2843,2845],{"className":2844},[653,654,655,656],[568,2846,2588],{"className":2847},[619,656],[568,2849],{"className":2850,"style":1857},[1175],[568,2852,1900],{"className":2853},[1861],[568,2855],{"className":2856,"style":1857},[1175],[568,2858,2860,2863,2867,2870,2873],{"className":2859},[610],[568,2861],{"className":2862,"style":717},[614],[568,2864,2866],{"className":2865},[619],"4∣",[568,2868],{"className":2869,"style":1176},[1175],[568,2871,1589],{"className":2872},[1180],[568,2874],{"className":2875,"style":1176},[1175],[568,2877,2879,2882,2885,2888,2891,2894],{"className":2878},[610],[568,2880],{"className":2881,"style":717},[614],[568,2883,1889],{"className":2884},[619],[568,2886,592],{"className":2887},[619,623],[568,2889],{"className":2890,"style":1857},[1175],[568,2892,1900],{"className":2893},[1861],[568,2895],{"className":2896,"style":1857},[1175],[568,2898,2900,2903,2907,2910,2913],{"className":2899},[610],[568,2901],{"className":2902,"style":717},[614],[568,2904,2906],{"className":2905},[619],"2∣",[568,2908],{"className":2909,"style":1857},[1175],[568,2911,2792],{"className":2912},[1861],[568,2914],{"className":2915,"style":1857},[1175],[568,2917,2919,2922,2925,2928,2931,2934],{"className":2918},[610],[568,2920],{"className":2921,"style":717},[614],[568,2923,1889],{"className":2924},[619],[568,2926,592],{"className":2927},[619,623],[568,2929],{"className":2930,"style":1857},[1175],[568,2932,1804],{"className":2933},[1861],[568,2935],{"className":2936,"style":1857},[1175],[568,2938,2940,2943],{"className":2939},[610],[568,2941],{"className":2942,"style":717},[614],[568,2944,2906],{"className":2945},[619],". Wählt man vorab ",[568,2948,2950,2969],{"className":2949},[571],[568,2951,2953],{"className":2952},[575],[577,2954,2955],{"xmlns":579},[581,2956,2957,2966],{},[584,2958,2959,2961,2964],{},[590,2960,965],{},[696,2962,2963],{},"≤",[594,2965,1807],{},[598,2967,2968],{"encoding":600},"\\delta \\leq 1",[568,2970,2972,2991],{"className":2971,"ariaHidden":606},[605],[568,2973,2975,2979,2982,2985,2988],{"className":2974},[610],[568,2976],{"className":2977,"style":2978},[614],"height:0.8304em;vertical-align:-0.136em;",[568,2980,965],{"className":2981,"style":982},[619,623],[568,2983],{"className":2984,"style":1176},[1175],[568,2986,2963],{"className":2987},[1180],[568,2989],{"className":2990,"style":1176},[1175],[568,2992,2994,2997],{"className":2993},[610],[568,2995],{"className":2996,"style":1599},[614],[568,2998,1807],{"className":2999},[619],", liegt ",[568,3002,3004,3017],{"className":3003},[571],[568,3005,3007],{"className":3006},[575],[577,3008,3009],{"xmlns":579},[581,3010,3011,3015],{},[584,3012,3013],{},[590,3014,592],{},[598,3016,592],{"encoding":600},[568,3018,3020],{"className":3019,"ariaHidden":606},[605],[568,3021,3023,3026],{"className":3022},[610],[568,3024],{"className":3025,"style":845},[614],[568,3027,592],{"className":3028},[619,623],[568,3030,3032,3055],{"className":3031},[571],[568,3033,3035],{"className":3034},[575],[577,3036,3037],{"xmlns":579},[581,3038,3039,3052],{},[584,3040,3041,3043,3045,3048,3050],{},[696,3042,699],{"stretchy":698},[594,3044,1807],{},[696,3046,3047],{"separator":606},",",[594,3049,1799],{},[696,3051,704],{"stretchy":698},[598,3053,3054],{"encoding":600},"(1, 3)",[568,3056,3058],{"className":3057,"ariaHidden":606},[605],[568,3059,3061,3064,3067,3070,3074,3077,3080],{"className":3060},[610],[568,3062],{"className":3063,"style":717},[614],[568,3065,699],{"className":3066},[725],[568,3068,1807],{"className":3069},[619],[568,3071,3047],{"className":3072},[3073],"mpunct",[568,3075],{"className":3076,"style":2052},[1175],[568,3078,1799],{"className":3079},[619],[568,3081,704],{"className":3082},[732]," und damit ",[568,3085,3087,3114],{"className":3086},[571],[568,3088,3090],{"className":3089},[575],[577,3091,3092],{"xmlns":579},[581,3093,3094,3111],{},[584,3095,3096,3098,3100,3102,3104,3106,3108],{},[590,3097,1889],{"mathvariant":1530},[590,3099,592],{},[696,3101,1804],{},[594,3103,2588],{},[590,3105,1889],{"mathvariant":1530},[696,3107,2278],{},[594,3109,3110],{},"5",[598,3112,3113],{"encoding":600},"|x + 2| \u003C 5",[568,3115,3117,3138,3156],{"className":3116,"ariaHidden":606},[605],[568,3118,3120,3123,3126,3129,3132,3135],{"className":3119},[610],[568,3121],{"className":3122,"style":717},[614],[568,3124,1889],{"className":3125},[619],[568,3127,592],{"className":3128},[619,623],[568,3130],{"className":3131,"style":1857},[1175],[568,3133,1804],{"className":3134},[1861],[568,3136],{"className":3137,"style":1857},[1175],[568,3139,3141,3144,3147,3150,3153],{"className":3140},[610],[568,3142],{"className":3143,"style":717},[614],[568,3145,2906],{"className":3146},[619],[568,3148],{"className":3149,"style":1176},[1175],[568,3151,2278],{"className":3152},[1180],[568,3154],{"className":3155,"style":1176},[1175],[568,3157,3159,3162],{"className":3158},[610],[568,3160],{"className":3161,"style":1599},[614],[568,3163,3110],{"className":3164},[619],". Also passt ",[568,3167,3169,3206],{"className":3168},[571],[568,3170,3172],{"className":3171},[575],[577,3173,3174],{"xmlns":579},[581,3175,3176,3203],{},[584,3177,3178,3180,3182,3185,3187],{},[590,3179,965],{},[696,3181,1589],{},[590,3183,3184],{},"min",[696,3186,1621],{},[584,3188,3189,3191,3193,3195,3201],{},[696,3190,699],{"fence":606},[594,3192,1807],{},[696,3194,3047],{"separator":606},[2135,3196,3197,3199],{},[590,3198,934],{},[594,3200,3110],{},[696,3202,704],{"fence":606},[598,3204,3205],{"encoding":600},"\\delta = \\min\\left(1, \\frac{\\varepsilon}{5}\\right)",[568,3207,3209,3227],{"className":3208,"ariaHidden":606},[605],[568,3210,3212,3215,3218,3221,3224],{"className":3211},[610],[568,3213],{"className":3214,"style":978},[614],[568,3216,965],{"className":3217,"style":982},[619,623],[568,3219],{"className":3220,"style":1176},[1175],[568,3222,1589],{"className":3223},[1180],[568,3225],{"className":3226,"style":1176},[1175],[568,3228,3230,3234,3237,3240],{"className":3229},[610],[568,3231],{"className":3232,"style":3233},[614],"height:1.2em;vertical-align:-0.35em;",[568,3235,3184],{"className":3236},[1638],[568,3238],{"className":3239,"style":2052},[1175],[568,3241,3244,3254,3257,3260,3263,3331],{"className":3242},[3243],"minner",[568,3245,3249],{"className":3246,"style":3248},[725,3247],"delimcenter","top:0em;",[568,3250,699],{"className":3251},[3252,3253],"delimsizing","size1",[568,3255,1807],{"className":3256},[619],[568,3258,3047],{"className":3259},[3073],[568,3261],{"className":3262,"style":2052},[1175],[568,3264,3266,3269,3328],{"className":3265},[619],[568,3267],{"className":3268},[725,2178],[568,3270,3272],{"className":3271},[2135],[568,3273,3275,3320],{"className":3274},[631,632],[568,3276,3278,3317],{"className":3277},[636],[568,3279,3281,3295,3303],{"className":3280,"style":2191},[640],[568,3282,3283,3286],{"style":2194},[568,3284],{"className":3285,"style":2198},[648],[568,3287,3289],{"className":3288},[653,654,655,656],[568,3290,3292],{"className":3291},[619,656],[568,3293,3110],{"className":3294},[619,656],[568,3296,3297,3300],{"style":2210},[568,3298],{"className":3299,"style":2198},[648],[568,3301],{"className":3302,"style":2218},[2217],[568,3304,3305,3308],{"style":2221},[568,3306],{"className":3307,"style":2198},[648],[568,3309,3311],{"className":3310},[653,654,655,656],[568,3312,3314],{"className":3313},[619,656],[568,3315,934],{"className":3316},[619,623,656],[568,3318,664],{"className":3319},[663],[568,3321,3323],{"className":3322},[636],[568,3324,3326],{"className":3325,"style":2243},[640],[568,3327],{},[568,3329],{"className":3330},[732,2178],[568,3332,3334],{"className":3333,"style":3248},[732,3247],[568,3335,704],{"className":3336},[3252,3253],[564,3338,3339,3340,3402,3403,3465,3466,1735,3594,3728,3729,2557],{},"Für ",[568,3341,3343,3362],{"className":3342},[571],[568,3344,3346],{"className":3345},[575],[577,3347,3348],{"xmlns":579},[581,3349,3350,3359],{},[584,3351,3352,3354,3356],{},[590,3353,934],{},[696,3355,1589],{},[594,3357,3358],{},"0,1",[598,3360,3361],{"encoding":600},"\\varepsilon = 0{,}1",[568,3363,3365,3383],{"className":3364,"ariaHidden":606},[605],[568,3366,3368,3371,3374,3377,3380],{"className":3367},[610],[568,3369],{"className":3370,"style":845},[614],[568,3372,934],{"className":3373},[619,623],[568,3375],{"className":3376,"style":1176},[1175],[568,3378,1589],{"className":3379},[1180],[568,3381],{"className":3382,"style":1176},[1175],[568,3384,3386,3390,3393,3399],{"className":3385},[610],[568,3387],{"className":3388,"style":3389},[614],"height:0.8389em;vertical-align:-0.1944em;",[568,3391,596],{"className":3392},[619],[568,3394,3396],{"className":3395},[619],[568,3397,3047],{"className":3398},[3073],[568,3400,1807],{"className":3401},[619]," ergibt das ",[568,3404,3406,3425],{"className":3405},[571],[568,3407,3409],{"className":3408},[575],[577,3410,3411],{"xmlns":579},[581,3412,3413,3422],{},[584,3414,3415,3417,3419],{},[590,3416,965],{},[696,3418,1589],{},[594,3420,3421],{},"0,02",[598,3423,3424],{"encoding":600},"\\delta = 0{,}02",[568,3426,3428,3446],{"className":3427,"ariaHidden":606},[605],[568,3429,3431,3434,3437,3440,3443],{"className":3430},[610],[568,3432],{"className":3433,"style":978},[614],[568,3435,965],{"className":3436,"style":982},[619,623],[568,3438],{"className":3439,"style":1176},[1175],[568,3441,1589],{"className":3442},[1180],[568,3444],{"className":3445,"style":1176},[1175],[568,3447,3449,3452,3455,3461],{"className":3448},[610],[568,3450],{"className":3451,"style":3389},[614],[568,3453,596],{"className":3454},[619],[568,3456,3458],{"className":3457},[619],[568,3459,3047],{"className":3460},[3073],[568,3462,3464],{"className":3463},[619],"02",". Am Rand des Intervalls ist ",[568,3467,3469,3497],{"className":3468},[571],[568,3470,3472],{"className":3471},[575],[577,3473,3474],{"xmlns":579},[581,3475,3476,3494],{},[584,3477,3478,3485,3487,3489,3491],{},[1685,3479,3480,3483],{},[594,3481,3482],{},"2,02",[594,3484,2588],{},[696,3486,1900],{},[594,3488,2775],{},[696,3490,1589],{},[594,3492,3493],{},"0,0804",[598,3495,3496],{"encoding":600},"2{,}02^2 - 4 = 0{,}0804",[568,3498,3500,3557,3575],{"className":3499,"ariaHidden":606},[605],[568,3501,3503,3507,3510,3516,3519,3548,3551,3554],{"className":3502},[610],[568,3504],{"className":3505,"style":3506},[614],"height:1.0085em;vertical-align:-0.1944em;",[568,3508,2588],{"className":3509},[619],[568,3511,3513],{"className":3512},[619],[568,3514,3047],{"className":3515},[3073],[568,3517,596],{"className":3518},[619],[568,3520,3522,3525],{"className":3521},[619],[568,3523,2588],{"className":3524},[619],[568,3526,3528],{"className":3527},[627],[568,3529,3531],{"className":3530},[631],[568,3532,3534],{"className":3533},[636],[568,3535,3537],{"className":3536,"style":2628},[640],[568,3538,3539,3542],{"style":1725},[568,3540],{"className":3541,"style":649},[648],[568,3543,3545],{"className":3544},[653,654,655,656],[568,3546,2588],{"className":3547},[619,656],[568,3549],{"className":3550,"style":1857},[1175],[568,3552,1900],{"className":3553},[1861],[568,3555],{"className":3556,"style":1857},[1175],[568,3558,3560,3563,3566,3569,3572],{"className":3559},[610],[568,3561],{"className":3562,"style":1599},[614],[568,3564,2775],{"className":3565},[619],[568,3567],{"className":3568,"style":1176},[1175],[568,3570,1589],{"className":3571},[1180],[568,3573],{"className":3574,"style":1176},[1175],[568,3576,3578,3581,3584,3590],{"className":3577},[610],[568,3579],{"className":3580,"style":3389},[614],[568,3582,596],{"className":3583},[619],[568,3585,3587],{"className":3586},[619],[568,3588,3047],{"className":3589},[3073],[568,3591,3593],{"className":3592},[619],"0804",[568,3595,3597,3629],{"className":3596},[571],[568,3598,3600],{"className":3599},[575],[577,3601,3602],{"xmlns":579},[581,3603,3604,3626],{},[584,3605,3606,3608,3615,3617,3619,3621,3623],{},[590,3607,1889],{"mathvariant":1530},[1685,3609,3610,3613],{},[594,3611,3612],{},"1,98",[594,3614,2588],{},[696,3616,1900],{},[594,3618,2775],{},[590,3620,1889],{"mathvariant":1530},[696,3622,1589],{},[594,3624,3625],{},"0,0796",[598,3627,3628],{"encoding":600},"|1{,}98^2 - 4| = 0{,}0796",[568,3630,3632,3691,3709],{"className":3631,"ariaHidden":606},[605],[568,3633,3635,3638,3642,3648,3652,3682,3685,3688],{"className":3634},[610],[568,3636],{"className":3637,"style":2815},[614],[568,3639,3641],{"className":3640},[619],"∣1",[568,3643,3645],{"className":3644},[619],[568,3646,3047],{"className":3647},[3073],[568,3649,3651],{"className":3650},[619],"9",[568,3653,3655,3659],{"className":3654},[619],[568,3656,3658],{"className":3657},[619],"8",[568,3660,3662],{"className":3661},[627],[568,3663,3665],{"className":3664},[631],[568,3666,3668],{"className":3667},[636],[568,3669,3671],{"className":3670,"style":2628},[640],[568,3672,3673,3676],{"style":1725},[568,3674],{"className":3675,"style":649},[648],[568,3677,3679],{"className":3678},[653,654,655,656],[568,3680,2588],{"className":3681},[619,656],[568,3683],{"className":3684,"style":1857},[1175],[568,3686,1900],{"className":3687},[1861],[568,3689],{"className":3690,"style":1857},[1175],[568,3692,3694,3697,3700,3703,3706],{"className":3693},[610],[568,3695],{"className":3696,"style":717},[614],[568,3698,2866],{"className":3699},[619],[568,3701],{"className":3702,"style":1176},[1175],[568,3704,1589],{"className":3705},[1180],[568,3707],{"className":3708,"style":1176},[1175],[568,3710,3712,3715,3718,3724],{"className":3711},[610],[568,3713],{"className":3714,"style":3389},[614],[568,3716,596],{"className":3717},[619],[568,3719,3721],{"className":3720},[619],[568,3722,3047],{"className":3723},[3073],[568,3725,3727],{"className":3726},[619],"0796",", beides kleiner als ",[568,3730,3732,3746],{"className":3731},[571],[568,3733,3735],{"className":3734},[575],[577,3736,3737],{"xmlns":579},[581,3738,3739,3743],{},[584,3740,3741],{},[594,3742,3358],{},[598,3744,3745],{"encoding":600},"0{,}1",[568,3747,3749],{"className":3748,"ariaHidden":606},[605],[568,3750,3752,3755,3758,3764],{"className":3751},[610],[568,3753],{"className":3754,"style":3389},[614],[568,3756,596],{"className":3757},[619],[568,3759,3761],{"className":3760},[619],[568,3762,3047],{"className":3763},[3073],[568,3765,1807],{"className":3766},[619],[564,3768,3769,3770,674,3773,1020,3810,3838,3839,3961,3962,3990,3991,4044,4045,2557],{},"Die ",[676,3771,3772],{},"Vorzeichenfunktion",[568,3774,3776,3793],{"className":3775},[571],[568,3777,3779],{"className":3778},[575],[577,3780,3781],{"xmlns":579},[581,3782,3783,3790],{},[584,3784,3785,3788],{},[590,3786,3787],{"mathvariant":1530},"sgn",[696,3789,1621],{},[598,3791,3792],{"encoding":600},"\\operatorname{sgn}",[568,3794,3796],{"className":3795,"ariaHidden":606},[605],[568,3797,3799,3803],{"className":3798},[610],[568,3800],{"className":3801,"style":3802},[614],"height:0.625em;vertical-align:-0.1944em;",[568,3804,3806],{"className":3805},[1638],[568,3807,3787],{"className":3808},[619,3809],"mathrm",[568,3811,3813,3826],{"className":3812},[571],[568,3814,3816],{"className":3815},[575],[577,3817,3818],{"xmlns":579},[581,3819,3820,3824],{},[584,3821,3822],{},[594,3823,596],{},[598,3825,596],{"encoding":600},[568,3827,3829],{"className":3828,"ariaHidden":606},[605],[568,3830,3832,3835],{"className":3831},[610],[568,3833],{"className":3834,"style":1599},[614],[568,3836,596],{"className":3837},[619]," unstetig: Für ",[568,3840,3842,3864],{"className":3841},[571],[568,3843,3845],{"className":3844},[575],[577,3846,3847],{"xmlns":579},[581,3848,3849,3861],{},[584,3850,3851,3853,3855],{},[590,3852,934],{},[696,3854,1589],{},[2135,3856,3857,3859],{},[594,3858,1807],{},[594,3860,2588],{},[598,3862,3863],{"encoding":600},"\\varepsilon = \\frac{1}{2}",[568,3865,3867,3885],{"className":3866,"ariaHidden":606},[605],[568,3868,3870,3873,3876,3879,3882],{"className":3869},[610],[568,3871],{"className":3872,"style":845},[614],[568,3874,934],{"className":3875},[619,623],[568,3877],{"className":3878,"style":1176},[1175],[568,3880,1589],{"className":3881},[1180],[568,3883],{"className":3884,"style":1176},[1175],[568,3886,3888,3892],{"className":3887},[610],[568,3889],{"className":3890,"style":3891},[614],"height:1.1901em;vertical-align:-0.345em;",[568,3893,3895,3898,3958],{"className":3894},[619],[568,3896],{"className":3897},[725,2178],[568,3899,3901],{"className":3900},[2135],[568,3902,3904,3950],{"className":3903},[631,632],[568,3905,3907,3947],{"className":3906},[636],[568,3908,3911,3925,3933],{"className":3909,"style":3910},[640],"height:0.8451em;",[568,3912,3913,3916],{"style":2194},[568,3914],{"className":3915,"style":2198},[648],[568,3917,3919],{"className":3918},[653,654,655,656],[568,3920,3922],{"className":3921},[619,656],[568,3923,2588],{"className":3924},[619,656],[568,3926,3927,3930],{"style":2210},[568,3928],{"className":3929,"style":2198},[648],[568,3931],{"className":3932,"style":2218},[2217],[568,3934,3935,3938],{"style":2221},[568,3936],{"className":3937,"style":2198},[648],[568,3939,3941],{"className":3940},[653,654,655,656],[568,3942,3944],{"className":3943},[619,656],[568,3945,1807],{"className":3946},[619,656],[568,3948,664],{"className":3949},[663],[568,3951,3953],{"className":3952},[636],[568,3954,3956],{"className":3955,"style":2243},[640],[568,3957],{},[568,3959],{"className":3960},[732,2178]," gibt es kein ",[568,3963,3965,3978],{"className":3964},[571],[568,3966,3968],{"className":3967},[575],[577,3969,3970],{"xmlns":579},[581,3971,3972,3976],{},[584,3973,3974],{},[590,3975,965],{},[598,3977,968],{"encoding":600},[568,3979,3981],{"className":3980,"ariaHidden":606},[605],[568,3982,3984,3987],{"className":3983},[610],[568,3985],{"className":3986,"style":978},[614],[568,3988,965],{"className":3989,"style":982},[619,623],", denn für jedes noch so kleine ",[568,3992,3994,4013],{"className":3993},[571],[568,3995,3997],{"className":3996},[575],[577,3998,3999],{"xmlns":579},[581,4000,4001,4010],{},[584,4002,4003,4005,4008],{},[590,4004,592],{},[696,4006,4007],{},">",[594,4009,596],{},[598,4011,4012],{"encoding":600},"x > 0",[568,4014,4016,4035],{"className":4015,"ariaHidden":606},[605],[568,4017,4019,4023,4026,4029,4032],{"className":4018},[610],[568,4020],{"className":4021,"style":4022},[614],"height:0.5782em;vertical-align:-0.0391em;",[568,4024,592],{"className":4025},[619,623],[568,4027],{"className":4028,"style":1176},[1175],[568,4030,4007],{"className":4031},[1180],[568,4033],{"className":4034,"style":1176},[1175],[568,4036,4038,4041],{"className":4037},[610],[568,4039],{"className":4040,"style":1599},[614],[568,4042,596],{"className":4043},[619]," ist ",[568,4046,4048,4090],{"className":4047},[571],[568,4049,4051],{"className":4050},[575],[577,4052,4053],{"xmlns":579},[581,4054,4055,4087],{},[584,4056,4057,4059,4061,4063,4065,4067,4069,4071,4073,4075,4077,4079,4081,4083,4085],{},[590,4058,1889],{"mathvariant":1530},[590,4060,3787],{"mathvariant":1530},[696,4062,1621],{},[696,4064,699],{"stretchy":698},[590,4066,592],{},[696,4068,704],{"stretchy":698},[696,4070,1900],{},[590,4072,3787],{"mathvariant":1530},[696,4074,1621],{},[696,4076,699],{"stretchy":698},[594,4078,596],{},[696,4080,704],{"stretchy":698},[590,4082,1889],{"mathvariant":1530},[696,4084,1589],{},[594,4086,1807],{},[598,4088,4089],{"encoding":600},"|\\operatorname{sgn}(x) - \\operatorname{sgn}(0)| = 1",[568,4091,4093,4129,4162],{"className":4092,"ariaHidden":606},[605],[568,4094,4096,4099,4102,4105,4111,4114,4117,4120,4123,4126],{"className":4095},[610],[568,4097],{"className":4098,"style":717},[614],[568,4100,1889],{"className":4101},[619],[568,4103],{"className":4104,"style":2052},[1175],[568,4106,4108],{"className":4107},[1638],[568,4109,3787],{"className":4110},[619,3809],[568,4112,699],{"className":4113},[725],[568,4115,592],{"className":4116},[619,623],[568,4118,704],{"className":4119},[732],[568,4121],{"className":4122,"style":1857},[1175],[568,4124,1900],{"className":4125},[1861],[568,4127],{"className":4128,"style":1857},[1175],[568,4130,4132,4135,4141,4144,4147,4150,4153,4156,4159],{"className":4131},[610],[568,4133],{"className":4134,"style":717},[614],[568,4136,4138],{"className":4137},[1638],[568,4139,3787],{"className":4140},[619,3809],[568,4142,699],{"className":4143},[725],[568,4145,596],{"className":4146},[619],[568,4148,704],{"className":4149},[732],[568,4151,1889],{"className":4152},[619],[568,4154],{"className":4155,"style":1176},[1175],[568,4157,1589],{"className":4158},[1180],[568,4160],{"className":4161,"style":1176},[1175],[568,4163,4165,4168],{"className":4164},[610],[568,4166],{"className":4167,"style":1599},[614],[568,4169,1807],{"className":4170},[619],[559,4172,4174],{"id":4173},"typische-fehler","Typische Fehler",[4176,4177,4178,4424,4581,4788],"ul",{},[4179,4180,4181,4209,4210,4238,4239,4267,4268,4296,4297,4325,4326,1735,4354,4423],"li",{},[568,4182,4184,4197],{"className":4183},[571],[568,4185,4187],{"className":4186},[575],[577,4188,4189],{"xmlns":579},[581,4190,4191,4195],{},[584,4192,4193],{},[590,4194,965],{},[598,4196,968],{"encoding":600},[568,4198,4200],{"className":4199,"ariaHidden":606},[605],[568,4201,4203,4206],{"className":4202},[610],[568,4204],{"className":4205,"style":978},[614],[568,4207,965],{"className":4208,"style":982},[619,623]," unabhängig von ",[568,4211,4213,4226],{"className":4212},[571],[568,4214,4216],{"className":4215},[575],[577,4217,4218],{"xmlns":579},[581,4219,4220,4224],{},[584,4221,4222],{},[590,4223,934],{},[598,4225,937],{"encoding":600},[568,4227,4229],{"className":4228,"ariaHidden":606},[605],[568,4230,4232,4235],{"className":4231},[610],[568,4233],{"className":4234,"style":845},[614],[568,4236,934],{"className":4237},[619,623]," wählen oder ",[568,4240,4242,4255],{"className":4241},[571],[568,4243,4245],{"className":4244},[575],[577,4246,4247],{"xmlns":579},[581,4248,4249,4253],{},[584,4250,4251],{},[590,4252,965],{},[598,4254,968],{"encoding":600},[568,4256,4258],{"className":4257,"ariaHidden":606},[605],[568,4259,4261,4264],{"className":4260},[610],[568,4262],{"className":4263,"style":978},[614],[568,4265,965],{"className":4266,"style":982},[619,623]," von ",[568,4269,4271,4284],{"className":4270},[571],[568,4272,4274],{"className":4273},[575],[577,4275,4276],{"xmlns":579},[581,4277,4278,4282],{},[584,4279,4280],{},[590,4281,592],{},[598,4283,592],{"encoding":600},[568,4285,4287],{"className":4286,"ariaHidden":606},[605],[568,4288,4290,4293],{"className":4289},[610],[568,4291],{"className":4292,"style":845},[614],[568,4294,592],{"className":4295},[619,623]," abhängig machen. ",[568,4298,4300,4313],{"className":4299},[571],[568,4301,4303],{"className":4302},[575],[577,4304,4305],{"xmlns":579},[581,4306,4307,4311],{},[584,4308,4309],{},[590,4310,965],{},[598,4312,968],{"encoding":600},[568,4314,4316],{"className":4315,"ariaHidden":606},[605],[568,4317,4319,4322],{"className":4318},[610],[568,4320],{"className":4321,"style":978},[614],[568,4323,965],{"className":4324,"style":982},[619,623]," darf nur von ",[568,4327,4329,4342],{"className":4328},[571],[568,4330,4332],{"className":4331},[575],[577,4333,4334],{"xmlns":579},[581,4335,4336,4340],{},[584,4337,4338],{},[590,4339,934],{},[598,4341,937],{"encoding":600},[568,4343,4345],{"className":4344,"ariaHidden":606},[605],[568,4346,4348,4351],{"className":4347},[610],[568,4349],{"className":4350,"style":845},[614],[568,4352,934],{"className":4353},[619,623],[568,4355,4357,4374],{"className":4356},[571],[568,4358,4360],{"className":4359},[575],[577,4361,4362],{"xmlns":579},[581,4363,4364,4372],{},[584,4365,4366],{},[587,4367,4368,4370],{},[590,4369,592],{},[594,4371,596],{},[598,4373,601],{"encoding":600},[568,4375,4377],{"className":4376,"ariaHidden":606},[605],[568,4378,4380,4383],{"className":4379},[610],[568,4381],{"className":4382,"style":615},[614],[568,4384,4386,4389],{"className":4385},[619],[568,4387,592],{"className":4388},[619,623],[568,4390,4392],{"className":4391},[627],[568,4393,4395,4415],{"className":4394},[631,632],[568,4396,4398,4412],{"className":4397},[636],[568,4399,4401],{"className":4400,"style":641},[640],[568,4402,4403,4406],{"style":644},[568,4404],{"className":4405,"style":649},[648],[568,4407,4409],{"className":4408},[653,654,655,656],[568,4410,596],{"className":4411},[619,656],[568,4413,664],{"className":4414},[663],[568,4416,4418],{"className":4417},[636],[568,4419,4421],{"className":4420,"style":671},[640],[568,4422],{}," abhängen.",[4179,4425,4426,4427,4529,4530,4580],{},"Bei nichtlinearen Funktionen den Faktor ",[568,4428,4430,4456],{"className":4429},[571],[568,4431,4433],{"className":4432},[575],[577,4434,4435],{"xmlns":579},[581,4436,4437,4453],{},[584,4438,4439,4441,4443,4445,4451],{},[590,4440,1889],{"mathvariant":1530},[590,4442,592],{},[696,4444,1804],{},[587,4446,4447,4449],{},[590,4448,592],{},[594,4450,596],{},[590,4452,1889],{"mathvariant":1530},[598,4454,4455],{"encoding":600},"|x + x_0|",[568,4457,4459,4480],{"className":4458,"ariaHidden":606},[605],[568,4460,4462,4465,4468,4471,4474,4477],{"className":4461},[610],[568,4463],{"className":4464,"style":717},[614],[568,4466,1889],{"className":4467},[619],[568,4469,592],{"className":4470},[619,623],[568,4472],{"className":4473,"style":1857},[1175],[568,4475,1804],{"className":4476},[1861],[568,4478],{"className":4479,"style":1857},[1175],[568,4481,4483,4486,4526],{"className":4482},[610],[568,4484],{"className":4485,"style":717},[614],[568,4487,4489,4492],{"className":4488},[619],[568,4490,592],{"className":4491},[619,623],[568,4493,4495],{"className":4494},[627],[568,4496,4498,4518],{"className":4497},[631,632],[568,4499,4501,4515],{"className":4500},[636],[568,4502,4504],{"className":4503,"style":641},[640],[568,4505,4506,4509],{"style":644},[568,4507],{"className":4508,"style":649},[648],[568,4510,4512],{"className":4511},[653,654,655,656],[568,4513,596],{"className":4514},[619,656],[568,4516,664],{"className":4517},[663],[568,4519,4521],{"className":4520},[636],[568,4522,4524],{"className":4523,"style":671},[640],[568,4525],{},[568,4527,1889],{"className":4528},[619]," unbeschränkt lassen. Erst durch eine Vorab-Einschränkung wie ",[568,4531,4533,4550],{"className":4532},[571],[568,4534,4536],{"className":4535},[575],[577,4537,4538],{"xmlns":579},[581,4539,4540,4548],{},[584,4541,4542,4544,4546],{},[590,4543,965],{},[696,4545,2963],{},[594,4547,1807],{},[598,4549,2968],{"encoding":600},[568,4551,4553,4571],{"className":4552,"ariaHidden":606},[605],[568,4554,4556,4559,4562,4565,4568],{"className":4555},[610],[568,4557],{"className":4558,"style":2978},[614],[568,4560,965],{"className":4561,"style":982},[619,623],[568,4563],{"className":4564,"style":1176},[1175],[568,4566,2963],{"className":4567},[1180],[568,4569],{"className":4570,"style":1176},[1175],[568,4572,4574,4577],{"className":4573},[610],[568,4575],{"className":4576,"style":1599},[614],[568,4578,1807],{"className":4579},[619]," wird er abschätzbar.",[4179,4582,4583,4584,4719,4720,4787],{},"Stetigkeit mit „Graph ohne Absetzen zeichenbar“ gleichsetzen. ",[568,4585,4587,4615],{"className":4586},[571],[568,4588,4590],{"className":4589},[575],[577,4591,4592],{"xmlns":579},[581,4593,4594,4612],{},[584,4595,4596,4598,4600,4602,4604,4606],{},[590,4597,694],{},[696,4599,699],{"stretchy":698},[590,4601,592],{},[696,4603,704],{"stretchy":698},[696,4605,1589],{},[2135,4607,4608,4610],{},[594,4609,1807],{},[590,4611,592],{},[598,4613,4614],{"encoding":600},"f(x) = \\frac{1}{x}",[568,4616,4618,4645],{"className":4617,"ariaHidden":606},[605],[568,4619,4621,4624,4627,4630,4633,4636,4639,4642],{"className":4620},[610],[568,4622],{"className":4623,"style":717},[614],[568,4625,694],{"className":4626,"style":721},[619,623],[568,4628,699],{"className":4629},[725],[568,4631,592],{"className":4632},[619,623],[568,4634,704],{"className":4635},[732],[568,4637],{"className":4638,"style":1176},[1175],[568,4640,1589],{"className":4641},[1180],[568,4643],{"className":4644,"style":1176},[1175],[568,4646,4648,4651],{"className":4647},[610],[568,4649],{"className":4650,"style":3891},[614],[568,4652,4654,4657,4716],{"className":4653},[619],[568,4655],{"className":4656},[725,2178],[568,4658,4660],{"className":4659},[2135],[568,4661,4663,4708],{"className":4662},[631,632],[568,4664,4666,4705],{"className":4665},[636],[568,4667,4669,4683,4691],{"className":4668,"style":3910},[640],[568,4670,4671,4674],{"style":2194},[568,4672],{"className":4673,"style":2198},[648],[568,4675,4677],{"className":4676},[653,654,655,656],[568,4678,4680],{"className":4679},[619,656],[568,4681,592],{"className":4682},[619,623,656],[568,4684,4685,4688],{"style":2210},[568,4686],{"className":4687,"style":2198},[648],[568,4689],{"className":4690,"style":2218},[2217],[568,4692,4693,4696],{"style":2221},[568,4694],{"className":4695,"style":2198},[648],[568,4697,4699],{"className":4698},[653,654,655,656],[568,4700,4702],{"className":4701},[619,656],[568,4703,1807],{"className":4704},[619,656],[568,4706,664],{"className":4707},[663],[568,4709,4711],{"className":4710},[636],[568,4712,4714],{"className":4713,"style":2243},[640],[568,4715],{},[568,4717],{"className":4718},[732,2178]," ist auf ihrem Definitionsbereich ",[568,4721,4723,4750],{"className":4722},[571],[568,4724,4726],{"className":4725},[575],[577,4727,4728],{"xmlns":579},[581,4729,4730,4747],{},[584,4731,4732,4736,4739,4742,4744],{},[590,4733,4735],{"mathvariant":4734},"double-struck","R",[696,4737,4738],{},"∖",[696,4740,4741],{"stretchy":698},"{",[594,4743,596],{},[696,4745,4746],{"stretchy":698},"}",[598,4748,4749],{"encoding":600},"\\mathbb{R} \\setminus \\{0\\}",[568,4751,4753,4772],{"className":4752,"ariaHidden":606},[605],[568,4754,4756,4759,4763,4766,4769],{"className":4755},[610],[568,4757],{"className":4758,"style":717},[614],[568,4760,4735],{"className":4761},[619,4762],"mathbb",[568,4764],{"className":4765,"style":1857},[1175],[568,4767,4738],{"className":4768},[1861],[568,4770],{"className":4771,"style":1857},[1175],[568,4773,4775,4778,4781,4784],{"className":4774},[610],[568,4776],{"className":4777,"style":717},[614],[568,4779,4741],{"className":4780},[725],[568,4782,596],{"className":4783},[619],[568,4785,4746],{"className":4786},[732]," stetig, obwohl der Graph aus zwei Ästen besteht.",[4179,4789,4790,4791,4819,4820,4044,4912,5010],{},"Stetigkeit an einer Stelle prüfen, die nicht in ",[568,4792,4794,4807],{"className":4793},[571],[568,4795,4797],{"className":4796},[575],[577,4798,4799],{"xmlns":579},[581,4800,4801,4805],{},[584,4802,4803],{},[590,4804,1245],{},[598,4806,1245],{"encoding":600},[568,4808,4810],{"className":4809,"ariaHidden":606},[605],[568,4811,4813,4816],{"className":4812},[610],[568,4814],{"className":4815,"style":1257},[614],[568,4817,1245],{"className":4818,"style":1261},[619,623]," liegt. Bei ",[568,4821,4823,4845],{"className":4822},[571],[568,4824,4826],{"className":4825},[575],[577,4827,4828],{"xmlns":579},[581,4829,4830,4842],{},[584,4831,4832,4838,4840],{},[587,4833,4834,4836],{},[590,4835,592],{},[594,4837,596],{},[696,4839,1589],{},[594,4841,596],{},[598,4843,4844],{"encoding":600},"x_0 = 0",[568,4846,4848,4903],{"className":4847,"ariaHidden":606},[605],[568,4849,4851,4854,4894,4897,4900],{"className":4850},[610],[568,4852],{"className":4853,"style":615},[614],[568,4855,4857,4860],{"className":4856},[619],[568,4858,592],{"className":4859},[619,623],[568,4861,4863],{"className":4862},[627],[568,4864,4866,4886],{"className":4865},[631,632],[568,4867,4869,4883],{"className":4868},[636],[568,4870,4872],{"className":4871,"style":641},[640],[568,4873,4874,4877],{"style":644},[568,4875],{"className":4876,"style":649},[648],[568,4878,4880],{"className":4879},[653,654,655,656],[568,4881,596],{"className":4882},[619,656],[568,4884,664],{"className":4885},[663],[568,4887,4889],{"className":4888},[636],[568,4890,4892],{"className":4891,"style":671},[640],[568,4893],{},[568,4895],{"className":4896,"style":1176},[1175],[568,4898,1589],{"className":4899},[1180],[568,4901],{"className":4902,"style":1176},[1175],[568,4904,4906,4909],{"className":4905},[610],[568,4907],{"className":4908,"style":1599},[614],[568,4910,596],{"className":4911},[619],[568,4913,4915,4933],{"className":4914},[571],[568,4916,4918],{"className":4917},[575],[577,4919,4920],{"xmlns":579},[581,4921,4922,4930],{},[584,4923,4924],{},[2135,4925,4926,4928],{},[594,4927,1807],{},[590,4929,592],{},[598,4931,4932],{"encoding":600},"\\frac{1}{x}",[568,4934,4936],{"className":4935,"ariaHidden":606},[605],[568,4937,4939,4942],{"className":4938},[610],[568,4940],{"className":4941,"style":3891},[614],[568,4943,4945,4948,5007],{"className":4944},[619],[568,4946],{"className":4947},[725,2178],[568,4949,4951],{"className":4950},[2135],[568,4952,4954,4999],{"className":4953},[631,632],[568,4955,4957,4996],{"className":4956},[636],[568,4958,4960,4974,4982],{"className":4959,"style":3910},[640],[568,4961,4962,4965],{"style":2194},[568,4963],{"className":4964,"style":2198},[648],[568,4966,4968],{"className":4967},[653,654,655,656],[568,4969,4971],{"className":4970},[619,656],[568,4972,592],{"className":4973},[619,623,656],[568,4975,4976,4979],{"style":2210},[568,4977],{"className":4978,"style":2198},[648],[568,4980],{"className":4981,"style":2218},[2217],[568,4983,4984,4987],{"style":2221},[568,4985],{"className":4986,"style":2198},[648],[568,4988,4990],{"className":4989},[653,654,655,656],[568,4991,4993],{"className":4992},[619,656],[568,4994,1807],{"className":4995},[619,656],[568,4997,664],{"className":4998},[663],[568,5000,5002],{"className":5001},[636],[568,5003,5005],{"className":5004,"style":2243},[640],[568,5006],{},[568,5008],{"className":5009},[732,2178]," weder stetig noch unstetig, sondern nicht definiert.",{"title":5012,"searchDepth":5013,"depth":5013,"links":5014},"",2,[5015,5016,5017],{"id":561,"depth":5013,"text":562},{"id":1771,"depth":5013,"text":1772},{"id":4173,"depth":5013,"text":4174},[5019,5022,5025,5028,5031,5034,5037],{"lhs":5020,"rhs":5021},"(3*(x + d) + 1) - (3*x + 1)","3*d",{"lhs":5023,"rhs":5024},"3*(u\u002F3)","u",{"lhs":5026,"rhs":5027},"x^2 - 4","(x - 2)*(x + 2)",{"lhs":5029,"rhs":5030},"min(1, 0.1\u002F5)","0.02",{"lhs":5032,"rhs":5033},"round(2.02^2 - 4, 4)","0.0804",{"lhs":5035,"rhs":5036},"round(abs(1.98^2 - 4), 4)","0.0796",{"lhs":5038,"rhs":1807},"abs(sign(0.001) - sign(0))","f: D \\to \\mathbb{R},\\ D \\subseteq \\mathbb{R},\\ x_0 \\in D","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmo>:\u003C\u002Fmo>\u003Cmi>D\u003C\u002Fmi>\u003Cmo>→\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f: D \\to \\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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">D\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">→\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>D\u003C\u002Fmi>\u003Cmo>⊆\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">D \\subseteq \\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:0.8193em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">D\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">⊆\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi>D\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_0 \\in D\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:0.6891em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;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\">0\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" 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47.59 L 164.34 46.57 L 165.15 45.56 L 165.96 44.55 L 166.77 43.54 L 167.58 42.52 L 168.39 41.51 L 169.2 40.5 L 170.01 39.49 L 170.82 38.47 L 171.63 37.46 L 172.44 36.45 L 173.25 35.44 L 174.06 34.42 L 174.87 33.41 L 175.68 32.4 L 176.49 31.39 L 177.3 30.38 L 178.11 29.36 L 178.92 28.35 L 179.73 27.34 L 180.54 26.32 L 181.35 25.31 L 182.16 24.3 L 182.97 23.29 L 183.78 22.27 L 184.59 21.26 L 185.4 20.25 L 186.21 19.24 L 187.02 18.22 L 187.83 17.21 L 188.64 16.2 L 189.45 15.19 L 190.26 14.18 L 191.07 13.16 L 191.88 12.15 L 192.69 11.14 L 193.5 10.13 L 194.31 9.11 L 195.12 8.1 L 195.93 7.09 L 196.74 6.07 L 197.55 5.06 L 198.36 4.05 L 199.17 3.04 L 199.98 2.02 L 200.79 1.01 L 201.6 0\" class=\"fig-main fig-graph\" clip-path=\"url(#fig-continuity-definition-clip)\"\u002F>\u003Ccircle cx=\"115.2\" cy=\"108\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"219.6\" y=\"85.5\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">ε\u003C\u002Ftext>\u003Ctext x=\"219.6\" y=\"130.5\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">ε\u003C\u002Ftext>\u003Ctext x=\"97.2\" y=\"21\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">δ\u003C\u002Ftext>\u003Ctext x=\"133.2\" y=\"21\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">δ\u003C\u002Ftext>\u003Ctext x=\"183.6\" y=\"30\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">f\u003C\u002Ftext>\u003C\u002Fsvg>","continuity-definition","\\begin{gathered} \\forall \\varepsilon > 0\\ \\exists \\delta > 0\\ \\forall x \\in D\\colon \\\\ |x - x_0| \u003C \\delta \\\\ \\Rightarrow\\; |f(x) - f(x_0)| \u003C \\varepsilon \\end{gathered}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmtable rowspacing=\"0.25em\" columnalign=\"center\" 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mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmo><\u003C\u002Fmo>\u003Cmi>δ\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"true\">\u003Cmrow>\u003Cmo>⇒\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmi 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style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">D\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1111em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:-0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">:\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.3333em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.01em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\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\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;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\">0\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\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>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0379em;\">δ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-1.51em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">⇒\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan 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