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x^2",[568,1148,1150,1177],{"className":1149,"ariaHidden":606},[605],[568,1151,1153,1156,1159,1162,1165,1168,1171,1174],{"className":1152},[610],[568,1154],{"className":1155,"style":778},[614],[568,1157,664],{"className":1158,"style":713},[619,620],[568,1160,1004],{"className":1161},[782],[568,1163,1130],{"className":1164},[619,620],[568,1166,1009],{"className":1167},[800],[568,1169],{"className":1170,"style":1046},[624],[568,1172,1012],{"className":1173},[1050],[568,1175],{"className":1176,"style":1046},[624],[568,1178,1180,1184],{"className":1179},[610],[568,1181],{"className":1182,"style":1183},[614],"height:0.8141em;",[568,1185,1187,1190],{"className":1186},[619],[568,1188,1130],{"className":1189},[619,620],[568,1191,1194],{"className":1192},[1193],"msupsub",[568,1195,1197],{"className":1196},[688],[568,1198,1200],{"className":1199},[693],[568,1201,1203],{"className":1202,"style":1183},[697],[568,1204,1206,1210],{"style":1205},"top:-3.063em;margin-right:0.05em;",[568,1207],{"className":1208,"style":1209},[705],"height:2.7em;",[568,1211,1217],{"className":1212},[1213,1214,1215,1216],"sizing","reset-size6","size3","mtight",[568,1218,1143],{"className":1219},[619,1216]," auf ",[568,1222,1224,1248],{"className":1223},[571],[568,1225,1227],{"className":1226},[575],[577,1228,1229],{"xmlns":579},[581,1230,1231,1245],{},[584,1232,1233,1235,1238,1240,1243],{},[591,1234,755],{"stretchy":754},[1141,1236,1237],{},"0",[591,1239,760],{"separator":606},[1141,1241,1242],{},"3",[591,1244,765],{"stretchy":754},[598,1246,1247],{"encoding":600},"[0, 3]",[568,1249,1251],{"className":1250,"ariaHidden":606},[605],[568,1252,1254,1257,1260,1263,1266,1269,1272],{"className":1253},[610],[568,1255],{"className":1256,"style":778},[614],[568,1258,755],{"className":1259},[782],[568,1261,1237],{"className":1262},[619],[568,1264,760],{"className":1265},[789],[568,1267],{"className":1268,"style":793},[624],[568,1270,1242],{"className":1271},[619],[568,1273,765],{"className":1274},[800],":",[568,1277,1280],{"className":1278},[1279],"katex-display",[568,1281,1283,1393],{"className":1282},[571],[568,1284,1286],{"className":1285},[575],[577,1287,1289],{"xmlns":579,"display":1288},"block",[581,1290,1291,1390],{},[584,1292,1293,1299,1301,1315,1325,1331,1335,1338,1340,1342,1348,1351,1373,1375,1381,1383,1386,1388],{},[660,1294,1295,1297],{"accent":606},[587,1296,664],{},[591,1298,667],{"stretchy":606},[591,1300,1012],{},[1302,1303,1304,1307],"mfrac",{},[1141,1305,1306],{},"1",[584,1308,1309,1311,1313],{},[1141,1310,1242],{},[591,1312,593],{},[1141,1314,1237],{},[1316,1317,1318,1321,1323],"msubsup",{},[591,1319,1320],{},"∫",[1141,1322,1237],{},[1141,1324,1242],{},[1136,1326,1327,1329],{},[587,1328,1130],{},[1141,1330,1143],{},[1332,1333,1334],"mtext",{}," ",[587,1336,1337],{},"d",[587,1339,1130],{},[591,1341,1012],{},[1302,1343,1344,1346],{},[1141,1345,1306],{},[1141,1347,1242],{},[591,1349,1350],{},"⋅",[1316,1352,1353,1369,1371],{},[584,1354,1355,1357,1367],{},[591,1356,755],{"fence":606},[1302,1358,1359,1365],{},[1136,1360,1361,1363],{},[587,1362,1130],{},[1141,1364,1242],{},[1141,1366,1242],{},[591,1368,765],{"fence":606},[1141,1370,1237],{},[1141,1372,1242],{},[591,1374,1012],{},[1302,1376,1377,1379],{},[1141,1378,1306],{},[1141,1380,1242],{},[591,1382,1350],{},[1141,1384,1385],{},"9",[591,1387,1012],{},[1141,1389,1242],{},[598,1391,1392],{"encoding":600},"\\overline{f} = \\frac{1}{3 - 0} \\int_0^3 x^2\\,dx = \\frac{1}{3} \\cdot \\left[\\frac{x^3}{3}\\right]_0^3 = \\frac{1}{3} \\cdot 9 = 3",[568,1394,1396,1453,1655,1734,1910,1987,2006],{"className":1395,"ariaHidden":606},[605],[568,1397,1399,1402,1444,1447,1450],{"className":1398},[610],[568,1400],{"className":1401,"style":680},[614],[568,1403,1405],{"className":1404},[619,684],[568,1406,1408,1436],{"className":1407},[688,689],[568,1409,1411,1433],{"className":1410},[693],[568,1412,1414,1425],{"className":1413,"style":698},[697],[568,1415,1416,1419],{"style":701},[568,1417],{"className":1418,"style":706},[705],[568,1420,1422],{"className":1421},[619],[568,1423,664],{"className":1424,"style":713},[619,620],[568,1426,1427,1430],{"style":716},[568,1428],{"className":1429,"style":706},[705],[568,1431],{"className":1432,"style":724},[723],[568,1434,729],{"className":1435},[728],[568,1437,1439],{"className":1438},[693],[568,1440,1442],{"className":1441,"style":736},[697],[568,1443],{},[568,1445],{"className":1446,"style":1046},[624],[568,1448,1012],{"className":1449},[1050],[568,1451],{"className":1452,"style":1046},[624],[568,1454,1456,1460,1541,1544,1603,1606,1637,1640,1643,1646,1649,1652],{"className":1455},[610],[568,1457],{"className":1458,"style":1459},[614],"height:2.476em;vertical-align:-0.9119em;",[568,1461,1463,1467,1538],{"className":1462},[619],[568,1464],{"className":1465},[782,1466],"nulldelimiter",[568,1468,1470],{"className":1469},[1302],[568,1471,1473,1529],{"className":1472},[688,689],[568,1474,1476,1526],{"className":1475},[693],[568,1477,1480,1504,1514],{"className":1478,"style":1479},[697],"height:1.3214em;",[568,1481,1483,1486],{"style":1482},"top:-2.314em;",[568,1484],{"className":1485,"style":706},[705],[568,1487,1489,1492,1495,1498,1501],{"className":1488},[619],[568,1490,1242],{"className":1491},[619],[568,1493],{"className":1494,"style":625},[624],[568,1496,593],{"className":1497},[629],[568,1499],{"className":1500,"style":625},[624],[568,1502,1237],{"className":1503},[619],[568,1505,1507,1510],{"style":1506},"top:-3.23em;",[568,1508],{"className":1509,"style":706},[705],[568,1511],{"className":1512,"style":724},[1513],"frac-line",[568,1515,1517,1520],{"style":1516},"top:-3.677em;",[568,1518],{"className":1519,"style":706},[705],[568,1521,1523],{"className":1522},[619],[568,1524,1306],{"className":1525},[619],[568,1527,729],{"className":1528},[728],[568,1530,1532],{"className":1531},[693],[568,1533,1536],{"className":1534,"style":1535},[697],"height:0.7693em;",[568,1537],{},[568,1539],{"className":1540},[800,1466],[568,1542],{"className":1543,"style":793},[624],[568,1545,1548,1554],{"className":1546},[1547],"mop",[568,1549,1320],{"className":1550,"style":1553},[1547,1551,1552],"op-symbol","large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[568,1555,1557],{"className":1556},[1193],[568,1558,1560,1594],{"className":1559},[688,689],[568,1561,1563,1591],{"className":1562},[693],[568,1564,1567,1579],{"className":1565,"style":1566},[697],"height:1.564em;",[568,1568,1570,1573],{"style":1569},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[568,1571],{"className":1572,"style":1209},[705],[568,1574,1576],{"className":1575},[1213,1214,1215,1216],[568,1577,1237],{"className":1578},[619,1216],[568,1580,1582,1585],{"style":1581},"top:-3.8129em;margin-right:0.05em;",[568,1583],{"className":1584,"style":1209},[705],[568,1586,1588],{"className":1587},[1213,1214,1215,1216],[568,1589,1242],{"className":1590},[619,1216],[568,1592,729],{"className":1593},[728],[568,1595,1597],{"className":1596},[693],[568,1598,1601],{"className":1599,"style":1600},[697],"height:0.9119em;",[568,1602],{},[568,1604],{"className":1605,"style":793},[624],[568,1607,1609,1612],{"className":1608},[619],[568,1610,1130],{"className":1611},[619,620],[568,1613,1615],{"className":1614},[1193],[568,1616,1618],{"className":1617},[688],[568,1619,1621],{"className":1620},[693],[568,1622,1625],{"className":1623,"style":1624},[697],"height:0.8641em;",[568,1626,1628,1631],{"style":1627},"top:-3.113em;margin-right:0.05em;",[568,1629],{"className":1630,"style":1209},[705],[568,1632,1634],{"className":1633},[1213,1214,1215,1216],[568,1635,1143],{"className":1636},[619,1216],[568,1638],{"className":1639,"style":793},[624],[568,1641,1337],{"className":1642},[619,620],[568,1644,1130],{"className":1645},[619,620],[568,1647],{"className":1648,"style":1046},[624],[568,1650,1012],{"className":1651},[1050],[568,1653],{"className":1654,"style":1046},[624],[568,1656,1658,1662,1725,1728,1731],{"className":1657},[610],[568,1659],{"className":1660,"style":1661},[614],"height:2.0074em;vertical-align:-0.686em;",[568,1663,1665,1668,1722],{"className":1664},[619],[568,1666],{"className":1667},[782,1466],[568,1669,1671],{"className":1670},[1302],[568,1672,1674,1713],{"className":1673},[688,689],[568,1675,1677,1710],{"className":1676},[693],[568,1678,1680,1691,1699],{"className":1679,"style":1479},[697],[568,1681,1682,1685],{"style":1482},[568,1683],{"className":1684,"style":706},[705],[568,1686,1688],{"className":1687},[619],[568,1689,1242],{"className":1690},[619],[56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",[568,2135,2137,2165],{"className":2136},[571],[568,2138,2140],{"className":2139},[575],[577,2141,2142],{"xmlns":579},[581,2143,2144,2162],{},[584,2145,2146,2148,2152,2158,2160],{},[591,2147,1004],{"stretchy":754},[2035,2149,2150],{},[1141,2151,1242],{},[1136,2153,2154,2156],{},[591,2155,1009],{"stretchy":754},[1141,2157,1143],{},[591,2159,1012],{},[1141,2161,1242],{},[598,2163,2164],{"encoding":600},"(\\sqrt{3})^2 = 3",[568,2166,2168,2263],{"className":2167,"ariaHidden":606},[605],[568,2169,2171,2175,2178,2225,2254,2257,2260],{"className":2170},[610],[568,2172],{"className":2173,"style":2174},[614],"height:1.1572em;vertical-align:-0.25em;",[568,2176,1004],{"className":2177},[782],[568,2179,2181],{"className":2180},[619,2073],[568,2182,2184,2217],{"className":2183},[688,689],[568,2185,2187,2214],{"className":2186},[693],[568,2188,2190,2202],{"className":2189,"style":2083},[697],[568,2191,2193,2196],{"className":2192,"style":701},[2087],[568,2194],{"className":2195,"style":706},[705],[568,2197,2199],{"className":2198,"style":2094},[619],[568,2200,1242],{"className":2201},[619],[568,2203,2204,2207],{"style":2100},[568,2205],{"className":2206,"style":706},[705],[568,2208,2210],{"className":2209,"style":2108},[2107],[2110,2211,2212],{"xmlns":2112,"width":2113,"height":2114,"viewBox":2115,"preserveAspectRatio":2116},[2118,2213],{"d":2120},[568,2215,729],{"className":2216},[728],[568,2218,2220],{"className":2219},[693],[568,2221,2223],{"className":2222,"style":2130},[697],[568,2224],{},[568,2226,2228,2231],{"className":2227},[800],[568,2229,1009],{"className":2230},[800],[568,2232,2234],{"className":2233},[1193],[568,2235,2237],{"className":2236},[688],[568,2238,2240],{"className":2239},[693],[568,2241,2243],{"className":2242,"style":1183},[697],[568,2244,2245,2248],{"style":1205},[568,2246],{"className":2247,"style":1209},[705],[568,2249,2251],{"className":2250},[1213,1214,1215,1216],[568,2252,1143],{"className":2253},[619,1216],[568,2255],{"className":2256,"style":1046},[624],[568,2258,1012],{"className":2259},[1050],[568,2261],{"className":2262,"style":1046},[624],[568,2264,2266,2269],{"className":2265},[610],[568,2267],{"className":2268,"style":1993},[614],[568,2270,1242],{"className":2271},[619],[564,2273,2274,2275,2453,2454,2483,2484,1275],{},"Die Temperatur an einem Tag wird modelliert durch ",[568,2276,2278,2327],{"className":2277},[571],[568,2279,2281],{"className":2280},[575],[577,2282,2283],{"xmlns":579},[581,2284,2285,2324],{},[584,2286,2287,2290,2292,2295,2297,2299,2301,2304,2306,2312,2315,2317,2319,2321],{},[587,2288,2289],{},"T",[591,2291,1004],{"stretchy":754},[587,2293,2294],{},"t",[591,2296,1009],{"stretchy":754},[591,2298,1012],{},[591,2300,593],{},[1141,2302,2303],{},"0,25",[1332,2305,1334],{},[1136,2307,2308,2310],{},[587,2309,2294],{},[1141,2311,1143],{},[591,2313,2314],{},"+",[1141,2316,1242],{},[587,2318,2294],{},[591,2320,2314],{},[1141,2322,2323],{},"10",[598,2325,2326],{"encoding":600},"T(t) = -0{,}25\\,t^2 + 3t + 10",[568,2328,2330,2358,2422,2444],{"className":2329,"ariaHidden":606},[605],[568,2331,2333,2336,2340,2343,2346,2349,2352,2355],{"className":2332},[610],[568,2334],{"className":2335,"style":778},[614],[568,2337,2289],{"className":2338,"style":2339},[619,620],"margin-right:0.1389em;",[568,2341,1004],{"className":2342},[782],[568,2344,2294],{"className":2345},[619,620],[568,2347,1009],{"className":2348},[800],[568,2350],{"className":2351,"style":1046},[624],[568,2353,1012],{"className":2354},[1050],[568,2356],{"className":2357,"style":1046},[624],[568,2359,2361,2365,2368,2371,2377,2381,2384,2413,2416,2419],{"className":2360},[610],[568,2362],{"className":2363,"style":2364},[614],"height:1.0085em;vertical-align:-0.1944em;",[568,2366,593],{"className":2367},[619],[568,2369,1237],{"className":2370},[619],[568,2372,2374],{"className":2373},[619],[568,2375,760],{"className":2376},[789],[568,2378,2380],{"className":2379},[619],"25",[568,2382],{"className":2383,"style":793},[624],[568,2385,2387,2390],{"className":2386},[619],[568,2388,2294],{"className":2389},[619,620],[568,2391,2393],{"className":2392},[1193],[568,2394,2396],{"className":2395},[688],[568,2397,2399],{"className":2398},[693],[568,2400,2402],{"className":2401,"style":1183},[697],[568,2403,2404,2407],{"style":1205},[568,2405],{"className":2406,"style":1209},[705],[568,2408,2410],{"className":2409},[1213,1214,1215,1216],[568,2411,1143],{"className":2412},[619,1216],[568,2414],{"className":2415,"style":625},[624],[568,2417,2314],{"className":2418},[629],[568,2420],{"className":2421,"style":625},[624],[568,2423,2425,2429,2432,2435,2438,2441],{"className":2424},[610],[568,2426],{"className":2427,"style":2428},[614],"height:0.7278em;vertical-align:-0.0833em;",[568,2430,1242],{"className":2431},[619],[568,2433,2294],{"className":2434},[619,620],[568,2436],{"className":2437,"style":625},[624],[568,2439,2314],{"className":2440},[629],[568,2442],{"className":2443,"style":625},[624],[568,2445,2447,2450],{"className":2446},[610],[568,2448],{"className":2449,"style":1993},[614],[568,2451,2323],{"className":2452},[619]," (in °C, ",[568,2455,2457,2470],{"className":2456},[571],[568,2458,2460],{"className":2459},[575],[577,2461,2462],{"xmlns":579},[581,2463,2464,2468],{},[584,2465,2466],{},[587,2467,2294],{},[598,2469,2294],{"encoding":600},[568,2471,2473],{"className":2472,"ariaHidden":606},[605],[568,2474,2476,2480],{"className":2475},[610],[568,2477],{"className":2478,"style":2479},[614],"height:0.6151em;",[568,2481,2294],{"className":2482},[619,620]," in Stunden ab 6 Uhr). Mittlere Temperatur zwischen 6 und 18 Uhr, also für ",[568,2485,2487,2511],{"className":2486},[571],[568,2488,2490],{"className":2489},[575],[577,2491,2492],{"xmlns":579},[581,2493,2494,2508],{},[584,2495,2496,2498,2501,2503,2505],{},[1141,2497,1237],{},[591,2499,2500],{},"≤",[587,2502,2294],{},[591,2504,2500],{},[1141,2506,2507],{},"12",[598,2509,2510],{"encoding":600},"0 \\leq t \\leq 12",[568,2512,2514,2533,2552],{"className":2513,"ariaHidden":606},[605],[568,2515,2517,2521,2524,2527,2530],{"className":2516},[610],[568,2518],{"className":2519,"style":2520},[614],"height:0.7804em;vertical-align:-0.136em;",[568,2522,1237],{"className":2523},[619],[568,2525],{"className":2526,"style":1046},[624],[568,2528,2500],{"className":2529},[1050],[568,2531],{"className":2532,"style":1046},[624],[568,2534,2536,2540,2543,2546,2549],{"className":2535},[610],[568,2537],{"className":2538,"style":2539},[614],"height:0.7719em;vertical-align:-0.136em;",[568,2541,2294],{"className":2542},[619,620],[568,2544],{"className":2545,"style":1046},[624],[568,2547,2500],{"className":2548},[1050],[568,2550],{"className":2551,"style":1046},[624],[568,2553,2555,2558],{"className":2554},[610],[568,2556],{"className":2557,"style":1993},[614],[568,2559,2507],{"className":2560},[619],[568,2562,2564],{"className":2563},[1279],[568,2565,2567,2680],{"className":2566},[571],[568,2568,2570],{"className":2569},[575],[577,2571,2572],{"xmlns":579,"display":1288},[581,2573,2574,2677],{},[584,2575,2576,2582,2584,2590,2598,2600,2602,2604,2606,2608,2610,2612,2614,2620,2663,2665,2672,2674],{},[660,2577,2578,2580],{"accent":606},[587,2579,2289],{},[591,2581,667],{"stretchy":606},[591,2583,1012],{},[1302,2585,2586,2588],{},[1141,2587,1306],{},[1141,2589,2507],{},[1316,2591,2592,2594,2596],{},[591,2593,1320],{},[1141,2595,1237],{},[1141,2597,2507],{},[587,2599,2289],{},[591,2601,1004],{"stretchy":754},[587,2603,2294],{},[591,2605,1009],{"stretchy":754},[1332,2607,1334],{},[587,2609,1337],{},[587,2611,2294],{},[591,2613,1012],{},[1302,2615,2616,2618],{},[1141,2617,1306],{},[1141,2619,2507],{},[1316,2621,2622,2659,2661],{},[584,2623,2624,2626,2628,2638,2640,2643,2645,2651,2653,2655,2657],{},[591,2625,755],{"fence":606},[591,2627,593],{},[1302,2629,2630,2636],{},[1136,2631,2632,2634],{},[587,2633,2294],{},[1141,2635,1242],{},[1141,2637,2507],{},[591,2639,2314],{},[1141,2641,2642],{},"1,5",[1332,2644,1334],{},[1136,2646,2647,2649],{},[587,2648,2294],{},[1141,2650,1143],{},[591,2652,2314],{},[1141,2654,2323],{},[587,2656,2294],{},[591,2658,765],{"fence":606},[1141,2660,1237],{},[1141,2662,2507],{},[591,2664,1012],{},[1302,2666,2667,2670],{},[1141,2668,2669],{},"192",[1141,2671,2507],{},[591,2673,1012],{},[1141,2675,2676],{},"16",[598,2678,2679],{"encoding":600},"\\overline{T} = \\frac{1}{12} \\int_0^{12} T(t)\\,dt = \\frac{1}{12} \\left[-\\frac{t^3}{12} + 1{,}5\\,t^2 + 10t\\right]_0^{12} = \\frac{192}{12} = 16",[568,2681,2683,2731,2889,3195,3272],{"className":2682,"ariaHidden":606},[605],[568,2684,2686,2690,2722,2725,2728],{"className":2685},[610],[568,2687],{"className":2688,"style":2689},[614],"height:0.8833em;",[568,2691,2693],{"className":2692},[619,684],[568,2694,2696],{"className":2695},[688],[568,2697,2699],{"className":2698},[693],[568,2700,2702,2713],{"className":2701,"style":2689},[697],[568,2703,2704,2707],{"style":701},[568,2705],{"className":2706,"style":706},[705],[568,2708,2710],{"className":2709},[619],[568,2711,2289],{"className":2712,"style":2339},[619,620],[568,2714,2716,2719],{"style":2715},"top:-3.8033em;",[568,2717],{"className":2718,"style":706},[705],[568,2720],{"className":2721,"style":724},[723],[568,2723],{"className":2724,"style":1046},[624],[568,2726,1012],{"className":2727},[1050],[568,2729],{"className":2730,"style":1046},[624],[568,2732,2734,2737,2799,2802,2856,2859,2862,2865,2868,2871,2874,2877,2880,2883,2886],{"className":2733},[610],[568,2735],{"className":2736,"style":1459},[614],[568,2738,2740,2743,2796],{"className":2739},[619],[568,2741],{"className":2742},[782,1466],[568,2744,2746],{"className":2745},[1302],[568,2747,2749,2788],{"className":2748},[688,689],[568,2750,2752,2785],{"className":2751},[693],[568,2753,2755,2766,2774],{"className":2754,"style":1479},[697],[568,2756,2757,2760],{"style":1482},[568,2758],{"className":2759,"style":706},[705],[568,2761,2763],{"className":2762},[619],[568,2764,2507],{"className":2765},[619],[568,2767,2768,2771],{"style":1506},[568,2769],{"className":2770,"style":706},[705],[568,2772],{"className":2773,"style":724},[1513],[568,2775,2776,2779],{"style":1516},[568,2777],{"className":2778,"style":706},[705],[568,2780,2782],{"className":2781},[619],[568,2783,1306],{"className":2784},[619],[568,2786,729],{"className":2787},[728],[568,2789,2791],{"className":2790},[693],[568,2792,2794],{"className":2793,"style":1719},[697],[568,2795],{},[568,2797],{"className":2798},[800,1466],[568,2800],{"className":2801,"style":793},[624],[568,2803,2805,2808],{"className":2804},[1547],[568,2806,1320],{"className":2807,"style":1553},[1547,1551,1552],[568,2809,2811],{"className":2810},[1193],[568,2812,2814,2848],{"className":2813},[688,689],[568,2815,2817,2845],{"className":2816},[693],[568,2818,2820,2831],{"className":2819,"style":1566},[697],[568,2821,2822,2825],{"style":1569},[568,2823],{"className":2824,"style":1209},[705],[568,2826,2828],{"className":2827},[1213,1214,1215,1216],[568,2829,1237],{"className":2830},[619,1216],[568,2832,2833,2836],{"style":1581},[568,2834],{"className":2835,"style":1209},[705],[568,2837,2839],{"className":2838},[1213,1214,1215,1216],[568,2840,2842],{"className":2841},[619,1216],[568,2843,2507],{"className":2844},[619,1216],[568,2846,729],{"className":2847},[728],[568,2849,2851],{"className":2850},[693],[568,2852,2854],{"className":2853,"style":1600},[697],[568,2855],{},[568,2857],{"className":2858,"style":793},[624],[568,2860,2289],{"className":2861,"style":2339},[619,620],[568,2863,1004],{"className":2864},[782],[568,2866,2294],{"className":2867},[619,620],[568,2869,1009],{"className":2870},[800],[568,2872],{"className":2873,"style":793},[624],[568,2875,1337],{"className":2876},[619,620],[568,2878,2294],{"className":2879},[619,620],[568,2881],{"className":2882,"style":1046},[624],[568,2884,1012],{"className":2885},[1050],[568,2887],{"className":2888,"style":1046},[624],[568,2890,2892,2895,2957,2960,3186,3189,3192],{"className":2891},[610],[568,2893],{"className":2894,"style":1740},[614],[568,2896,2898,2901,2954],{"className":2897},[619],[568,2899],{"className":2900},[782,1466],[568,2902,2904],{"className":2903},[1302],[568,2905,2907,2946],{"className":2906},[688,689],[568,2908,2910,2943],{"className":2909},[693],[568,2911,2913,2924,2932],{"className":2912,"style":1479},[697],[568,2914,2915,2918],{"style":1482},[568,2916],{"className":2917,"style":706},[705],[568,2919,2921],{"className":2920},[619],[568,2922,2507],{"className":2923},[619],[568,2925,2926,2929],{"style":1506},[568,2927],{"className":2928,"style":706},[705],[568,2930],{"className":2931,"style":724},[1513],[568,2933,2934,2937],{"style":1516},[568,2935],{"className":2936,"style":706},[705],[568,2938,2940],{"className":2939},[619],[568,2941,1306],{"className":2942},[619],[568,2944,729],{"className":2945},[728],[568,2947,2949],{"className":2948},[693],[568,2950,2952],{"className":2951,"style":1719},[697],[568,2953],{},[568,2955],{"className":2956},[800,1466],[568,2958],{"className":2959,"style":793},[624],[568,2961,2963,3138],{"className":2962},[1744],[568,2964,2966,2972,2975,3063,3066,3069,3072,3075,3081,3085,3088,3117,3120,3123,3126,3129,3132],{"className":2965},[1744],[568,2967,2969],{"className":2968,"style":1752},[782,1751],[568,2970,755],{"className":2971},[1756,1215],[568,2973,593],{"className":2974},[619],[568,2976,2978,2981,3060],{"className":2977},[619],[568,2979],{"className":2980},[782,1466],[568,2982,2984],{"className":2983},[1302],[568,2985,2987,3052],{"className":2986},[688,689],[568,2988,2990,3049],{"className":2989},[693],[568,2991,2993,3004,3012],{"className":2992,"style":1775},[697],[568,2994,2995,2998],{"style":1482},[568,2996],{"className":2997,"style":706},[705],[568,2999,3001],{"className":3000},[619],[568,3002,2507],{"className":3003},[619],[568,3005,3006,3009],{"style":1506},[568,3007],{"className":3008,"style":706},[705],[568,3010],{"className":3011,"style":724},[1513],[568,3013,3014,3017],{"style":1516},[568,3015],{"className":3016,"style":706},[705],[568,3018,3020],{"className":3019},[619],[568,3021,3023,3026],{"className":3022},[619],[568,3024,2294],{"className":3025},[619,620],[568,3027,3029],{"className":3028},[1193],[568,3030,3032],{"className":3031},[688],[568,3033,3035],{"className":3034},[693],[568,3036,3038],{"className":3037,"style":1183},[697],[568,3039,3040,3043],{"style":1205},[568,3041],{"className":3042,"style":1209},[705],[568,3044,3046],{"className":3045},[1213,1214,1215,1216],[568,3047,1242],{"className":3048},[619,1216],[568,3050,729],{"className":3051},[728],[568,3053,3055],{"className":3054},[693],[568,3056,3058],{"className":3057,"style":1719},[697],[568,3059],{},[568,3061],{"className":3062},[800,1466],[568,3064],{"className":3065,"style":625},[624],[568,3067,2314],{"className":3068},[629],[568,3070],{"className":3071,"style":625},[624],[568,3073,1306],{"className":3074},[619],[568,3076,3078],{"className":3077},[619],[568,3079,760],{"className":3080},[789],[568,3082,3084],{"className":3083},[619],"5",[568,3086],{"className":3087,"style":793},[624],[568,3089,3091,3094],{"className":3090},[619],[568,3092,2294],{"className":3093},[619,620],[568,3095,3097],{"className":3096},[1193],[568,3098,3100],{"className":3099},[688],[568,3101,3103],{"className":3102},[693],[568,3104,3106],{"className":3105,"style":1624},[697],[568,3107,3108,3111],{"style":1627},[568,3109],{"className":3110,"style":1209},[705],[568,3112,3114],{"className":3113},[1213,1214,1215,1216],[568,3115,1143],{"className":3116},[619,1216],[568,3118],{"className":3119,"style":625},[624],[568,3121,2314],{"className":3122},[629],[568,3124],{"className":3125,"style":625},[624],[568,3127,2323],{"className":3128},[619],[568,3130,2294],{"className":3131},[619,620],[568,3133,3135],{"className":3134,"style":1752},[800,1751],[568,3136,765],{"className":3137},[1756,1215],[568,3139,3141],{"className":3140},[1193],[568,3142,3144,3178],{"className":3143},[688,689],[568,3145,3147,3175],{"className":3146},[693],[568,3148,3150,3161],{"className":3149,"style":1864},[697],[568,3151,3152,3155],{"style":1867},[568,3153],{"className":3154,"style":1209},[705],[568,3156,3158],{"className":3157},[1213,1214,1215,1216],[568,3159,1237],{"className":3160},[619,1216],[568,3162,3163,3166],{"style":1879},[568,3164],{"className":3165,"style":1209},[705],[568,3167,3169],{"className":3168},[1213,1214,1215,1216],[568,3170,3172],{"className":3171},[619,1216],[568,3173,2507],{"className":3174},[619,1216],[568,3176,729],{"className":3177},[728],[568,3179,3181],{"className":3180},[693],[568,3182,3184],{"className":3183,"style":1898},[697],[568,3185],{},[568,3187],{"className":3188,"style":1046},[624],[568,3190,1012],{"className":3191},[1050],[568,3193],{"className":3194,"style":1046},[624],[568,3196,3198,3201,3263,3266,3269],{"className":3197},[610],[568,3199],{"className":3200,"style":1661},[614],[568,3202,3204,3207,3260],{"className":3203},[619],[568,3205],{"className":3206},[782,1466],[568,3208,3210],{"className":3209},[1302],[568,3211,3213,3252],{"className":3212},[688,689],[568,3214,3216,3249],{"className":3215},[693],[568,3217,3219,3230,3238],{"className":3218,"style":1479},[697],[568,3220,3221,3224],{"style":1482},[568,3222],{"className":3223,"style":706},[705],[568,3225,3227],{"className":3226},[619],[568,3228,2507],{"className":3229},[619],[568,3231,3232,3235],{"style":1506},[568,3233],{"className":3234,"style":706},[705],[568,3236],{"className":3237,"style":724},[1513],[568,3239,3240,3243],{"style":1516},[568,3241],{"className":3242,"style":706},[705],[568,3244,3246],{"className":3245},[619],[568,3247,2669],{"className":3248},[619],[568,3250,729],{"className":3251},[728],[568,3253,3255],{"className":3254},[693],[568,3256,3258],{"className":3257,"style":1719},[697],[568,3259],{},[568,3261],{"className":3262},[800,1466],[568,3264],{"className":3265,"style":1046},[624],[568,3267,1012],{"className":3268},[1050],[568,3270],{"className":3271,"style":1046},[624],[568,3273,3275,3278],{"className":3274},[610],[568,3276],{"className":3277,"style":1993},[614],[568,3279,2676],{"className":3280},[619],[564,3282,3283,3284,831],{},"Die mittlere Temperatur beträgt ",[568,3285,3287,3306],{"className":3286},[571],[568,3288,3290],{"className":3289},[575],[577,3291,3292],{"xmlns":579},[581,3293,3294,3303],{},[584,3295,3296,3298,3300],{},[1141,3297,2676],{},[1332,3299,1334],{},[1332,3301,3302],{},"°C",[598,3304,3305],{"encoding":600},"16\\,\\text{°C}",[568,3307,3309],{"className":3308,"ariaHidden":606},[605],[568,3310,3312,3315,3318,3321],{"className":3311},[610],[568,3313],{"className":3314,"style":954},[614],[568,3316,2676],{"className":3317},[619],[568,3319],{"className":3320,"style":793},[624],[568,3322,3325],{"className":3323},[619,3324],"text",[568,3326,3302],{"className":3327},[619],[559,3329,3331],{"id":3330},"typische-fehler","Typische Fehler",[3333,3334,3335,3630,3684],"ul",{},[3336,3337,3338,3339,3518,3519,1220,3578,3629],"li",{},"Nur die Randwerte mitteln: ",[568,3340,3342,3383],{"className":3341},[571],[568,3343,3345],{"className":3344},[575],[577,3346,3347],{"xmlns":579},[581,3348,3349,3380],{},[584,3350,3351,3375,3377],{},[1302,3352,3353,3373],{},[584,3354,3355,3357,3359,3361,3363,3365,3367,3369,3371],{},[587,3356,664],{},[591,3358,1004],{"stretchy":754},[1141,3360,1237],{},[591,3362,1009],{"stretchy":754},[591,3364,2314],{},[587,3366,664],{},[591,3368,1004],{"stretchy":754},[1141,3370,1242],{},[591,3372,1009],{"stretchy":754},[1141,3374,1143],{},[591,3376,1012],{},[1141,3378,3379],{},"4,5",[598,3381,3382],{"encoding":600},"\\frac{f(0) + f(3)}{2} = 4{,}5",[568,3384,3386,3498],{"className":3385,"ariaHidden":606},[605],[568,3387,3389,3393,3489,3492,3495],{"className":3388},[610],[568,3390],{"className":3391,"style":3392},[614],"height:1.355em;vertical-align:-0.345em;",[568,3394,3396,3399,3486],{"className":3395},[619],[568,3397],{"className":3398},[782,1466],[568,3400,3402],{"className":3401},[1302],[568,3403,3405,3477],{"className":3404},[688,689],[568,3406,3408,3474],{"className":3407},[693],[568,3409,3412,3427,3435],{"className":3410,"style":3411},[697],"height:1.01em;",[568,3413,3415,3418],{"style":3414},"top:-2.655em;",[568,3416],{"className":3417,"style":706},[705],[568,3419,3421],{"className":3420},[1213,1214,1215,1216],[568,3422,3424],{"className":3423},[619,1216],[568,3425,1143],{"className":3426},[619,1216],[568,3428,3429,3432],{"style":1506},[568,3430],{"className":3431,"style":706},[705],[568,3433],{"className":3434,"style":724},[1513],[568,3436,3438,3441],{"style":3437},"top:-3.485em;",[568,3439],{"className":3440,"style":706},[705],[568,3442,3444],{"className":3443},[1213,1214,1215,1216],[568,3445,3447,3450,3453,3456,3459,3462,3465,3468,3471],{"className":3446},[619,1216],[568,3448,664],{"className":3449,"style":713},[619,620,1216],[568,3451,1004],{"className":3452},[782,1216],[568,3454,1237],{"className":3455},[619,1216],[568,3457,1009],{"className":3458},[800,1216],[568,3460,2314],{"className":3461},[629,1216],[568,3463,664],{"className":3464,"style":713},[619,620,1216],[568,3466,1004],{"className":3467},[782,1216],[568,3469,1242],{"className":3470},[619,1216],[568,3472,1009],{"className":3473},[800,1216],[568,3475,729],{"className":3476},[728],[568,3478,3480],{"className":3479},[693],[568,3481,3484],{"className":3482,"style":3483},[697],"height:0.345em;",[568,3485],{},[568,3487],{"className":3488},[800,1466],[568,3490],{"className":3491,"style":1046},[624],[568,3493,1012],{"className":3494},[1050],[568,3496],{"className":3497,"style":1046},[624],[568,3499,3501,3505,3509,3515],{"className":3500},[610],[568,3502],{"className":3503,"style":3504},[614],"height:0.8389em;vertical-align:-0.1944em;",[568,3506,3508],{"className":3507},[619],"4",[568,3510,3512],{"className":3511},[619],[568,3513,760],{"className":3514},[789],[568,3516,3084],{"className":3517},[619]," ist nicht der Mittelwert von ",[568,3520,3522,3540],{"className":3521},[571],[568,3523,3525],{"className":3524},[575],[577,3526,3527],{"xmlns":579},[581,3528,3529,3537],{},[584,3530,3531],{},[1136,3532,3533,3535],{},[587,3534,1130],{},[1141,3536,1143],{},[598,3538,3539],{"encoding":600},"x^2",[568,3541,3543],{"className":3542,"ariaHidden":606},[605],[568,3544,3546,3549],{"className":3545},[610],[568,3547],{"className":3548,"style":1183},[614],[568,3550,3552,3555],{"className":3551},[619],[568,3553,1130],{"className":3554},[619,620],[568,3556,3558],{"className":3557},[1193],[568,3559,3561],{"className":3560},[688],[568,3562,3564],{"className":3563},[693],[568,3565,3567],{"className":3566,"style":1183},[697],[568,3568,3569,3572],{"style":1205},[568,3570],{"className":3571,"style":1209},[705],[568,3573,3575],{"className":3574},[1213,1214,1215,1216],[568,3576,1143],{"className":3577},[619,1216],[568,3579,3581,3602],{"className":3580},[571],[568,3582,3584],{"className":3583},[575],[577,3585,3586],{"xmlns":579},[581,3587,3588,3600],{},[584,3589,3590,3592,3594,3596,3598],{},[591,3591,755],{"stretchy":754},[1141,3593,1237],{},[591,3595,760],{"separator":606},[1141,3597,1242],{},[591,3599,765],{"stretchy":754},[598,3601,1247],{"encoding":600},[568,3603,3605],{"className":3604,"ariaHidden":606},[605],[568,3606,3608,3611,3614,3617,3620,3623,3626],{"className":3607},[610],[568,3609],{"className":3610,"style":778},[614],[568,3612,755],{"className":3613},[782],[568,3615,1237],{"className":3616},[619],[568,3618,760],{"className":3619},[789],[568,3621],{"className":3622,"style":793},[624],[568,3624,1242],{"className":3625},[619],[568,3627,765],{"className":3628},[800],". Das stimmt nur bei linearen Funktionen.",[3336,3631,3632,3633,3683],{},"Das Teilen durch ",[568,3634,3636,3653],{"className":3635},[571],[568,3637,3639],{"className":3638},[575],[577,3640,3641],{"xmlns":579},[581,3642,3643,3651],{},[584,3644,3645,3647,3649],{},[587,3646,589],{},[591,3648,593],{},[587,3650,596],{},[598,3652,601],{"encoding":600},[568,3654,3656,3674],{"className":3655,"ariaHidden":606},[605],[568,3657,3659,3662,3665,3668,3671],{"className":3658},[610],[568,3660],{"className":3661,"style":615},[614],[568,3663,589],{"className":3664},[619,620],[568,3666],{"className":3667,"style":625},[624],[568,3669,593],{"className":3670},[629],[568,3672],{"className":3673,"style":625},[624],[568,3675,3677,3680],{"className":3676},[610],[568,3678],{"className":3679,"style":639},[614],[568,3681,596],{"className":3682},[619,620]," vergessen und das Integral selbst als Mittelwert angeben.",[3336,3685,3686,3687,3841],{},"Mittelwert der Funktion und mittlere Steigung ",[568,3688,3690,3732],{"className":3689},[571],[568,3691,3693],{"className":3692},[575],[577,3694,3695],{"xmlns":579},[581,3696,3697,3729],{},[584,3698,3699],{},[1302,3700,3701,3721],{},[584,3702,3703,3705,3707,3709,3711,3713,3715,3717,3719],{},[587,3704,664],{},[591,3706,1004],{"stretchy":754},[587,3708,589],{},[591,3710,1009],{"stretchy":754},[591,3712,593],{},[587,3714,664],{},[591,3716,1004],{"stretchy":754},[587,3718,596],{},[591,3720,1009],{"stretchy":754},[584,3722,3723,3725,3727],{},[587,3724,589],{},[591,3726,593],{},[587,3728,596],{},[598,3730,3731],{"encoding":600},"\\frac{f(b) - f(a)}{b - 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verwechseln.",{"title":3843,"searchDepth":3844,"depth":3844,"links":3845},"",2,[3846,3847,3848],{"id":561,"depth":3844,"text":562},{"id":1107,"depth":3844,"text":1108},{"id":3330,"depth":3844,"text":3331},[3850,3852,3854,3856,3858,3860],{"lhs":3851,"rhs":1242},"1\u002F(3 - 0) * (3^3\u002F3 - 0)",{"lhs":3853,"rhs":1242},"sqrt(3)^2",{"lhs":3855,"rhs":2669},"-(12^3)\u002F12 + 1.5*12^2 + 10*12",{"lhs":3857,"rhs":2676},"192 \u002F 12",{"lhs":3859,"rhs":2676},"round(sum(map(0:999, f(k) = -0.25 * ((k + 0.5) * 12 \u002F 1000)^2 + 3 * (k + 0.5) * 12 \u002F 1000 + 10)) * 12 \u002F 1000 \u002F 12, 4)",{"lhs":3861,"rhs":3862},"(0^2 + 3^2) \u002F 2","4.5","f \\text{ stetig auf } [a, b],\\ a \u003C b","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation 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