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Funktion: f(x) = sin(π·ex), Df = R, Wf = [-1; 1], x -> -∞: f(x) -> 0 = y als Grenzkurve, reelle Funktion ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -3 | 0.1558 | 0.15 | 0.15 | 0.14 | |
| -2.5 | 0.255 | 0.25 | 0.23 | 0.18 | |
| -2 | 0.4125 | 0.39 | 0.31 | 0.09 | |
| -1.5 | 0.645 | 0.54 | 0.22 | -0.68 | |
| -1.2955 | 0.7579 | 0.56 | 0 | -1.54 | Wendepunkt W(-1.3|0.76) |
| -1 | 0.9151 | 0.47 | -0.76 | -3.83 | |
| -0.6935 | 1 | 0 | -2.46 | -7.4 | Hochpunkt H(-0.69|1) |
| -0.5 | 0.9445 | -0.63 | -4.06 | -8.64 | |
| 0 | 0 | -3.14 | -3.14 | 27.91 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) |
| 0.0865 | -0.2801 | -3.29 | 0 | 45.21 | Wendepunkt W(0.09|-0.28) |
| 0.405 | -1 | 0 | 22.18 | 66.69 | Tiefpunkt T(0.41|-1) |
| 0.5 | -0.8928 | 2.33 | 26.29 | 11.39 | |
| 0.693 | 0 | 6.28 | 6.32 | -241.92 | Nullstelle N(0.69|0) |
| 0.717 | 0.1511 | 6.36 | 0 | -276.14 | Wendepunkt W(0.72|0.15) |
| 0.916 | 1 | 0 | -61.63 | -185.19 | Hochpunkt H(0.92|1) |
| 1 | 0.7739 | -5.41 | -61.85 | 221.17 | |
| 1.0985 | 0.0011 | -9.42 | -9.52 | 828.43 | Nullstelle N(1.1|0) |
| 1.1095 | -0.103 | -9.48 | 0 | 880.03 | Wendepunkt W(1.11|-0.1) |
| 1.2525 | -1 | 0 | 120.81 | 362.88 | Tiefpunkt T(1.25|-1) |
| 1.386 | 0 | 12.56 | 13.15 | -1971.3 | Nullstelle N(1.39|0) |
| 1.3925 | 0.0781 | 12.61 | 0 | -2042.91 | Wendepunkt W(1.39|0.08) |
| 1.5 | 0.9983 | 0.81 | -197.1 | -744.14 | |
| 1.504 | 1 | 0 | -199.81 | -592.91 | Hochpunkt H(1.5|1) |
| 1.609 | 0 | -15.7 | -17.4 | 3855.67 | Nullstelle N(1.61|0.01) |
| 1.613 | -0.056 | -15.74 | 0 | 3942.26 | Wendepunkt W(1.61|-0.06) |
| 1.7045 | -1 | 0 | 298.33 | 895.47 | Tiefpunkt T(1.7|-1) |
| 1.7915 | 0 | 18.84 | 20.58 | -6678.06 | Nullstelle N(1.79|0) |
| 1.7945 | 0.0517 | 18.88 | 0 | -6788.5 | Wendepunkt W(1.79|0.05) |
| 1.8715 | 1 | 0.13 | -416.6 | -1259.84 | Hochpunkt H(1.87|1) |
| 1.9455 | 0 | -21.98 | -26.34 | 10602.73 | Nullstelle N(1.95|0) |
| 1.9475 | -0.035 | -22.01 | 0 | 10722.03 | Wendepunkt W(1.95|-0.03) |
| 2 | -0.9399 | -7.93 | 498.53 | 5722.31 | |
| 2.0145 | -1 | 0 | 554.46 | 1711.93 | Tiefpunkt T(2.01|-1) |
| 2.079 | 0 | 25.12 | 32.12 | -15831.36 | Nullstelle N(2.08|0) |
| 2.081 | 0.0392 | 25.15 | 0.32 | -16006.09 | Wendepunkt W(2.08|0.04) |
| 2.14 | 1 | 0 | -712.93 | -2046.43 | Hochpunkt H(2.14|1) |
| 2.197 | 0.0063 | -28.27 | -33.34 | 22578.2 | Nullstelle N(2.2|0.01) |
| 2.198 | -0.0219 | -28.29 | 0 | 22704.54 | Wendepunkt W(2.2|-0.02) |
| 2.251 | -1 | 0 | 889.9 | 2704.84 | Tiefpunkt T(2.25|-1) |
| 2.3025 | 0 | 31.41 | 34.05 | -31004.19 | Nullstelle N(2.3|0) |
| 2.3035 | 0.0288 | 31.43 | 3 | -31170.24 | Wendepunkt W(2.3|0.03) |
| 2.351 | 1 | 0 | -1086.79 | -3411.26 | Hochpunkt H(2.35|1) |
| 2.3975 | 0 | -34.54 | -50.83 | 41196.82 | Nullstelle N(2.4|0) |
| 2.3985 | -0.0209 | -34.57 | 0 | 41427.18 | Wendepunkt W(2.4|-0.02) |
| 2.442 | -1 | 0 | 1303.76 | 4079.58 | Tiefpunkt T(2.44|-1) |
| 2.4845 | 0 | 37.68 | 59.44 | -53487.54 | Nullstelle N(2.48|-0.02) |
| 2.4855 | 0.0224 | 37.71 | 0 | -53783.15 | Wendepunkt W(2.49|0.02) |
| 2.5 | 0.5424 | 32.15 | -762.36 | -49224.34 | |
| 2.5255 | 1 | 0 | -1540.96 | -4575.08 | Hochpunkt H(2.53|1) |
| 2.5645 | 0 | -40.81 | -71.38 | 67992.77 | Nullstelle N(2.56|0.02) |
| 2.5655 | -0.0225 | -40.85 | 0 | 68367.61 | Wendepunkt W(2.57|-0.02) |
| 2.6025 | -1 | 0 | 1797.59 | 5200.76 | Tiefpunkt T(2.6|-1) |
| 2.639 | 0 | 43.98 | 48.85 | -85127.48 | Nullstelle N(2.64|0) |
| 2.674 | 1 | 0.31 | -2074.02 | -5788.78 | Hochpunkt H(2.67|1) |
| 2.708 | 0 | -47.12 | -52.36 | 104712.71 | Nullstelle N(2.71|0) |
| 2.7405 | -1 | 0 | 2368.31 | 7616.16 | Tiefpunkt T(2.74|-1) |
| 2.7725 | -0.0045 | 50.26 | 61.51 | -127060.24 | Nullstelle N(2.77|0) = Wendepunkt W(2.77|0) |
| 2.803 | 0.9998 | 0 | -2683.48 | -8853.11 | Hochpunkt H(2.8|1) |
| 2.833 | 0 | -53.39 | -85.85 | 152300.18 | Nullstelle N(2.83|0) |
| 2.862 | -1 | 0 | 3020.37 | 8617.07 | Tiefpunkt T(2.86|-1) |
| 2.89 | 0 | 56.51 | 123.65 | -180617.81 | Nullstelle N(2.89|0) |
| 2.9175 | 1 | 0.91 | -3374.48 | -10366.07 | Hochpunkt H(2.92|1) |
| 2.944 | 0.0262 | -59.63 | -152.86 | 212334.36 | Nullstelle N(2.94|0.03) |
| 2.97 | -1 | 0 | 3746.75 | 13564.22 | Tiefpunkt T(2.97|-1) |
| 2.9955 | 0 | 62.8 | 120.35 | -247983.19 | Nullstelle N(3|0) = Wendepunkt W(3|0) |
| 3 | 0.2655 | 60.83 | -996.24 | -244590.42 | |
| Graph: | |||||
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Abkürzungen: Df = (maximaler) Definitionsbereich, f(x) = Funktion, f'(x) = 1. Ableitung, f''(x) = 2. Ableitung, f'''(x) = 3. Ableitung, H = Hochpunkt, L = Lücke, N = Nullstelle, P = Polstelle, R = reelle Zahlen, S = Sprungstelle, T = Tiefpunkt, W = Wendepunkt, WS = Sattelpunkt, Wf = Wertebereich, {.} = ein-/mehrelementige Menge, [.; .] = abgeschlossenes Intervall, (.; .) = offenes Intervall, [.; .), (.; .] = halboffenes Intervall, ∞ = unendlich.
Bearbeiter: Michael Buhlmann