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Funktion: f(x) = sin(x), Df = R, Wf = [-1; 1], Periode: p = 2π, reelle Funktion ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | 0.544 | -0.84 | -0.54 | 0.84 | |
| -9.5 | 0.0752 | -1 | -0.08 | 1 | |
| -9.43 | 0 | -1 | 0 | 1 | Nullstelle N(-9.43|0) = Wendepunkt W(-9.43|0) |
| -9 | -0.4121 | -0.91 | 0.41 | 0.91 | |
| -8.5 | -0.7985 | -0.6 | 0.8 | 0.6 | |
| -8 | -0.9894 | -0.15 | 0.99 | 0.14 | |
| -7.86 | -1 | 0 | 1 | 0 | Tiefpunkt T(-7.86|-1) |
| -7.5 | -0.938 | 0.35 | 0.94 | -0.35 | |
| -7 | -0.657 | 0.75 | 0.66 | -0.76 | |
| -6.5 | -0.2151 | 0.98 | 0.22 | -0.98 | |
| -6.29 | 0 | 1 | 0 | -1 | Nullstelle N(-6.29|0) = Wendepunkt W(-6.29|0) |
| -6 | 0.2794 | 0.96 | -0.28 | -0.96 | |
| -5.5 | 0.7055 | 0.71 | -0.71 | -0.71 | |
| -5 | 0.9589 | 0.28 | -0.96 | -0.28 | |
| -4.72 | 1 | 0 | -1 | 0 | Hochpunkt H(-4.72|1) |
| -4.5 | 0.9775 | -0.21 | -0.98 | 0.22 | |
| -4 | 0.7568 | -0.65 | -0.76 | 0.66 | |
| -3.5 | 0.3508 | -0.94 | -0.35 | 0.94 | |
| -3.15 | 0.0084 | -1 | -0.01 | 1 | Nullstelle N(-3.15|0.01) = Wendepunkt W(-3.15|0.01) |
| -3 | -0.1411 | -0.99 | 0.14 | 0.99 | |
| -2.5 | -0.5985 | -0.8 | 0.6 | 0.8 | |
| -2 | -0.9093 | -0.42 | 0.91 | 0.41 | |
| -1.58 | -1 | 0 | 1 | 0 | Tiefpunkt T(-1.58|-1) |
| -1.5 | -0.9975 | 0.07 | 1 | -0.08 | |
| -1 | -0.8415 | 0.54 | 0.84 | -0.54 | |
| -0.5 | -0.4794 | 0.88 | 0.48 | -0.88 | |
| 0 | 0 | 1 | 0 | -1 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Wendepunkt W(0|0) |
| 0.5 | 0.4794 | 0.88 | -0.48 | -0.88 | |
| 1 | 0.8415 | 0.54 | -0.84 | -0.54 | |
| 1.5 | 0.9975 | 0.07 | -1 | -0.07 | |
| 1.57 | 1 | 0 | -1 | 0 | Hochpunkt H(1.57|1) |
| 2 | 0.9093 | -0.42 | -0.91 | 0.42 | |
| 2.5 | 0.5985 | -0.8 | -0.6 | 0.8 | |
| 3 | 0.1411 | -0.99 | -0.14 | 0.99 | |
| 3.14 | -1 | 0 | 1 | Nullstelle N(3.14|0) = Wendepunkt W(3.14|0) | |
| 3.5 | -0.3508 | -0.94 | 0.35 | 0.93 | |
| 4 | -0.7568 | -0.65 | 0.76 | 0.65 | |
| 4.5 | -0.9775 | -0.21 | 0.98 | 0.21 | |
| 4.71 | -1 | 0 | 1 | 0 | Tiefpunkt T(4.71|-1) |
| 5 | -0.9589 | 0.28 | 0.96 | -0.29 | |
| 5.5 | -0.7055 | 0.71 | 0.71 | -0.71 | |
| 6 | -0.2794 | 0.96 | 0.28 | -0.96 | |
| 6.28 | 0 | 1 | 0 | -1 | Nullstelle N(6.28|0) = Wendepunkt W(6.28|0) |
| 6.5 | 0.2151 | 0.98 | -0.22 | -0.98 | |
| 7 | 0.657 | 0.75 | -0.66 | -0.75 | |
| 7.5 | 0.938 | 0.35 | -0.94 | -0.34 | |
| 7.85 | 1 | 0 | -1 | 0 | Hochpunkt H(7.85|1) |
| 8 | 0.9894 | -0.15 | -0.99 | 0.15 | |
| 8.5 | 0.7985 | -0.6 | -0.8 | 0.61 | |
| 9 | 0.4121 | -0.91 | -0.41 | 0.91 | |
| 9.42 | 0 | -1 | 0 | 1 | Nullstelle N(9.42|0) = Wendepunkt W(9.42|0) |
| 9.5 | -0.0752 | -1 | 0.08 | 1 | |
| 10 | -0.544 | -0.84 | 0.54 | 0.84 | |
| 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