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Funktion: f(x) = esin(x), Df = R, Wf = [1/e; e], reelle Funktion, Periode: p = 2π ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | 1.7229 | -1.45 | 0.28 | 2.78 | |
| -9.5 | 1.078 | -1.07 | 0.99 | 0.24 | |
| -9 | 0.6622 | -0.6 | 0.82 | -0.64 | |
| -8.5 | 0.45 | -0.27 | 0.52 | -0.48 | |
| -8 | 0.3718 | -0.05 | 0.38 | -0.11 | |
| -7.854 | 0.3679 | 0 | 0.37 | 0 | Tiefpunkt T(-7.85|0.37) |
| -7.5 | 0.3914 | 0.14 | 0.41 | 0.26 | |
| -7 | 0.5184 | 0.39 | 0.64 | 0.6 | |
| -6.5 | 0.8064 | 0.79 | 0.94 | 0.47 | |
| -6 | 1.3224 | 1.27 | 0.85 | -1.17 | |
| -5.618 | 1.8537 | 1.46 | 0 | -3.26 | Wendepunkt W(-5.62|1.85) |
| -5.5 | 2.0249 | 1.44 | -0.41 | -3.76 | |
| -5 | 2.6089 | 0.74 | -2.29 | -2.8 | |
| -4.714 | 2.7183 | 0 | -2.72 | -0.01 | Hochpunkt H(-4.71|2.72) |
| -4.5 | 2.6579 | -0.56 | -2.48 | 2.19 | |
| -4 | 2.1314 | -1.39 | -0.7 | 3.96 | |
| -3.808 | 1.8555 | -1.46 | 0 | 3.26 | Wendepunkt W(-3.81|1.86) |
| -3.5 | 1.4202 | -1.33 | 0.75 | 1.56 | |
| -3 | 0.8684 | -0.86 | 0.97 | -0.35 | |
| -2.5 | 0.5497 | -0.44 | 0.68 | -0.63 | |
| -2 | 0.4028 | -0.17 | 0.44 | -0.32 | |
| -1.572 | 0.3679 | 0 | 0.37 | 0 | Tiefpunkt T(-1.57|0.37) |
| -1.5 | 0.3688 | 0.03 | 0.37 | 0.05 | |
| -1 | 0.4311 | 0.23 | 0.49 | 0.42 | |
| -0.5 | 0.6191 | 0.54 | 0.77 | 0.66 | |
| 0 | 1 | 1 | 1 | 0 | Schnittpunkt Sy(0|1) |
| 0.5 | 1.6151 | 1.42 | 0.47 | -2.37 | |
| 0.666 | 1.8549 | 1.46 | 0 | -3.27 | Wendepunkt W(0.67|1.85) |
| 1 | 2.3198 | 1.25 | -1.27 | -4.05 | |
| 1.5 | 2.7115 | 0.19 | -2.69 | -0.75 | |
| 1.57 | 2.7183 | 0 | -2.72 | 0 | Hochpunkt H(1.57|2.72) |
| 2 | 2.4826 | -1.03 | -1.83 | 3.68 | |
| 2.474 | 1.8573 | -1.46 | 0 | 3.26 | Wendepunkt W(2.47|1.86) |
| 2.5 | 1.8193 | -1.46 | 0.08 | 3.13 | |
| 3 | 1.1516 | -1.14 | 0.97 | 0.5 | |
| 3.5 | 0.7041 | -0.66 | 0.86 | -0.61 | |
| 4 | 0.4692 | -0.31 | 0.56 | -0.52 | |
| 4.5 | 0.3762 | -0.08 | 0.38 | -0.16 | |
| 4.712 | 0.3679 | 0 | 0.37 | 0 | Tiefpunkt T(4.71|0.37) |
| 5 | 0.3833 | 0.11 | 0.4 | 0.21 | |
| 5.5 | 0.4938 | 0.35 | 0.6 | 0.57 | |
| 6 | 0.7562 | 0.73 | 0.91 | 0.55 | |
| 6.5 | 1.24 | 1.21 | 0.92 | -0.84 | |
| 6.948 | 1.8532 | 1.46 | 0 | -3.26 | Wendepunkt W(6.95|1.85) |
| 7 | 1.929 | 1.45 | -0.17 | -3.5 | |
| 7.5 | 2.5549 | 0.89 | -2.09 | -3.27 | |
| 7.852 | 2.7183 | 0.01 | -2.72 | -0.01 | Hochpunkt H(7.85|2.72) |
| 8 | 2.6895 | -0.39 | -2.6 | 1.55 | |
| 8.5 | 2.2222 | -1.34 | -0.97 | 4.06 | |
| 8.758 | 1.8561 | -1.46 | 0 | 3.26 | Wendepunkt W(8.76|1.86) |
| 9 | 1.51 | -1.38 | 0.63 | 1.93 | |
| 9.5 | 0.9276 | -0.92 | 0.99 | -0.21 | |
| 10 | 0.5804 | -0.49 | 0.72 | -0.65 | |
| 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