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Funktion: f(x) = 4-2/ex/5, Df = R, Wf = (-∞; 4), reelle Funktion, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> 4 = y als Grenzkurve ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -10.7781 | 2.96 | -0.59 | 0.12 | |
| -9.5 | -9.3718 | 2.67 | -0.53 | 0.11 | |
| -9 | -8.0993 | 2.42 | -0.48 | 0.1 | |
| -8.5 | -6.9479 | 2.19 | -0.44 | 0.09 | |
| -8 | -5.9061 | 1.98 | -0.4 | 0.08 | |
| -7.5 | -4.9634 | 1.79 | -0.36 | 0.07 | |
| -7 | -4.1104 | 1.62 | -0.32 | 0.06 | |
| -6.5 | -3.3386 | 1.47 | -0.29 | 0.06 | |
| -6 | -2.6402 | 1.33 | -0.27 | 0.05 | |
| -5.5 | -2.0083 | 1.2 | -0.24 | 0.05 | |
| -5 | -1.4366 | 1.09 | -0.22 | 0.04 | |
| -4.5 | -0.9192 | 0.98 | -0.2 | 0.04 | |
| -4 | -0.4511 | 0.89 | -0.18 | 0.04 | |
| -3.5 | -0.0275 | 0.81 | -0.16 | 0.03 | |
| -3.47 | -0.0034 | 0.8 | -0.16 | 0.03 | Nullstelle N(-3.47|0) |
| -3 | 0.3558 | 0.73 | -0.15 | 0.03 | |
| -2.5 | 0.7026 | 0.66 | -0.13 | 0.03 | |
| -2 | 1.0164 | 0.6 | -0.12 | 0.02 | |
| -1.5 | 1.3003 | 0.54 | -0.11 | 0.02 | |
| -1 | 1.5572 | 0.49 | -0.1 | 0.02 | |
| -0.5 | 1.7897 | 0.44 | -0.09 | 0.02 | |
| 0 | 2 | 0.4 | -0.08 | 0.02 | Schnittpunkt Sy(0|2) |
| 0.5 | 2.1903 | 0.36 | -0.07 | 0.01 | |
| 1 | 2.3625 | 0.33 | -0.07 | 0.01 | |
| 1.5 | 2.5184 | 0.3 | -0.06 | 0.01 | |
| 2 | 2.6594 | 0.27 | -0.05 | 0.01 | |
| 2.5 | 2.7869 | 0.24 | -0.05 | 0.01 | |
| 3 | 2.9024 | 0.22 | -0.04 | 0.01 | |
| 3.5 | 3.0068 | 0.2 | -0.04 | 0.01 | |
| 4 | 3.1013 | 0.18 | -0.04 | 0.01 | |
| 4.5 | 3.1869 | 0.16 | -0.03 | 0.01 | |
| 5 | 3.2642 | 0.15 | -0.03 | 0.01 | |
| 5.5 | 3.3343 | 0.13 | -0.03 | 0.01 | |
| 6 | 3.3976 | 0.12 | -0.02 | 0 | |
| 6.5 | 3.4549 | 0.11 | -0.02 | 0 | |
| 7 | 3.5068 | 0.1 | -0.02 | 0 | |
| 7.5 | 3.5537 | 0.09 | -0.02 | 0 | |
| 8 | 3.5962 | 0.08 | -0.02 | 0 | |
| 8.5 | 3.6346 | 0.07 | -0.01 | 0 | |
| 9 | 3.6694 | 0.07 | -0.01 | 0 | |
| 9.5 | 3.7009 | 0.06 | -0.01 | 0 | |
| 10 | 3.7293 | 0.05 | -0.01 | 0 | |
| Graph: | |||||
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Graph(en) der Asymptote(n), Grenzkurve(n).
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