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Funktion: f(x) = , Df = R\[-4.5; -2], Wf = [0; +∞), reelle Funktion, x -> -∞: f(x) -> (ln(2))4 = y als Grenzkurve, x -> +∞: f(x) -> (ln(2))4 = y als Grenzkurve ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-20 | 0.0873 | -0.01 | 0 | 0 | |
-19.5 | 0.0844 | -0.01 | 0 | 0 | |
-19 | 0.0814 | -0.01 | 0 | 0 | |
-18.5 | 0.0782 | -0.01 | 0 | 0 | |
-18 | 0.075 | -0.01 | 0 | 0 | |
-17.5 | 0.0716 | -0.01 | 0 | 0 | |
-17 | 0.0681 | -0.01 | 0 | 0 | |
-16.5 | 0.0645 | -0.01 | 0 | 0 | |
-16 | 0.0607 | -0.01 | 0 | 0 | |
-15.5 | 0.0569 | -0.01 | 0 | 0 | |
-15 | 0.0529 | -0.01 | 0 | 0 | |
-14.5 | 0.0488 | -0.01 | 0 | 0 | |
-14 | 0.0446 | -0.01 | 0 | 0 | |
-13.5 | 0.0403 | -0.01 | 0 | 0 | |
-13 | 0.0359 | -0.01 | 0 | 0 | |
-12.5 | 0.0315 | -0.01 | 0 | 0 | |
-12.295 | 0.0297 | -0.01 | 0 | 0 | Wendepunkt W(-12.29|0.03) |
-12 | 0.027 | -0.01 | 0 | 0 | |
-11.5 | 0.0226 | -0.01 | 0 | 0 | |
-11 | 0.0183 | -0.01 | 0 | 0 | |
-10.5 | 0.0141 | -0.01 | 0 | 0 | |
-10 | 0.0103 | -0.01 | 0 | 0 | |
-9.5 | 0.0068 | -0.01 | 0 | 0 | |
-9 | 0.004 | -0.01 | 0 | 0 | |
-8.5 | 0.0019 | 0 | 0 | 0 | |
-8 | 0.0006 | 0 | 0 | 0 | |
-7.5 | 0.0001 | 0 | 0 | 0 | |
-7.005 | 0 | 0 | 0 | 0 | Tiefpunkt T(-7|0) |
-7 | 0 | 0 | 0 | 0 | |
-6.5 | 0.0002 | 0 | 0.01 | 0.09 | |
-6 | 0.0068 | 0.04 | 0.21 | 1.04 | |
-5.5 | 0.0981 | 0.5 | 2.56 | 13.86 | |
-5 | 1.4567 | 8.84 | 60.87 | 499.98 | |
-4.5 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = -4.5 |
-2 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = -2 |
-1.5 | 38.1277 | -102.3 | 444.55 | -2642.67 | |
-1 | 14.3381 | -21.05 | 50.25 | -162.33 | |
-0.5 | 7.8523 | -7.82 | 13 | -29.28 | |
0 | 5.1178 | -3.78 | 4.83 | -8.37 | Schnittpunkt Sy(0|5.12) |
0.5 | 3.6934 | -2.13 | 2.2 | -3.11 | |
1 | 2.8498 | -1.33 | 1.15 | -1.37 | |
1.5 | 2.3049 | -0.89 | 0.66 | -0.68 | |
2 | 1.93 | -0.63 | 0.41 | -0.37 | |
2.5 | 1.6594 | -0.46 | 0.27 | -0.21 | |
3 | 1.4567 | -0.35 | 0.18 | -0.13 | |
3.5 | 1.3002 | -0.28 | 0.13 | -0.08 | |
4 | 1.1764 | -0.22 | 0.09 | -0.06 | |
4.5 | 1.0764 | -0.18 | 0.07 | -0.04 | |
5 | 0.9941 | -0.15 | 0.05 | -0.03 | |
5.5 | 0.9255 | -0.13 | 0.04 | -0.02 | |
6 | 0.8675 | -0.11 | 0.03 | -0.01 | |
6.5 | 0.8179 | -0.09 | 0.03 | -0.01 | |
7 | 0.775 | -0.08 | 0.02 | -0.01 | |
7.5 | 0.7377 | -0.07 | 0.02 | -0.01 | |
8 | 0.7049 | -0.06 | 0.02 | -0.01 | |
8.5 | 0.6759 | -0.05 | 0.01 | 0 | |
9 | 0.6501 | -0.05 | 0.01 | 0 | |
9.5 | 0.627 | -0.04 | 0.01 | 0 | |
10 | 0.6062 | -0.04 | 0.01 | 0 | |
10.5 | 0.5874 | -0.04 | 0.01 | 0 | |
11 | 0.5704 | -0.03 | 0.01 | 0 | |
11.5 | 0.5548 | -0.03 | 0.01 | 0 | |
12 | 0.5405 | -0.03 | 0 | 0 | |
12.5 | 0.5275 | -0.03 | 0 | 0 | |
13 | 0.5154 | -0.02 | 0 | 0 | |
13.5 | 0.5043 | -0.02 | 0 | 0 | |
14 | 0.4939 | -0.02 | 0 | 0 | |
14.5 | 0.4843 | -0.02 | 0 | 0 | |
15 | 0.4754 | -0.02 | 0 | 0 | |
15.5 | 0.467 | -0.02 | 0 | 0 | |
16 | 0.4592 | -0.02 | 0 | 0 | |
16.5 | 0.4519 | -0.01 | 0 | 0 | |
17 | 0.445 | -0.01 | 0 | 0 | |
17.5 | 0.4385 | -0.01 | 0 | 0 | |
18 | 0.4324 | -0.01 | 0 | 0 | |
18.5 | 0.4267 | -0.01 | 0 | 0 | |
19 | 0.4212 | -0.01 | 0 | 0 | |
19.5 | 0.4161 | -0.01 | 0 | 0 | |
20 | 0.4112 | -0.01 | 0 | 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