www.michael-buhlmann.de
Funktion: f(x) = ln(x), Df = (0; +∞), Wf = R, reelle Funktion, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
0 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 0 mit: x -> 0+: f(x) -> -∞ |
0.5 | -0.6931 | 2 | -4 | 15.54 | |
1 | 0 | 1 | -1 | 1.97 | Nullstelle N(1|0) |
1.5 | 0.4055 | 0.67 | -0.44 | 0.59 | |
2 | 0.6931 | 0.5 | -0.25 | 0.25 | |
2.5 | 0.9163 | 0.4 | -0.16 | 0.13 | |
3 | 1.0986 | 0.33 | -0.11 | 0.07 | |
3.5 | 1.2528 | 0.29 | -0.08 | 0.05 | |
4 | 1.3863 | 0.25 | -0.06 | 0.03 | |
4.5 | 1.5041 | 0.22 | -0.05 | 0.02 | |
5 | 1.6094 | 0.2 | -0.04 | 0.02 | |
5.5 | 1.7047 | 0.18 | -0.03 | 0.01 | |
6 | 1.7918 | 0.17 | -0.03 | 0.01 | |
6.5 | 1.8718 | 0.15 | -0.02 | 0.01 | |
7 | 1.9459 | 0.14 | -0.02 | 0.01 | |
7.5 | 2.0149 | 0.13 | -0.02 | 0 | |
8 | 2.0794 | 0.13 | -0.02 | 0 | |
8.5 | 2.1401 | 0.12 | -0.01 | 0 | |
9 | 2.1972 | 0.11 | -0.01 | 0 | |
9.5 | 2.2513 | 0.11 | -0.01 | 0 | |
10 | 2.3026 | 0.1 | -0.01 | 0 | |
10.5 | 2.3514 | 0.1 | -0.01 | 0 | |
11 | 2.3979 | 0.09 | -0.01 | 0 | |
11.5 | 2.4423 | 0.09 | -0.01 | 0 | |
12 | 2.4849 | 0.08 | -0.01 | 0 | |
12.5 | 2.5257 | 0.08 | -0.01 | 0 | |
13 | 2.5649 | 0.08 | -0.01 | 0 | |
13.5 | 2.6027 | 0.07 | -0.01 | 0 | |
14 | 2.6391 | 0.07 | -0.01 | 0 | |
14.5 | 2.6741 | 0.07 | 0 | 0 | |
15 | 2.7081 | 0.07 | 0 | 0 | |
15.5 | 2.7408 | 0.06 | 0 | 0 | |
16 | 2.7726 | 0.06 | 0 | 0 | |
16.5 | 2.8034 | 0.06 | 0 | 0 | |
17 | 2.8332 | 0.06 | 0 | 0 | |
17.5 | 2.8622 | 0.06 | 0 | 0 | |
18 | 2.8904 | 0.06 | 0 | 0 | |
18.5 | 2.9178 | 0.05 | 0 | 0 | |
19 | 2.9444 | 0.05 | 0 | 0 | |
19.5 | 2.9704 | 0.05 | 0 | 0 | |
20 | 2.9957 | 0.05 | 0 | 0 | |
Graph: | |||||
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