www.michael-buhlmann.de
Funktion: f(x) = = arsinh(x), Df = R, Wf = R, reelle Funktion, Funktion punktsymmetrisch zu O(0|0), x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | -2.9982 | 0.1 | 0.01 | 0 | |
-9.5 | -2.9472 | 0.1 | 0.01 | 0 | |
-9 | -2.8934 | 0.11 | 0.01 | 0 | |
-8.5 | -2.8367 | 0.12 | 0.01 | 0 | |
-8 | -2.7765 | 0.12 | 0.02 | 0 | |
-7.5 | -2.7125 | 0.13 | 0.02 | 0 | |
-7 | -2.6441 | 0.14 | 0.02 | 0.01 | |
-6.5 | -2.5708 | 0.15 | 0.02 | 0.01 | |
-6 | -2.4918 | 0.16 | 0.03 | 0.01 | |
-5.5 | -2.4061 | 0.18 | 0.03 | 0.01 | |
-5 | -2.3124 | 0.2 | 0.04 | 0.01 | |
-4.5 | -2.2093 | 0.22 | 0.05 | 0.02 | |
-4 | -2.0947 | 0.24 | 0.06 | 0.03 | |
-3.5 | -1.9657 | 0.27 | 0.07 | 0.04 | |
-3 | -1.8184 | 0.32 | 0.09 | 0.05 | |
-2.5 | -1.6472 | 0.37 | 0.13 | 0.08 | |
-2 | -1.4436 | 0.45 | 0.18 | 0.13 | |
-1.5 | -1.1948 | 0.55 | 0.26 | 0.18 | |
-1 | -0.8814 | 0.71 | 0.35 | 0.18 | |
-0.5 | -0.4812 | 0.89 | 0.36 | -0.29 | |
0 | 0 | 1 | 0 | -1 | Schnittpunkt Sy(0|0) = Wendepunkt W(0|0) |
0.5 | 0.4812 | 0.89 | -0.36 | -0.28 | |
1 | 0.8814 | 0.71 | -0.35 | 0.18 | |
1.5 | 1.1948 | 0.55 | -0.26 | 0.18 | |
2 | 1.4436 | 0.45 | -0.18 | 0.12 | |
2.5 | 1.6472 | 0.37 | -0.13 | 0.08 | |
3 | 1.8184 | 0.32 | -0.09 | 0.05 | |
3.5 | 1.9657 | 0.27 | -0.07 | 0.04 | |
4 | 2.0947 | 0.24 | -0.06 | 0.03 | |
4.5 | 2.2093 | 0.22 | -0.05 | 0.02 | |
5 | 2.3124 | 0.2 | -0.04 | 0.01 | |
5.5 | 2.4061 | 0.18 | -0.03 | 0.01 | |
6 | 2.4918 | 0.16 | -0.03 | 0.01 | |
6.5 | 2.5708 | 0.15 | -0.02 | 0.01 | |
7 | 2.6441 | 0.14 | -0.02 | 0.01 | |
7.5 | 2.7125 | 0.13 | -0.02 | 0 | |
8 | 2.7765 | 0.12 | -0.02 | 0 | |
8.5 | 2.8367 | 0.12 | -0.01 | 0 | |
9 | 2.8934 | 0.11 | -0.01 | 0 | |
9.5 | 2.9472 | 0.1 | -0.01 | 0 | |
10 | 2.9982 | 0.1 | -0.01 | 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