www.michael-buhlmann.de
Funktion: f(x) = , Df = R, Wf = (1; +∞), reelle Funktion, x -> -∞: f(x) -> 1 = y als Grenzkurve, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | 1 | 0 | 0 | 0 | |
-9.5 | 1 | 0 | 0 | 0 | |
-9 | 1.0001 | 0 | 0 | 0 | |
-8.5 | 1.0001 | 0 | 0 | 0 | |
-8 | 1.0002 | 0 | 0 | 0 | |
-7.5 | 1.0003 | 0 | 0 | 0 | |
-7 | 1.0005 | 0 | 0 | 0 | |
-6.5 | 1.0008 | 0 | 0 | 0 | |
-6 | 1.0012 | 0 | 0 | 0 | |
-5.5 | 1.002 | 0 | 0 | 0 | |
-5 | 1.0034 | 0 | 0 | 0 | |
-4.5 | 1.0055 | 0.01 | 0.01 | 0.01 | |
-4 | 1.0091 | 0.01 | 0.01 | 0.01 | |
-3.5 | 1.015 | 0.01 | 0.01 | 0.01 | |
-3 | 1.0246 | 0.02 | 0.02 | 0.02 | |
-2.5 | 1.0402 | 0.04 | 0.04 | 0.04 | |
-2 | 1.0655 | 0.06 | 0.06 | 0.05 | |
-1.5 | 1.106 | 0.1 | 0.09 | 0.08 | |
-1 | 1.1696 | 0.16 | 0.14 | 0.1 | |
-0.5 | 1.2675 | 0.24 | 0.19 | 0.13 | |
0 | 1.4142 | 0.35 | 0.27 | 0.15 | Schnittpunkt Sy(0|1.41) |
0.5 | 1.6275 | 0.51 | 0.35 | 0.18 | |
1 | 1.9283 | 0.7 | 0.45 | 0.21 | |
1.5 | 2.3413 | 0.96 | 0.57 | 0.26 | |
2 | 2.8964 | 1.28 | 0.71 | 0.33 | |
2.5 | 3.6308 | 1.68 | 0.9 | 0.43 | |
3 | 4.5919 | 2.19 | 1.15 | 0.55 | |
3.5 | 5.8408 | 2.83 | 1.46 | 0.71 | |
4 | 7.4564 | 3.66 | 1.86 | 0.92 | |
4.5 | 9.5403 | 4.72 | 2.38 | 1.18 | |
5 | 12.2235 | 6.07 | 3.06 | 1.52 | |
5.5 | 15.6746 | 7.81 | 3.92 | 1.96 | |
6 | 20.1104 | 10.03 | 5.03 | 2.51 | |
6.5 | 25.8097 | 12.89 | 6.45 | 3.23 | |
7 | 33.1305 | 16.55 | 8.28 | 4.15 | |
7.5 | 42.5328 | 21.25 | 10.63 | 5.33 | |
8 | 54.6073 | 27.29 | 13.65 | 6.84 | |
8.5 | 70.1125 | 35.05 | 17.53 | 8.78 | |
9 | 90.0227 | 45.01 | 22.51 | 11.28 | |
9.5 | 115.5886 | 57.79 | 28.9 | 14.48 | |
10 | 148.4165 | 74.21 | 37.1 | 18.6 | |
Graph: | |||||
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