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Funktion: f(x) = , Df = (0; e-2] ∪ (1; +∞), Wf = [0; +∞)\{√5}, reelle Funktion, x -> 0: f(x) -> +√5, x -> +∞: f(x) -> √5 = y als Grenzkurve ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
0 | 2.236 | - | - | - | Lücke L(0|2.24) |
0.045 | 1.3324 | -8.68 | 12.21 | -2514.47 | Wendepunkt W(0.05|1.33) |
0.1353 | 0 | - | - | - | Nullstelle N(0.14|0) |
1 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 1 |
1.5 | 5.4464 | -3.72 | 12.18 | -62.1 | |
2 | 4.4076 | -1.18 | 1.98 | -5.2 | |
2.5 | 3.9892 | -0.6 | 0.67 | -1.19 | |
3 | 3.7553 | -0.37 | 0.31 | -0.42 | |
3.5 | 3.6031 | -0.25 | 0.17 | -0.18 | |
4 | 3.4948 | -0.19 | 0.1 | -0.09 | |
4.5 | 3.413 | -0.14 | 0.07 | -0.05 | |
5 | 3.3486 | -0.12 | 0.05 | -0.03 | |
5.5 | 3.2964 | -0.09 | 0.03 | -0.02 | |
6 | 3.2529 | -0.08 | 0.03 | -0.01 | |
6.5 | 3.216 | -0.07 | 0.02 | -0.01 | |
7 | 3.1842 | -0.06 | 0.02 | -0.01 | |
7.5 | 3.1564 | -0.05 | 0.01 | -0.01 | |
8 | 3.1319 | -0.05 | 0.01 | 0 | |
8.5 | 3.1101 | -0.04 | 0.01 | 0 | |
9 | 3.0905 | -0.04 | 0.01 | 0 | |
9.5 | 3.0728 | -0.03 | 0.01 | 0 | |
10 | 3.0566 | -0.03 | 0.01 | 0 | |
10.5 | 3.0418 | -0.03 | 0 | 0 | |
11 | 3.0283 | -0.03 | 0 | 0 | |
11.5 | 3.0157 | -0.02 | 0 | 0 | |
12 | 3.004 | -0.02 | 0 | 0 | |
12.5 | 2.9932 | -0.02 | 0 | 0 | |
13 | 2.9831 | -0.02 | 0 | 0 | |
13.5 | 2.9736 | -0.02 | 0 | 0 | |
14 | 2.9647 | -0.02 | 0 | 0 | |
14.5 | 2.9563 | -0.02 | 0 | 0 | |
15 | 2.9483 | -0.02 | 0 | 0 | |
15.5 | 2.9408 | -0.01 | 0 | 0 | |
16 | 2.9337 | -0.01 | 0 | 0 | |
16.5 | 2.927 | -0.01 | 0 | 0 | |
17 | 2.9205 | -0.01 | 0 | 0 | |
17.5 | 2.9144 | -0.01 | 0 | 0 | |
18 | 2.9086 | -0.01 | 0 | 0 | |
18.5 | 2.903 | -0.01 | 0 | 0 | |
19 | 2.8976 | -0.01 | 0 | 0 | |
19.5 | 2.8925 | -0.01 | 0 | 0 | |
20 | 2.8876 | -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