Ha 2020

n_c

n_c immer zu klein

Cauchy-Konvergenzkriterium

Asymptoten kurz

Asymptoten lang

a = 0.5 (slider from 0 to 1, step 0.1)
n_c = 16 (slider from 1 to 50, step 1)
f(x) = 2 + ((4 / x + a) * sin((((2 * x) + 1) / 2 * π)))
m = 17 (slider from 1 to 50, step 1)
ε = 1.7 (slider from 0 to 2, step 0.01)
s: 50
S: (s, f(m))
T: (n_c, f(m))
A: (n_c, f(m) + ε)
D: (50, f(m) + ε)
n = 24 (slider from 1 to 50, step 1)
r: y = f(m) - ε
l1 = Sequence((n, f(n)), n, 2, 70, 2)
E: (n_c, 0)
E_f: (n_c, f(n_c))
l2 = Sequence((n, f(n)), n, 3, 70, 2)
M: (m, 0)
N: (n, 0)
M_f: (m, f(m))
N_f: (n, f(n))
M_n: (m, f(n))
N_m: (n, f(m))
f_{3} = Segment(E_f, E)
h_{2}: y = f(m) + ε
p: y = f(m)
q: y = f(m) + ε
B: (n_c, f(m) - ε)
C: (s, f(m) - ε)
Vieleck1 = Polygon({A, T, S, D, A})
i = Segment(M_f, M_n)
Vieleck2 = Polygon({T, B, C, S, T})
Text3: "|a_m-a_n|=" + (LaTeX[i]) + ""
g(x) = 2 + 4 / x + a
h(x) = 2 - 4 / x - a
t: y = 2 + a
f_1: y = 2 - a
F = Point(t)
G = Point(f_1)
H = Intersect(t, yAxis)
j = Segment(H, F)
I = Intersect(f_1, yAxis)
k = Segment(I, G)
b = false
c = false
J = (25.5, -2.5)