24 - Vom Sinus zur Geraden (Sin2Lin)

Version Stand
29.10.2018
Andreas Jäger

n =

ε =

ε = 10^{(\ \ \ \ \ \ \ \ \ \ \ )}

ε=0.01

n=1

x_0   =

x0=0

Version

x0 = 0 (slider from -20 to 20, step 0.01)
n = 1 (slider from 1 to 9, step 1)
f(x) = sin(x)
ε = -2 (slider from -7 to -1, step 1)
Eingabefeld1 = Textfield(n)
Eingabefeld2 = Textfield(ε)
eps: 10^(ε)
X0: (x0, 0)
f9 = If(n ≟ 9, ((x - x0) * cos(x0)) - ((1 / 6 * (x - x0)^(3)) * cos(x0)) + ((1 / 120 * (x - x0)^(5)) * cos(x0)) - (((x - x0)^(7) * cos(x0))) / 5040 + (((x - x0)^(9) * cos(x0))) / 362880 + sin(x0) - ((1 / 2 * (x - x0)^(2)) * sin(x0)) + ((1 / 24 * (x - x0)^(4)) * sin(x0)) - ((1 / 720 * (x - x0)^(6)) * sin(x0)) + (((x - x0)^(8) * sin(x0))) / 40320)
f8 = If(n ≟ 8, ((x - x0) * cos(x0)) - ((1 / 6 * (x - x0)^(3)) * cos(x0)) + ((1 / 120 * (x - x0)^(5)) * cos(x0)) - (((x - x0)^(7) * cos(x0))) / 5040 + sin(x0) - ((1 / 2 * (x - x0)^(2)) * sin(x0)) + ((1 / 24 * (x - x0)^(4)) * sin(x0)) - ((1 / 720 * (x - x0)^(6)) * sin(x0)) + (((x - x0)^(8) * sin(x0))) / 40320)
f7 = If(n ≟ 7, ((x - x0) * cos(x0)) - ((1 / 6 * (x - x0)^(3)) * cos(x0)) + ((1 / 120 * (x - x0)^(5)) * cos(x0)) - (((x - x0)^(7) * cos(x0))) / 5040 + sin(x0) - ((1 / 2 * (x - x0)^(2)) * sin(x0)) + ((1 / 24 * (x - x0)^(4)) * sin(x0)) - ((1 / 720 * (x - x0)^(6)) * sin(x0)))
f6 = If(n ≟ 6, ((x - x0) * cos(x0)) - ((1 / 6 * (x - x0)^(3)) * cos(x0)) + ((1 / 120 * (x - x0)^(5)) * cos(x0)) + sin(x0) - ((1 / 2 * (x - x0)^(2)) * sin(x0)) + ((1 / 24 * (x - x0)^(4)) * sin(x0)) - ((1 / 720 * (x - x0)^(6)) * sin(x0)))
f5 = If(n ≟ 5, ((x - x0) * cos(x0)) - ((1 / 6 * (x - x0)^(3)) * cos(x0)) + ((1 / 120 * (x - x0)^(5)) * cos(x0)) + sin(x0) - ((1 / 2 * (x - x0)^(2)) * sin(x0)) + ((1 / 24 * (x - x0)^(4)) * sin(x0)))
f4 = If(n ≟ 4, ((x - x0) * cos(x0)) - ((1 / 6 * (x - x0)^(3)) * cos(x0)) + sin(x0) - ((1 / 2 * (x - x0)^(2)) * sin(x0)) + ((1 / 24 * (x - x0)^(4)) * sin(x0)))
f3 = If(n ≟ 3, ((x - x0) * cos(x0)) - ((1 / 6 * (x - x0)^(3)) * cos(x0)) + sin(x0) - ((1 / 2 * (x - x0)^(2)) * sin(x0)))
f2 = If(n ≟ 2, ((x - x0) * cos(x0)) + sin(x0) - ((1 / 2 * (x - x0)^(2)) * sin(x0)))
f1 = If(n ≟ 1, ((x - x0) * cos(x0)) + sin(x0))
ff = If(n ≟ 9, f9, If[n ≟ 8, f8, If[n ≟ 7, f7, If[n ≟ 6, f6, If[n ≟ 5, f5, If[n ≟ 4, f4, If[n ≟ 3, f3, If[n ≟ 2, f2, If[n ≟ 1, f1]]]]]]]])
Eingabefeld3 = Textfield(x0)
dx(x) = If[abs(f(x) - ff(x)) ≤ eps, ff(x)]
a = false
Text3 = LaTeX(ff, true, true)
nn = 1