泰勒展開式
Author: 藍邦偉老師

$ a= $

$ b= $

c=

$ d= $

$ e= $

$ f= $

1

2

3

4

5

6

$ 泰勒展開式 $

n = 0 (slider from 0 to 5, step 1)
a = 0
b = 0
c_1 = 3
d = 0
e = 0
f = 0
inputBox1 = Textfield(a)
inputBox2 = Textfield(b)
inputBox3 = Textfield(c_1)
inputBox4 = Textfield(d)
inputBox5 = Textfield(e)
inputBox6 = Textfield(f)
f_2(x) = a * x^(2) + b * x + c_1
f_3(x) = a * x^(3) + b * x^(2) + c_1 * x + d
f_4(x) = a * x^(4) + b * x^(3) + c_1 * x^(2) + d * x + e
f_1(x) = a * x + b
f_5(x) = a * x^(5) + b * x^(4) + c_1 * x^(3) + d * x^(2) + e * x + f
c = 0 (slider from -5 to 5, step 1)
g_1 = TaylorSeries(f_1, c, 1)
k = 1 (slider from 1 to If[n ≤ 1, 1, n], step 1)
g_2 = TaylorSeries(f_2, c, k)
g_3 = TaylorSeries(f_3, c, k)
g_4 = TaylorSeries(f_4, c, k)
g_5 = TaylorSeries(f_5, c, k)
text1: "$f(x)= " + (LaTeX[g_1]) + " $"
text2: "$ f(x)=" + (LaTeX[g_2]) + " $"
text3: "$ f(x)=" + (LaTeX[g_3]) + " $"
text4: "$ f(x)=" + (LaTeX[g_4]) + " $"
t_{TE}: "$ f(x)=" + (LaTeX[g_5]) + " $"
text7: "$ " + (LaTeX[k]) + "次近似 $"
A = (-3.7, 0.84)
text6: "$ f(x)=" + (LaTeX[If[n ≟ 1, f_1, If[n ≟ 2, f_2, If[n ≟ 3, f_3, If[n ≟ 4, f_4, f_5]]]]]) + "\;在\;x=" + (LaTeX[c]) + " \;附近的泰勒展開式$"
t_{form}: "$f(x)=" + (LaTeX[If[n ≟ 1, "ax", If[n ≟ 2, "ax^2", If[n ≟ 3, "ax^3", If[n ≟ 4, "ax^4", If[n ≟ 5, "ax⁵"]]]]]]) + " " + (LaTeX[If[n ≟ 1, "+b", If[n ≟ 2, "+bx", If[n ≟ 3, "+bx^2", If[n ≟ 4, "+bx^3", If[n ≟ 5, "+bx^4"]]]]]]) + "" + (LaTeX[If[n ≟ 2, "+c", If[n ≟ 3, "+cx", If[n ≟ 4, "+cx^2", If[n ≟ 5, "+cx^3"]]]]]) + "" + (LaTeX[If[n ≟ 3, "+d", If[n ≟ 4, "+dx", If[n ≟ 5, "+dx^2"]]]]) + "" + (LaTeX[If[n ≟ 4, "+e", If[n ≟ 5, "+ex"]]]) + "" + (LaTeX[If[n ≟ 5, "+f"]]) + "$"