2D 座標架
Author: 藍邦偉  老師

$ O $

$ 漸近線 $

$ 水平漸近線 ：\;若\lim_{ x \to ±\infty }f(x)=a，\;則\;y=a\;為\;f(x)\;的一條水平漸近線$
$鉛直漸近線：\;若\lim_{ x \to a^+ }f(x)=±\infty\;或\lim_{ x \to a^- }f(x)=±\infty，\;則\;x=a\;稱為\;f(x)\;的一條鉛直漸近線$
$斜漸近線：\;若\lim_{ x \to ±\infty }\left [ f(x)-(ax+b) \right ]=0，\;則\;y=ax+b為\;f(x)\;的一條斜漸近線 $

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
Q_2: 0.72 * Corner[1] + 0.28 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
n = 0 (slider from 0 to 6, step 1)
a = -2 (slider from -5 to 5, step 1)
b = 1 (slider from If[n ≟ 3, 1, -5] to 5, step 0.1)
f_1(x) = b + 1 / (x - a)
L_{1a}: x = a
L_{1b}: y = b
f_2(x) = b * (x - a) + 1 / (x - a)
L_{2a}: x = a
L_{2b}: y = b * (x - a)
L_{3a}: x = a
c = 1 (slider from 1 to 16, step 1)
L_{4c}: y = a
f_3(x) = (x^(2) - c) / (x - a)^(3)
f_5(x) = a / (x - b)^(2)
L_{5a}: x = b
f_4(x) = a * x^(2) / (x^(2) - b)
L_{4b}: x = -sqrt(b)
L_{4a}: x = sqrt(b)
f_6(x) = a * x + b + 1 / (x - c)
A = (-10.166001951661604, 1.817880114764293)
text5: "$ f(x)=" + (LaTeX[f_5]) + " $
$鉛直漸近線\;" + (LaTeX[L_{5a}]) + "$"
text1: "$ f(x)=" + (LaTeX[f_1]) + " $
$\lim_{ x \to " + (LaTeX[a]) + "^+ }f(x)=\infty$
$\lim_{ x \to " + (LaTeX[a]) + " ^-}f(x)=-\infty$
$鉛直漸近線\;" + (LaTeX[L_{1a}]) + "$
$\lim_{ x \to \infty }f(x)=" + (LaTeX[b]) + "$
$\lim_{ x \to -\infty }f(x)=" + (LaTeX[b]) + "$
$水平漸近線\;" + (LaTeX[L_{1b}]) + "$"
text2: "$f(x)= " + (LaTeX[f_2]) + " $
$\lim_{ x \to " + (LaTeX[a]) + "^-} =-\infty $
$\lim_{ x \to " + (LaTeX[a]) + "^+ }=\infty$
$鉛直漸近線" + (LaTeX[L_{2a}]) + "$
$\lim_{ x \to \infty }\left [f(x)-(ax+b)  \right ]=0 $
$\lim_{ x \to -\infty }\left [f(x)-(ax+b)  \right ]=0$
$斜漸近線" + (LaTeX[L_{2b}]) + "$"
text3: "$ f(x)=" + (LaTeX[f_3]) + " $
$\lim_{ x \to " + (LaTeX[a]) + "^+ }f(x)=\infty$
$\lim_{ x \to " + (LaTeX[a]) + "^-}f(x)=-\infty$
$鉛直漸近線\;" + (LaTeX[L_{3a}]) + "$
$\lim_{ x \to \infty }f(x)=0$
$\lim_{ x \to- \infty }f(x)=0$
$水平漸近線\;" + (LaTeX[L_{3b}]) + "$"
text4: "$ f(x)=" + (LaTeX[f_4]) + " $
$水平漸近線\;" + (LaTeX[L_{4c}]) + "$
$" + (LaTeX[If[b > 0, "鉛直漸近線"]]) + "\;" + (LaTeX[If[b > 0, L_{4b}]]) + "$
$" + (LaTeX[If[b > 0, "鉛直漸近線"]]) + "\;" + (LaTeX[If[b > 0, L_{4a}]]) + "$"