連續函數示例
Author: 藍邦偉  老師

$ O $

$ 連續函數示例 $

$f(x)=\left\lbrace  \begin{array}{ll} 2x+3\;,當x>0 \ 1\;,\;\;\;\;\;\;\;\;當x=0 \ -x+3\;,當x<0 \end{array} \right.\ $

$g(x)=\frac{x+2}{x-1}$

$ h(x)=\frac{|x|}{x} $

$ y=f(x)在x=0處不連續 $

$ y=g(x)在x=1處不連續 $

$  y=h(x)在x=0處不連續 $ 

$x=1 $

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: 0.7 * Corner[1] + 0.3 * 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])
g(x) = (x + 2) / (x - 1)
n = 0 (slider from 0 to 3, step 1)
A = (0, 1)
B = (-15.04088531440176, 6.235803440599068)
P_1 = (0, 1)
P_2 = (0, -1)
B_1 = (0, 3)
f_1 = Function(2 * x + 3, 0.07, x(Corner[2]))
f_2 = Function(-x + 3, x(Corner[1]), -0.07)
h_1 = Segment((x(Q_2), -1), (-0.09, -1))
h_2 = Segment((0.09, 1), (x(Corner[2]), 1))