calc-014continuidad-evitable

x

x

f(x)

\(\displaystyle\lim_{x \to 2^+}{f(x)}=4\) \text{   }

\(\displaystyle\lim_{x \to 2^{-}}{f(x)}=4\) 

Límites

ver = 5 (slider from -5 to 7, step 0.1)
hor = 1.5 (slider from -5 to 5, step 0.1)
AA = (1.8000000000000003, 0)
xx: x(AA) - 0.1
g(x) = x^(2)
C = Point(xAxis)
P2: (x(C), g(x(C)))
a = OrthogonalLine(P2, xAxis)
E: (2, ver)
r = 0.07
c = Circle(P2, r)
d = Circle(P2, r)
xa: x(P2)
f = If(y(E) ≟ 4, x^(2), If[x ≠ x(C), x^(2), If[x ≟ x(C), y(E)]])
texto1 = LaTeX(f, true, true)
A: (hor, 0)
F: (x(A), f(x(A)))
yy: f(x(A))
h = Segment(F, A)
B: (0, y(F))
i = Segment(B, F)
texto3: "\text{La función f(x) es continua en } ℝ-\{" + (LaTeX[xa]) + "\}.\\
\text{En x=" + (LaTeX[xa]) + " tiene una discontinuidad evitable.}\\
\\
\text{Se puede \textit{evitar} moviendo el punto azul}\\ \text{y tapando el hueco.}"
b = false
texto2: "x=" + (LaTeX[hor]) + "\text{     } f(" + (LaTeX[hor]) + ")=" + (LaTeX[yy]) + ""