calc-014-2-continuidad-salto-infinito
Date: 18 Febrero 2014

x

f(x)

Límites

ver = 3 (slider from -2 to 7, step 0.1)
g(x) = x^(2)
B = Point(xAxis)
A: (x(B), g(x(B)))
a = OrthogonalLine(A, xAxis)
E: (2, ver)
r = 0.07
xa: x(A)
f(x) = If[x < x(B), 1 / (2 - x), If[x ≥ x(B), (-(x - 2)^(2)) + y(E)]]
texto1 = LaTeX(f, true, true)
D = Intersect(xAxis, a)
C = Point(xAxis)
xx: x(C)
yy: f(x(C))
F: (x(C), f(x(C)))
h = OrthogonalLine(F, yAxis)
G = Intersect(yAxis, h)
i = Segment(G, F)
j = Segment(F, C)
texto3: "\text{La función f(x) es continua en ℝ-\{" + (LaTeX[xa]) + "\}.\\
En x=" + (LaTeX[xa]) + " tiene una discontinuidad\\de salto infinito.\\Para resolverla hay que traer una rama\\desde el infinito.} "
texto2: "x=" + (LaTeX[xx]) + "\text{     } f(" + (LaTeX[xx]) + ")=" + (LaTeX[yy]) + ""
b = false
fde2: f(2)
texto4: "\(\displaystyle\lim_{x \to 2^+}{f(x)}=" + (LaTeX[fde2]) + "\) \text{   }

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