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

x

f(x)

Límites

hor = 3 (slider from -15 to 15, step 0.1)
ver = 6 (slider from -1 to 8, 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
c = Circle(A, r)
d = Circle(A, r)
xa: x(A)
f(x) = If[x < x(B), x^(2), If[x ≥ x(B), (-(x - 2)^(2)) + y(E)]]
D = Intersect(xAxis, a)
C: (hor, 0)
F: (x(C), f(x(C)))
xx: x(C)
yy: f(xx)
texto1: "f(x)=" + (LaTeX[f]) + ""
h = OrthogonalLine(F, yAxis)
G = Intersect(h, yAxis)
i = Segment(G, F)
j = Segment(F, C)
texto3: "\text{La función f(x) es continua en ℝ-\{" + (LaTeX[xa]) + "\}.}\\
\text{En x=" + (LaTeX[xa]) + " tiene una discontinuidad de salto finito.}\\
\text{Se puede resolver moviendo el punto azul}\\
\text{y empalmando ambas ramas.}\\
\text{Pero ello implica mover infinitos puntos}"
b = false
fde2: f(2)
texto4: "\(\displaystyle\lim_{x \to 2^+}{f(x)}=" + (LaTeX[fde2]) + "\) \text{   }

\(\displaystyle\lim_{x \to 2^{-}}{f(x)}=4\) "
texto2: "x=" + (LaTeX[xx]) + "\text{      } f(" + (LaTeX[xx]) + ")=" + (LaTeX[yy]) + ""