x=

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f(x)=

x                    f(x)

Tendencia por la izquierda

Tendencia por la derecha

\lim_{ x \to +∞ }f(x)

\lim_{ x \to -∞}f(x)

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x               f(x)

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f(x) = If[x ≤ 0, -1 / x, x  <  1, -2 / ((x * (x - 2))), x ≤ 3, 4 / (((x - 3) * (x + 1))) + 2, ((-3 * x) + 5) / (3 - x)]
a = -1
CasillaDeEntrada1 = Textfield(a)
P: (a, f(a))
h = 0.81 (slider from 0.01 to 1.6, step 0.05)
b = OrthogonalLine(P, xAxis)
d_1 = OrthogonalLine(P, b)
F: (a, 0)
G: (0, f(a))
e = Segment(P, F)
g = Segment(P, G)
d = false
i = false
masinfinito = false
menosinfinito = false
CasillaDeEntrada2 = Textfield(f)
lista1 = Sequence(a - 1 / 10^(k), k, 1, 6)
lista2 = Sequence(f(Element[lista1, k]), k, 1, 6)
lista3 = Sequence(a + 1 / 10^(k), k, 1, 6)
lista4 = Sequence(f(Element[lista3, k]), k, 1, 6)
texto1 = TableText({lista1, lista2}, "v")
texto2 = TableText({lista3, lista4}, "v")
texto7: "\lim_{ x \to" + (LaTeX[a]) + "^{+}}f(x)"
texto10: "\lim_{ x \to " + (LaTeX[a]) + "^{-} }f(x)"
A: (a + h, f(a + h))
B: (a + h, 0)
C: (0, f(a + h))
c = Segment(C, A)
l = Segment(A, B)
D: (a - 1.6 + h, f(a - 1.6 + h))
E: (a - 1.6 + h, 0)
H: (0, f(a - 1.6 + h))
j = Segment(D, H)
k = Segment(D, E)
t = false
o = false
I: (3 + 10^(h), f(3 + 10^(h)))
J: (0, y(I))
K: (x(I), 0)
m = Segment(J, I)
n = Segment(I, K)
L: ((-10^(1.5 - h)), f((-10^(1.5 - h))))
M: (x(L), 0)
N: (0, y(L))
p = Segment(L, N)
q = Segment(L, M)
lista5 = Sequence(10^(k), k, 1, 6)
lista7 = Sequence((-10^(k)), k, 1, 6)
lista6 = Sequence(f(Element[lista5, k]), k, 1, 6)
lista8 = Sequence(f(Element[lista7, k]), k, 1, 6)
texto11 = TableText({lista5, lista6}, "v")
texto13 = TableText({lista7, lista8}, "v")
texto14: "" + (y(A)) + ""
texto15: "" + (y(D)) + ""
r = LimitBelow(f, a)
s = LimitAbove(f, a)
texto16: "" + r + ""
texto17: "" + s + ""
u = Limit(f, Infinity)
v = Limit(f, -Infinity)
w = false
texto18: "\lim_{ x \to +∞ }f(x)=" + (LaTeX[u]) + ""
texto19: "\lim_{ x \to -∞}f(x)=" + (LaTeX[v]) + ""
texto4: "\lim_{ x \to " + (LaTeX[a]) + "^{+}}f(x)=" + (LaTeX[s]) + ""
texto20: "\lim_{ x \to " + (LaTeX[a]) + "^{-} }f(x)=" + (LaTeX[r]) + ""