Ασυνεχής συνάρτηση σε σημείο

Κίνηση

Κίνηση

=f(2)

\lim_{ x \to 2^- }f(χ)≠\lim_{ x \to 2^+ }f(χ)⇒\,Δεν\,\,υπάρχει\,το\,\lim_{ x \to 2 }f(χ)

οπότε\,η\,f\,δεν\,είναι\,συνεχής\,στο\,2

Σπύρος Γιαννακόπουλος

f(x) = If[x ≤ 2, ℯ^(x),If[x > 2,1 / x]]
Α = (2, 7.38905609893065)
Β = (2, 0.5)
κείμενο2 = LaTeX(f, true, true)
a_1 = Line(Α, Β)
Γ = Intersect(xAxis, a_1)
b_1 = Segment(Α, Β)
c = Segment(Β, Γ)
a = -3 (slider from -3 to 2, step 0.001)
M: (a, f(a))
d = OrthogonalLine(M, xAxis)
e = OrthogonalLine(M, yAxis)
Ε = Intersect(xAxis, d)
Ζ = Intersect(yAxis, e)
g = Segment(M, Ζ)
h = Segment(M, Ε)
Η = Point(f)
u = Vector(Η, Ε)
v = Vector(M, Ζ)
b = 7 (slider from 2.01 to 7, step 0.001)
N: (b, f(b))
κείμενο1: "\lim_{ x \to 2^- }f(χ)=" + (LaTeX[f(a)]) + ""
i = OrthogonalLine(Α, yAxis)
Δ = Intersect(i, yAxis)
w = Vector(Α, Δ)
j = OrthogonalLine(N, xAxis)
k = OrthogonalLine(N, yAxis)
Ι = Intersect(xAxis, j)
Κ = Intersect(k, yAxis)
Λ = Point(xAxis)
l = Vector(Λ, Ι)
m = Vector(N, Κ)
κείμενο3: "\lim_{ x \to 2^+ }f(χ)=" + (LaTeX[f(b)]) + ""
n = Segment(N, Ι)
p = OrthogonalLine(Β, yAxis)
Μ = Intersect(p, yAxis)
q = Vector(Β, Μ)
o = false
t = 0 (slider from 0 to 3, step 0.01)