=f(1)

=f(1)

H f είναι συνεχής στο χ_0=1

Συνεχής συνάρτηση σε σημείο

★ Σπύρος Γιαννακόπουλος

\lim_{ x \to 1 }f(χ)=f(1)_

f = If(x > -1, If[x ≤ 1, 2^(x), 2^(x) - log(x)])
Α: (1, f(1))
a = 0 (slider from 0 to 1, step 0.0010)
Β: (a, f(a))
b = 1 (slider from 0.99 to 2, step 0.0010)
Γ: (b, f(b))
κείμενο1 = LaTeX(f, true, true)
Δ = (1, 0)
c = OrthogonalLine(Α, xAxis)
d = OrthogonalLine(Α, yAxis)
e = OrthogonalLine(Γ, xAxis)
g = OrthogonalLine(Γ, yAxis)
h = Segment(Α, Δ)
Ε = Intersect(d, yAxis)
Ζ = Intersect(e, xAxis)
j = Segment(Γ, Ζ)
Η = Intersect(g, yAxis)
k = Segment(Γ, Η)
l = OrthogonalLine(Β, xAxis)
m = OrthogonalLine(Β, yAxis)
Θ = Intersect(l, xAxis)
n = Segment(Β, Θ)
Ι = Intersect(m, yAxis)
p = Segment(Β, Ι)
O = Intersect(xAxis, yAxis)
Λ = Point(yAxis)
Μ = Point(xAxis)
v = Vector(Μ, Ζ)
Ν = Point(n)
Ξ = Point(j)
κείμενο2: "\lim_{ x \to 1^- }f(χ)=" + (LaTeX[f(a)]) + ""
κείμενο4: "\lim_{ x \to 1^+ }f(χ)=" + (LaTeX[f(b)]) + ""
o = false
Κ = Intersect(yAxis, k)
Ο = Intersect(f, yAxis, (0, 1))
Π = Point(yAxis)
u = Vector(O, Ν)
Σ = Point(yAxis)
z = Vector(Σ, Κ)
w = Vector(O, Ι)
i = Vector(Α, Ε)
Ρ = (-1.02, 0.5)
f_1 = If(x > -1, If[x ≤ 1, 2^(x), 2^(x) - log(x)])
Α_1: (1, f_1(1))
a_1 = 1.01 (slider from 0 to 1.01, step 0.0010)
Β_1: (a_1, f_1(a_1))
f_2 = If(x > -1, If[x ≤ 1, 2^(x), 2^(x) - log(x)])
Α_2: (1, f_2(1))
a_2 = 1.01 (slider from 0 to 1.01, step 0.0010)
Β_2: (a_2, f_2(a_2))
f_3 = If(x > -1, If[x ≤ 1, 2^(x), 2^(x) - log(x)])
Α_3: (1, f_3(1))
t = 1 (slider from 0 to 1, step 0.0010)