ψ=f(x)

ψ=f(x)

ΟΡΙΟ ΣΤΟ χ_0

Η συνάρτηση h

h(x)=\binom{\frac{x^4-1}{x-1} \; , \; άν \; \;  x≠1}{-1  \;   , \;  \;  \; άν \;   \;  \; x=1}


 

Η συνάρτηση φ

φ(x)=\binom{\frac{x^4-1}{x-1} \;  \; , \;  \; άν \;  \;x<1}{x+4 \;  \; , \;  \; άν \;  \; x>1}

ψ=h(x)

ψ=φ(χ)

ψ=φ(χ)

ψ=h(x)

x_0 = 1 (slider from -3 to 3, step 0.05)
ε = 1 (slider from 0.01 to 1, step 0.01)
g(x) = x^(3) + x^(2) + x + 1
a: x = x_0
Σ: (x_0, g(x_0))
Α: (x_0 - ε, g(x_0 - ε))
b = OrthogonalLine(Α, xAxis)
Β: (x_0 + ε, g(x_0 + ε))
c = OrthogonalLine(Β, xAxis)
d = OrthogonalLine(Α, yAxis)
e = OrthogonalLine(Β, yAxis)
ψ = Intersect(e, yAxis)
ψ_. = Intersect(d, yAxis)
χ_. = Intersect(b, xAxis)
χ = Intersect(c, xAxis)
g_1 = Segment(χ_., Α)
h_1 = Segment(Β, χ)
i = Segment(Β, ψ)
j = Segment(ψ_., Α)
χ_0 = Intersect(a, xAxis)
k = Segment(Σ, χ_0)
n = Segment(χ_., χ)
A2: x_0 - ε
B2: g(A2)
C2: x_0 + ε
D2: g(C2)
f(x) = (x^(4) - 1) / (x - 1)
κείμενο1: "f(x)=" + (LaTeX[f]) + ""
Σ_.: (x_0, f(x_0))
p = Segment(χ_., χ_0)
q = Segment(χ, χ_0)
l_2 = Integral(g, x_0 - ε, x_0)
o = Integral(g, x_0, x_0 + ε)
l: (0, g(x_0))
m = Segment(ψ_., l)
r = Segment(ψ, l)
s = Segment(l, Σ_.)
t = Segment(l, Σ)
A1(x) = x  <  x_0
C1(x) = x > x_0
u = false
Δ: (0, f(x_0))
h(x) = If[x ≠ 1, g, -1]
Ε: (1, h(1))
v = false
Ζ: (0, h(1))
a_1 = Segment(Ε, Ζ)
b_1 = OrthogonalLine(Ε, xAxis)
Η = Intersect(b_1, xAxis)
c_1 = Segment(Ε, Η)
w = false
φ_1(x) = x + 4
φ(x) = If[x  <  1, g(x), φ_1(x)]
Θ: (1, φ_1(1))
d_1 = OrthogonalLine(Θ, xAxis)
Ι = Intersect(d_1, xAxis)
e_1 = Segment(Θ, Ι)
i_1 = OrthogonalLine(Θ, yAxis)
Κ = Intersect(i_1, yAxis)
j_1 = Segment(Κ, Θ)
k_1 = OrthogonalLine(χ, xAxis)
Λ = Intersect(φ, k_1, (2, 6))
l_1 = Segment(Λ, χ)
m_1 = Integral(φ_1, x_0, x_0 + ε)
n_1 = OrthogonalLine(Λ, yAxis)
ψ' = Intersect(n_1, yAxis)
p_1 = Segment(ψ', Λ)
q_1 = Segment(ψ', Κ)
Μ = Intersect(g, h)
Ν: (1, g(1))
r_1 = Segment(Ν, Ε)
A8: x_0 - ε
C8: x_0 + ε
A7(x) = x  <  x_0
C7(x) = x > x_0
B8: φ(A8)
A13: x_0 - ε
C13: x_0 + ε
A12(x) = x  <  x_0
C12(x) = x > x_0
B13: φ(A13)
D13: φ(C13)
D8: g(C8)