x

x_0

L+ε

L-ε

L

f(x)

∀ε>0 ∃δ>0 : |x-x₀|<δ
⇒ |f(x)-L|<ε

lim_x_→x_₀f(x)=L

f(x_0)

f(x)=

δ=

ε

x_0+δ

x_0-δ

X = 6.6 (slider from -10 to 10, step 0.1)
I: (X, 0)
L = 2.25 (slider from -10 to 10, step 0.25)
ε = 0.8 (slider from 0.1 to 5, step 0.1)
f(x) = If[x ≟ 3, 5,(x^(2) - (4 * x) + 3) / (x - 3)]
x_0 = 4.75 (slider from -5 to 5, step 0.25)
C: (x_0, 0)
A: (x_0, f(x_0))
Y_+: (0, L + ε)
y_+: y = y(Y_+)
Y_-: (0, L - ε)
y_-: y = y(Y_-)
P_+ = Intersect(f, y_+, (4.050000000000001, 3.050000000000002))
P_- = Intersect(f, y_-, (2.4499999999999997, 1.45))
B: (0, L)
c: y = y(B)
k: x = x(I)
P = Intersect(f, k, (6.6, 5.6))
f_X: (0, f(P))
m = Segment(f_X, P)
j(y) = L - ε  <  y  <  L + ε
e = OrthogonalLine(C, xAxis)
f_C: (0, f(x_0))
campoInserimento = Textfield(f)
a = Segment(f_C, A)
testo3: "x=" + X + ""
testo4: "f(x)=" + (f(X)) + ""
l = Segment(I, P)
δ = 0.7 (slider from 0.1 to 10, step 0.1)
b(x) = x_0 - δ  <  x  <  x_0 + δ
testo5: "" + (δ / ε) + ""
E = (3, 2)
D = (-2.12, -0.64)
F = (-1.36, -0.66)
u = Vector(D, F)
G = (3, 5)
H: (x_0 + δ, 0)
J: (x_0 - δ, 0)