lim x->2 [tex] \frac{x^{3} - 8}{ x^{2} +x-6} [/tex]

lim (x^3 - 8) / (x^2 + x - 6)
x -> 2

Dalil L'Hospital
lim (f(x)) / (g(x))
x-> n
=
lim x-> n (f'(x)) /(g'(x))

f(x) = x^3 - 8
f'(x) = 3x^2

g(x) = x^2 + x - 6
g'(x) = 2x + 1

Maka :
lim 3x^2 / (2x + 1)
x-> 2

3 . 2^2 / (2(2) + 1)
= (3.4) / (4+1)
= 12/5

Limit Fungsi Aljabar.
Keompok wajib kelas XI kurikulum 2013 revisi 2016.

lim x→2 (x³ - 8) / (x² + x - 6)
= (2³ - 8) / (2² + 2 + 6)
= 0 / 0 ← Bentuk tak tentu.

a³ - b³ = (a - b)(a² + ab + b²)
= lim x→2 (x - 2)(x² + 2x + 4) / [(x - 2)(x + 3)]
= lim x→2 (x² + 2x + 4) / (x + 3)
= [2² + 2(2) + 4] / (2 + 3)
= 12 / 5