Jawaban:

Pembahasan

Jika f(x) = (x - 2)/(x² + x - 6) dan g(x) = (x² - 5x + 6)/(x² - 3x + 2)

Fungsi f(x) dan g(x) kita sederhanakan terlebih dahulu

f(x) = (x - 2)/(x² + x - 6)

f(x) = (x - 2)/(x - 2)(x + 3)

f(x) = 1/(x + 3)

.

g(x) = (x² - 5x + 6)/(x² - 3x + 2)

g(x) = (x - 2)(x - 3)/(x - 2)(x - 1)

g(x) = (x - 3)/(x - 1)

.

Maka:

lim x → 2 { f(x) . g(x) }

lim x → 2 { 1/(x + 3) . (x - 3)/(x - 1) }

Substitusi nilai x = 2

= { 1/(x + 3) . (x - 3)/(x - 1) }

= { 1/(2 + 3) . (2 - 3)/(2 - 1) }

= { 1/5 . (-1)/(1) }

= { 1/5 . (-1) }

= -1/5

Opsi { C }