Question

Nilai dari lim x sampe 3 ( 2^x-9x+9/9-x² ) adalah..

Answer 1

Faktorkan pembilang
(2x² - 9x + 9) = (2x-3)(x-3)
Faktorkan penyebut:
9-x² = -(x²-9)
9-x² = -(x+3)(x-3)

Sehingga:
lim_x⇒3 (2x²-9x+9)/(9-x²)
= lim_x⇒3 (2x-3)(x-3)/[-(x+3)(x-3)]
= lim_x⇒3 (2x-3)/-(x+3)
= - (2(3)-3)/(3+3)
= - (6-3)/9
= - 3/9
= - 1/3