Nilai \( \displaystyle \lim_{x \to 2} \ \frac{x^2+2x-8}{x^2-x-2} = \cdots \)
- 3
- 2
- 0
- -2
- -3
(EBTANAS SMA IPS 1998)
Pembahasan:
\begin{aligned} \lim_{x \to 2} \ \frac{x^2+2x-8}{x^2-x-2} &= \lim_{x \to 2} \ \frac{(x+4)(x-2)}{(x-2)(x+1)} \\[8pt] &= \lim_{x \to 2} \ \frac{x+4}{x+1} \\[8pt] &= \frac{2+4}{2+1} = \frac{6}{3} \\[8pt] &= 2 \end{aligned}
Jawaban B.