Nilai \( \displaystyle \lim_{x \to 2} \ \frac{x^2+2x-8}{x^2+4x-12} = \cdots \)
- ∞
- 1
- 3/4
- 1/2
- 0
(EBTANAS SMA IPS 2000)
Pembahasan:
\begin{aligned} \lim_{x \to 2} \ \frac{x^2+2x-8}{x^2+4x-12} &= \lim_{x \to 2} \ \frac{(x+4)(x-2)}{(x+6)(x-2)} \\[8pt] &= \lim_{x \to 2} \ \frac{x+4}{x+6} \\[8pt] &= \frac{2+4}{2+6} = \frac{6}{8} \\[8pt] &= \frac{3}{4} \end{aligned}
Jawaban C.