Nilai \( \displaystyle \lim_{x \to 2} \ \left( \frac{2}{x-2} - \frac{8}{x^2-4} \right) = \cdots \)
- 1/4
- 1/2
- 2
- 4
- ∞
(UN SMA IPA 2010)
Pembahasan:
\begin{aligned} \lim_{x \to 2} \ \left( \frac{2}{x-2} - \frac{8}{x^2-4} \right) &= \lim_{x \to 2} \ \frac{2(x^2-4)-8(x-2)}{(x-2)(x^2-4)} \\[8pt] &= \lim_{x \to 2} \ \frac{2x^2-8-8x+16}{(x-2)(x-2)(x+2)} \\[8pt] &= \lim_{x \to 2} \ \frac{2x^2-8x+8}{(x-2)(x-2)(x+2)} \\[8pt] &= \lim_{x \to 2} \ \frac{2(x-2)(x-2)}{(x-2)(x-2)(x+2)} \\[8pt] &= \lim_{x \to 2} \ \frac{2}{x+2} = \frac{2}{2+2} \\[8pt] &= \frac{1}{2} \end{aligned}
Jawaban B.