Nilai \( \displaystyle \lim_{x \to -2} \ \frac{(x+6) \sin (x+2)}{x^2-3x-10} = \cdots \)
- -4/3
- -4/7
- -2/5
- 0
- 1
(UN SMA IPA 2004)
Pembahasan:
\begin{aligned} \lim_{x \to -2} \ \frac{(x+6) \sin (x+2)}{x^2-3x-10} &= \lim_{x \to -2} \ \frac{(x+6) \sin (x+2)}{(x-5)(x+2)} \\[8pt] &= \lim_{x \to -2} \ \frac{(x+6)}{(x-5)} \cdot \lim_{x \to -2} \ \frac{\sin (x+2)}{(x+2)} \\[8pt] &= \frac{-2+6}{-2-5} \cdot 1 \\[8pt] &= -\frac{4}{7} \end{aligned}
Jawaban B.