Nilai \( \displaystyle \lim_{x \to 2} \frac{(x^2-5x-6) \sin 2(x-2)}{(x^2-x-2)} = \cdots \)
- -8
- -5
- -2
- 3/4
- 5
(UM STIS 2017)
Pembahasan:
\begin{aligned} \lim_{x \to 2} \frac{(x^2-5x-6) \sin 2(x-2)}{(x^2-x-2)} &= \lim_{x \to 2} \frac{(x+1)(x-6) \sin 2(x-2)}{(x+1)(x-2)} \\[8pt] &= \lim_{x \to 2} \frac{(x-6) \sin 2(x-2)}{(x-2)} \\[8pt] &= \lim_{x \to 2} (x-6) \cdot \lim_{x \to 2} \frac{\sin 2(x-2)}{(x-2)} \\[8pt] &= (2-6) \cdot 2 = -8 \end{aligned}
Jawaban A.