Nilai \( \displaystyle \lim_{x \to 4} \ \frac{\sin (4-2\sqrt{x})}{4-x} = \cdots \)
- -1/6
- -1/2
- 0
- 1/4
- 1/2
(SPMB 2006)
Pembahasan:
\begin{aligned} \lim_{x \to 4} \ \frac{\sin (4-2\sqrt{x})}{4-x} &= \lim_{x \to 4} \ \frac{\sin 2(2-\sqrt{x})}{(2+\sqrt{x})(2-\sqrt{x})} \\[8pt] &= \frac{1}{(2+\sqrt{x})} \cdot \lim_{x \to 4} \ \frac{\sin 2(2-\sqrt{x})}{(2-\sqrt{x})} \\[8pt] &= \frac{1}{2+\sqrt{4}} \cdot 2 = \frac{2}{4} = \frac{1}{2} \end{aligned}
Jawaban E.