Nilai \( \displaystyle \lim_{x \to 0} \ \frac{2 \sin x}{2 \sin x + \sin 2x} = \cdots \)
- -1/2
- -1/4
- 1/4
- 1/2
- 1
(EBTANAS SMA IPA 2001)
Pembahasan:
\begin{aligned} \lim_{x \to 0} \ \frac{2x}{2 \sin x + \sin 2x} &= \lim_{x \to 0} \ \frac{2x}{2 \sin x + 2 \sin x \cos x} \\[8pt] &= \lim_{x \to 0} \ \frac{2x}{2 \sin x (1 + \cos x)} \\[8pt] &= \lim_{x \to 0} \ \frac{1}{1+ \cos x} = \frac{1}{1+ \cos 0} \\[8pt] &= \frac{1}{1+1} = \frac{1}{2} \end{aligned}
Jawaban D.