Nilai \( \displaystyle \lim_{x\to 0} \ \frac{2 \sin^2 \frac{1}{2}x}{x \tan x} = \cdots \)
- -2
- -1
- -1/2
- 1/2
- 1
Pembahasan:
\begin{aligned} \lim_{x\to 0} \ \frac{2 \sin^2 \frac{1}{2}x}{x \tan x} &= 2 \cdot \lim_{x\to 0} \ \frac{\sin \frac{1}{2}x}{x} \cdot \lim_{x\to 0} \ \frac{\sin \frac{1}{2}x}{\tan x} \\[8pt] &= 2 \cdot \frac{1}{2} \cdot \frac{1}{2} \\[8pt] &= \frac{1}{2} \end{aligned}
Jawaban D.