Nilai \( \displaystyle \lim_{x\to 0} \ \frac{1-\cos 2x}{x \tan 2x} = \cdots \)
- -1
- 0
- 1
- 2
- 3
Pembahasan:
\begin{aligned} \lim_{x\to 0} \ \frac{1-\cos 2x}{x \tan 2x} &= \lim_{x\to 0} \ \frac{2 \sin^2 x}{x \tan 2x} \\[8pt] &= 2 \cdot \lim_{x\to 0} \ \frac{\sin x}{x} \cdot \lim_{x\to 0} \ \frac{\sin x}{\tan 2x} \\[8pt] &= 2 \cdot 1 \cdot \frac{1}{2} \\[8pt] &= 1 \end{aligned}
Jawaban C.