Nilai \( \displaystyle \lim_{x\to 0} \ \frac{1-\cos 4x}{x \sin x} = \cdots \)
- 1
- 2
- 4
- 8
- 16
Pembahasan:
\begin{aligned} \lim_{x\to 0} \ \frac{1-\cos 4x}{x \sin x} &= \lim_{x\to 0} \ \frac{1-\cos (2 \cdot 2x)}{x \sin x} \\[8pt] &= \lim_{x\to 0} \ \frac{2 \sin^2 2x}{x \sin x} \\[8pt] &= 2 \cdot \lim_{x\to 0} \ \frac{\sin 2x}{x} \cdot \lim_{x\to 0} \ \frac{\sin 2x}{\sin x} \\[8pt] &= 2 \cdot 2 \cdot 2 \\[8pt] &= 8 \end{aligned}
Jawaban D.