Nilai \( \displaystyle \lim_{x\to 0} \ \frac{\cos 4x - 1}{x \tan 2x} = \cdots \)
- 4
- 2
- -1
- -2
- -4
(UN SMA IPA 2012)
Pembahasan:
\begin{aligned} \lim_{x\to 0} \ \frac{\cos 4x - 1}{x \tan 2x} &= \lim_{x\to 0} \ \frac{\cos (2 \cdot 2x) - 1}{x \tan 2x} \\[8pt] &= \lim_{x\to 0} \ \frac{-2 \sin^2 2x}{x \tan 2x} \\[8pt] &= \lim_{x\to 0} \ \frac{-2\sin 2x}{x} \cdot \lim_{x\to 0} \ \frac{\sin 2x}{\tan 2x} \\[8pt] &= -2 \cdot 2 \cdot \frac{2}{2} \\[8pt] &= -4 \end{aligned}
Jawaban E.