Nilai \( \displaystyle \lim_{x \to 0} \ \frac{\sin 4x + \sin 2x}{3x \cos x} = \cdots \)
- 1/4
- 1/2
- 1
- 3/2
- 2
(EBTANAS SMA IPA 1996)
Pembahasan:
\begin{aligned} \lim_{x \to 0} \ \frac{\sin 4x + \sin 2x}{3x \cos x} &= \lim_{x \to 0} \ \frac{2 \sin \left( \frac{4x+2x}{2} \right) \cos \left( \frac{4x-2x}{2} \right) }{3x \cos x} \\[8pt] &= \lim_{x \to 0} \ \frac{2 \sin 3x \cos x }{3x \cos x} \\[8pt] &= \lim_{x \to 0} \ \frac{2 \sin 3x}{3x} \\[8pt] &= \frac{2 \cdot 3}{3} = 2 \end{aligned}
Jawaban E.