Nilai \( \displaystyle \lim_{x\to 0} \ \frac{\sin 5x - \sin 3x}{\sin x} = \cdots \)
Pembahasan:
\begin{aligned} \lim_{x\to 0} \ \frac{\sin 5x - \sin 3x}{\sin x} &= \lim_{x\to 0} \ \frac{2 \cos \frac{1}{2} (5x+3x) \sin \frac{1}{2} (5x-3x)}{\sin x} \\[8pt] &= \lim_{x\to 0} \ \frac{2 \cos 4x \sin x}{\sin x} \\[8pt] &= \lim_{x\to 0} \ 2 \cos 4x \\[8pt] &= 2 \ \cos 0 = 2 \cdot 1 \\[8pt] &= 2 \end{aligned}