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