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