Nilai \( \displaystyle \lim_{x \to 0} \ \frac{1-\cos 2x}{2x \sin 2x} = \cdots \)
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(UN SMA IPA 2011)
Pembahasan:
\begin{aligned} \lim_{x \to 0} \ \frac{1-\cos 2x}{2x \sin 2x} &= \lim_{x \to 0} \ \frac{2 \sin^2 x}{2x \sin 2x} \\[8pt] &= \lim_{x \to 0} \ \frac{2 \sin x}{2x} \cdot \lim_{x \to 0} \ \frac{\sin x}{\sin 2x} \\[8pt] &= \frac{2}{2} \cdot \frac{1}{2} = \frac{1}{2} \end{aligned}
Jawaban D.