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