Nilai \( \displaystyle \lim_{x \to 0} \ \frac{-x^2}{1-\cos x} = \cdots \)
- -2
- -1
- 0
- 1
- 2
(SPMB 2005)
Pembahasan:
\begin{aligned} \lim_{x \to 0} \ \frac{-x^2}{1-\cos x} &= \lim_{x \to 0} \ \frac{-x^2}{2 \sin^2 \frac{1}{2} x} \\[8pt] &= -\frac{1}{2} \cdot \lim_{x \to 0} \ \frac{x}{\sin \frac{1}{2} x} \cdot \lim_{x \to 0} \ \frac{x}{\sin \frac{1}{2} x} \\[8pt] &= -\frac{1}{2} \cdot \frac{1}{\frac{1}{2}} \cdot \frac{1}{\frac{1}{2}} \\[8pt] &= -2 \end{aligned}
Jawaban A.