Nilai \( \displaystyle \lim_{x\to \frac{\pi}{2}} \ \frac{\cos x}{(x-\frac{\pi}{2})} = \cdots \)
- -3
- -2
- -1
- 0
- 1
Pembahasan:
\begin{aligned} \lim_{x\to \frac{\pi}{2}} \ \frac{\cos x}{(x-\frac{\pi}{2})} &= \lim_{x\to \frac{\pi}{2}} \ \frac{\sin (\frac{\pi}{2}-x) }{-(\frac{\pi}{2}-x)} \\[8pt] &= \frac{1}{-1} = -1 \end{aligned}
Jawaban C.