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