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