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