Chapter 2: Limits and Continuity - Additional and Advanced Exercises - Page 104: 29

$$4$$

\begin{align*} \lim _{x \rightarrow 2} \frac{\sin \left(x^{2}-4\right)}{x-2}&=\lim _{x \rightarrow 2} \frac{\sin \left(x^{2}-4\right)}{x^{2}-4} \cdot(x+2)\\ &=\lim _{x \rightarrow 2} \frac{\sin \left(x^{2}-4\right)}{x^{2}-4} \cdot \lim _{x \rightarrow 2}(x+2)\\ &=1 \cdot 4\\ &=4 \end{align*}