Chapter 2: Limits and Continuity - Practice Exercises - Page 101: 12

$$\frac{1}{2 a^{2}}$$

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