Evaluate
![\[ \lim_{x \to 0} \frac{x^2 - a^2}{x^2 + 2ax + a^2} \qquad \text{for } a \neq 0. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-75c442210e0f7420534a3cef6701885b_l3.png "Rendered by QuickLaTeX.com")
The numerator and denominator are both continuous since they are polynomials. Since 
is non-zero we may then apply Theorem 3.2 to compute the limit,
![\[ \lim_{x \to 0} \frac{x^2-a^2}{x^2 + 2ax + a^2} = \frac{-a^2}{a^2} = -1. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-1ef4506c63018d63924bff313dc640ac_l3.png "Rendered by QuickLaTeX.com")
Evaluate
The numerator and denominator are both continuous since they are polynomials. Since is non-zero we may then apply Theorem 3.2 to compute the limit,