Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -8}\frac{2 x^{2} - 128}{9 x^{2} + 63 x - 72}$

The limit is an indeterminate form of the type $LaTeX: \displaystyle \frac{0}{0}$ . Using L'Hospitial's rule and then the evaluation theorem gives: $LaTeX: \lim_{x \to -8}\frac{2 x^{2} - 128}{9 x^{2} + 63 x - 72} = \lim_{x \to -8}\frac{4 x}{18 x + 63} = \frac{4 (-8)}{18 (-8) + 63} = \frac{32}{81}$