Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 8}\frac{2 x^{2} - 12 x - 32}{5 x^{2} - 34 x - 48}$

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: $LaTeX: \lim_{x \to 8}\frac{2 x^{2} - 12 x - 32}{5 x^{2} - 34 x - 48} = \lim_{x \to 8}\frac{4 x - 12}{10 x - 34} = \frac{4 (8) - 12}{10 (8) - 34} = \frac{10}{23}$