Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 8}\frac{5 x^{2} - 10 x - 240}{7 x^{2} - 49 x - 56}$

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: $LaTeX: \lim_{x \to 8}\frac{5 x^{2} - 10 x - 240}{7 x^{2} - 49 x - 56} = \lim_{x \to 8}\frac{10 x - 10}{14 x - 49} = \frac{10 (8) - 10}{14 (8) - 49} = \frac{10}{9}$