Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 5}\frac{2 x^{2} + 2 x - 60}{- 9 x^{2} + 50 x - 25}$

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: $LaTeX: \lim_{x \to 5}\frac{2 x^{2} + 2 x - 60}{- 9 x^{2} + 50 x - 25} = \lim_{x \to 5}\frac{4 x + 2}{50 - 18 x} = \frac{4 (5) + 2}{50 - 18 (5)} = - \frac{11}{20}$