Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -5}\frac{2 x^{2} + 22 x + 60}{- 5 x^{2} - 28 x - 15}$

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: $LaTeX: \lim_{x \to -5}\frac{2 x^{2} + 22 x + 60}{- 5 x^{2} - 28 x - 15} = \lim_{x \to -5}\frac{4 x + 22}{- 10 x - 28} = \frac{4 (-5) + 22}{- 10 (-5) - 28} = \frac{1}{11}$