Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -2}\frac{2 x^{2} + 14 x + 20}{7 x^{2} + 13 x - 2}$

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: $LaTeX: \lim_{x \to -2}\frac{2 x^{2} + 14 x + 20}{7 x^{2} + 13 x - 2} = \lim_{x \to -2}\frac{4 x + 14}{14 x + 13} = \frac{4 (-2) + 14}{14 (-2) + 13} = - \frac{2}{5}$