Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -2}\frac{2 x^{2} - 8}{7 x^{2} + 11 x - 6}$

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: $LaTeX: \lim_{x \to -2}\frac{2 x^{2} - 8}{7 x^{2} + 11 x - 6} = \lim_{x \to -2}\frac{4 x}{14 x + 11} = \frac{4 (-2)}{14 (-2) + 11} = \frac{8}{17}$