Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -3}\frac{4 x^{2} - 36}{- 3 x^{2} - 3 x + 18}$

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: $LaTeX: \lim_{x \to -3}\frac{4 x^{2} - 36}{- 3 x^{2} - 3 x + 18} = \lim_{x \to -3}\frac{8 x}{- 6 x - 3} = \frac{8 (-3)}{- 6 (-3) - 3} = - \frac{8}{5}$