Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -3}\frac{4 x^{2} - 16 x - 84}{- 2 x^{2} - 11 x - 15}$

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: $LaTeX: \lim_{x \to -3}\frac{4 x^{2} - 16 x - 84}{- 2 x^{2} - 11 x - 15} = \lim_{x \to -3}\frac{8 x - 16}{- 4 x - 11} = \frac{8 (-3) - 16}{- 4 (-3) - 11} = -40$