Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -8}\frac{2 x^{2} + 32 x + 128}{- 5 x^{2} - 49 x - 72}$

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: $LaTeX: \lim_{x \to -8}\frac{2 x^{2} + 32 x + 128}{- 5 x^{2} - 49 x - 72} = \lim_{x \to -8}\frac{4 x + 32}{- 10 x - 49} = \frac{4 (-8) + 32}{- 10 (-8) - 49} = 0$