Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 8}\frac{4 x^{2} - 56 x + 192}{- x^{2} + 3 x + 40}$

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: $LaTeX: \lim_{x \to 8}\frac{4 x^{2} - 56 x + 192}{- x^{2} + 3 x + 40} = \lim_{x \to 8}\frac{8 x - 56}{3 - 2 x} = \frac{8 (8) - 56}{3 - 2 (8)} = - \frac{8}{13}$