Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 8}\frac{3 x^{2} - 48 x + 192}{- 3 x^{2} + 22 x + 16}$

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: $LaTeX: \lim_{x \to 8}\frac{3 x^{2} - 48 x + 192}{- 3 x^{2} + 22 x + 16} = \lim_{x \to 8}\frac{6 x - 48}{22 - 6 x} = \frac{6 (8) - 48}{22 - 6 (8)} = 0$