Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 6}\frac{4 x^{2} - 48 x + 144}{- x^{2} + 14 x - 48}$

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: $LaTeX: \lim_{x \to 6}\frac{4 x^{2} - 48 x + 144}{- x^{2} + 14 x - 48} = \lim_{x \to 6}\frac{8 x - 48}{14 - 2 x} = \frac{8 (6) - 48}{14 - 2 (6)} = 0$