Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 7}\frac{2 x^{2} - 16 x + 14}{- 3 x^{2} + 29 x - 56}$

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: $LaTeX: \lim_{x \to 7}\frac{2 x^{2} - 16 x + 14}{- 3 x^{2} + 29 x - 56} = \lim_{x \to 7}\frac{4 x - 16}{29 - 6 x} = \frac{4 (7) - 16}{29 - 6 (7)} = - \frac{12}{13}$