Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 7}\frac{4 x^{2} + 4 x - 224}{2 x^{2} - 13 x - 7}$

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: $LaTeX: \lim_{x \to 7}\frac{4 x^{2} + 4 x - 224}{2 x^{2} - 13 x - 7} = \lim_{x \to 7}\frac{8 x + 4}{4 x - 13} = \frac{8 (7) + 4}{4 (7) - 13} = 4$