Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 2}\frac{4 x^{2} + 24 x - 64}{2 x^{2} - 2 x - 4}$

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: $LaTeX: \lim_{x \to 2}\frac{4 x^{2} + 24 x - 64}{2 x^{2} - 2 x - 4} = \lim_{x \to 2}\frac{8 x + 24}{4 x - 2} = \frac{8 (2) + 24}{4 (2) - 2} = \frac{20}{3}$