Evaluate the limit LaTeX: \displaystyle \lim_{x \to 4}\frac{5 x^{2} - 80}{5 x^{2} - 18 x - 8}

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 4}\frac{5 x^{2} - 80}{5 x^{2} - 18 x - 8} = \lim_{x \to 4}\frac{10 x}{10 x - 18} = \frac{10 (4)}{10 (4) - 18} = \frac{20}{11}