Evaluate the limit LaTeX: \displaystyle \lim_{x \to 7}\frac{5 x^{2} - 25 x - 70}{8 x^{2} - 47 x - 63}

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{5 x^{2} - 25 x - 70}{8 x^{2} - 47 x - 63} = \lim_{x \to 7}\frac{10 x - 25}{16 x - 47} = \frac{10 (7) - 25}{16 (7) - 47} = \frac{9}{13}