Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 4}\frac{5 x^{2} + 15 x - 140}{7 x^{2} - 26 x - 8}$

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: $LaTeX: \lim_{x \to 4}\frac{5 x^{2} + 15 x - 140}{7 x^{2} - 26 x - 8} = \lim_{x \to 4}\frac{10 x + 15}{14 x - 26} = \frac{10 (4) + 15}{14 (4) - 26} = \frac{11}{6}$