Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 2}\frac{5 x^{2} + 20 x - 60}{- 7 x^{2} + 5 x + 18}$

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: $LaTeX: \lim_{x \to 2}\frac{5 x^{2} + 20 x - 60}{- 7 x^{2} + 5 x + 18} = \lim_{x \to 2}\frac{10 x + 20}{5 - 14 x} = \frac{10 (2) + 20}{5 - 14 (2)} = - \frac{40}{23}$