Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 5}\frac{2 x^{2} - 50}{- 8 x^{2} + 43 x - 15}$

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: $LaTeX: \lim_{x \to 5}\frac{2 x^{2} - 50}{- 8 x^{2} + 43 x - 15} = \lim_{x \to 5}\frac{4 x}{43 - 16 x} = \frac{4 (5)}{43 - 16 (5)} = - \frac{20}{37}$