Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 2}\frac{5 x^{2} - 20 x + 20}{- 8 x^{2} + 19 x - 6}$

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: $LaTeX: \lim_{x \to 2}\frac{5 x^{2} - 20 x + 20}{- 8 x^{2} + 19 x - 6} = \lim_{x \to 2}\frac{10 x - 20}{19 - 16 x} = \frac{10 (2) - 20}{19 - 16 (2)} = 0$