Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 2}\frac{4 x^{2} - 16 x + 16}{- 4 x^{2} + 9 x - 2}$

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: $LaTeX: \lim_{x \to 2}\frac{4 x^{2} - 16 x + 16}{- 4 x^{2} + 9 x - 2} = \lim_{x \to 2}\frac{8 x - 16}{9 - 8 x} = \frac{8 (2) - 16}{9 - 8 (2)} = 0$