Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 2}\frac{4 x^{2} - 44 x + 72}{- 6 x^{2} + 16 x - 8}$

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: $LaTeX: \lim_{x \to 2}\frac{4 x^{2} - 44 x + 72}{- 6 x^{2} + 16 x - 8} = \lim_{x \to 2}\frac{8 x - 44}{16 - 12 x} = \frac{8 (2) - 44}{16 - 12 (2)} = \frac{7}{2}$