Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 2}\frac{4 x^{2} - 44 x + 72}{- 3 x^{2} + 7 x - 2}$

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: $LaTeX: \lim_{x \to 2}\frac{4 x^{2} - 44 x + 72}{- 3 x^{2} + 7 x - 2} = \lim_{x \to 2}\frac{8 x - 44}{7 - 6 x} = \frac{8 (2) - 44}{7 - 6 (2)} = \frac{28}{5}$