Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 9}\frac{2 x^{2} - 26 x + 72}{8 x^{2} - 80 x + 72}$

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: $LaTeX: \lim_{x \to 9}\frac{2 x^{2} - 26 x + 72}{8 x^{2} - 80 x + 72} = \lim_{x \to 9}\frac{4 x - 26}{16 x - 80} = \frac{4 (9) - 26}{16 (9) - 80} = \frac{5}{32}$