Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 9}\frac{2 x^{2} - 34 x + 144}{6 x^{2} - 56 x + 18}$

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: $LaTeX: \lim_{x \to 9}\frac{2 x^{2} - 34 x + 144}{6 x^{2} - 56 x + 18} = \lim_{x \to 9}\frac{4 x - 34}{12 x - 56} = \frac{4 (9) - 34}{12 (9) - 56} = \frac{1}{26}$