Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 6}\frac{2 x^{2} - 24 x + 72}{9 x^{2} - 59 x + 30}$

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: $LaTeX: \lim_{x \to 6}\frac{2 x^{2} - 24 x + 72}{9 x^{2} - 59 x + 30} = \lim_{x \to 6}\frac{4 x - 24}{18 x - 59} = \frac{4 (6) - 24}{18 (6) - 59} = 0$