Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 4}\frac{2 x^{2} - 14 x + 24}{3 x^{2} - 10 x - 8}$

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: $LaTeX: \lim_{x \to 4}\frac{2 x^{2} - 14 x + 24}{3 x^{2} - 10 x - 8} = \lim_{x \to 4}\frac{4 x - 14}{6 x - 10} = \frac{4 (4) - 14}{6 (4) - 10} = \frac{1}{7}$