Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 4}\frac{3 x^{2} - 48}{4 x^{2} - 14 x - 8}$

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: $LaTeX: \lim_{x \to 4}\frac{3 x^{2} - 48}{4 x^{2} - 14 x - 8} = \lim_{x \to 4}\frac{6 x}{8 x - 14} = \frac{6 (4)}{8 (4) - 14} = \frac{4}{3}$