Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 7}\frac{2 x^{2} - 8 x - 42}{- 3 x^{2} + 24 x - 21}$

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: $LaTeX: \lim_{x \to 7}\frac{2 x^{2} - 8 x - 42}{- 3 x^{2} + 24 x - 21} = \lim_{x \to 7}\frac{4 x - 8}{24 - 6 x} = \frac{4 (7) - 8}{24 - 6 (7)} = - \frac{10}{9}$