Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 7}\frac{5 x^{2} - 40 x + 35}{- 7 x^{2} + 48 x + 7}$

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: $LaTeX: \lim_{x \to 7}\frac{5 x^{2} - 40 x + 35}{- 7 x^{2} + 48 x + 7} = \lim_{x \to 7}\frac{10 x - 40}{48 - 14 x} = \frac{10 (7) - 40}{48 - 14 (7)} = - \frac{3}{5}$