Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 7}\frac{2 x^{2} - 28 x + 98}{9 x^{2} - 58 x - 35}$

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: $LaTeX: \lim_{x \to 7}\frac{2 x^{2} - 28 x + 98}{9 x^{2} - 58 x - 35} = \lim_{x \to 7}\frac{4 x - 28}{18 x - 58} = \frac{4 (7) - 28}{18 (7) - 58} = 0$