Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 1}\frac{2 x^{2} - 16 x + 14}{x^{2} + 6 x - 7}$

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: $LaTeX: \lim_{x \to 1}\frac{2 x^{2} - 16 x + 14}{x^{2} + 6 x - 7} = \lim_{x \to 1}\frac{4 x - 16}{2 x + 6} = \frac{4 (1) - 16}{2 (1) + 6} = - \frac{3}{2}$