Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 7}\frac{4 x^{2} - 56 x + 196}{4 x^{2} - 31 x + 21}$

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: $LaTeX: \lim_{x \to 7}\frac{4 x^{2} - 56 x + 196}{4 x^{2} - 31 x + 21} = \lim_{x \to 7}\frac{8 x - 56}{8 x - 31} = \frac{8 (7) - 56}{8 (7) - 31} = 0$