Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 7}\frac{4 x^{2} - 60 x + 224}{- 6 x^{2} + 45 x - 21}$

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: $LaTeX: \lim_{x \to 7}\frac{4 x^{2} - 60 x + 224}{- 6 x^{2} + 45 x - 21} = \lim_{x \to 7}\frac{8 x - 60}{45 - 12 x} = \frac{8 (7) - 60}{45 - 12 (7)} = \frac{4}{39}$