Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 3}\frac{4 x^{2} - 40 x + 84}{- 8 x^{2} + 32 x - 24}$

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: $LaTeX: \lim_{x \to 3}\frac{4 x^{2} - 40 x + 84}{- 8 x^{2} + 32 x - 24} = \lim_{x \to 3}\frac{8 x - 40}{32 - 16 x} = \frac{8 (3) - 40}{32 - 16 (3)} = 1$