Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -1}\frac{5 x^{2} - 35 x - 40}{- 3 x^{2} - 9 x - 6}$

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: $LaTeX: \lim_{x \to -1}\frac{5 x^{2} - 35 x - 40}{- 3 x^{2} - 9 x - 6} = \lim_{x \to -1}\frac{10 x - 35}{- 6 x - 9} = \frac{10 (-1) - 35}{- 6 (-1) - 9} = 15$