Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 5 x^{2} - 9 x - 9}{- 2 x^{2} + 7 x - 5}

The limit is an indeterminate form of the type LaTeX: \displaystyle \frac{\infty}{\infty} . Using L'Hospitial's rule 2 times gives: LaTeX: \lim_{x \to -\infty}\frac{- 5 x^{2} - 9 x - 9}{- 2 x^{2} + 7 x - 5} = \lim_{x \to -\infty}\frac{- 10 x - 9}{7 - 4 x} = \lim_{x \to -\infty}\frac{-10}{-4} = \frac{5}{2}