Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 8 x^{2} - 5 x + 2}{7 x^{2} - 2 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{- 8 x^{2} - 5 x + 2}{7 x^{2} - 2 x - 5} = \lim_{x \to -\infty}\frac{- 16 x - 5}{14 x - 2} = \lim_{x \to -\infty}\frac{-16}{14} = - \frac{8}{7}