Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 8 x^{2} + 3 x - 7}{- 7 x^{2} - 2 x - 2}

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} + 3 x - 7}{- 7 x^{2} - 2 x - 2} = \lim_{x \to -\infty}\frac{3 - 16 x}{- 14 x - 2} = \lim_{x \to -\infty}\frac{-16}{-14} = \frac{8}{7}