Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 8 x^{2} - 4 x + 6}{- 7 x^{2} - 6 x + 7}

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} - 4 x + 6}{- 7 x^{2} - 6 x + 7} = \lim_{x \to -\infty}\frac{- 16 x - 4}{- 14 x - 6} = \lim_{x \to -\infty}\frac{-16}{-14} = \frac{8}{7}