Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 7 x^{2} - 4 x - 6}{- 3 x^{2} - 4 x - 1}

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{- 7 x^{2} - 4 x - 6}{- 3 x^{2} - 4 x - 1} = \lim_{x \to -\infty}\frac{- 14 x - 4}{- 6 x - 4} = \lim_{x \to -\infty}\frac{-14}{-6} = \frac{7}{3}