Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- x^{3} + 8 x^{2} + 8 x - 1}{3 x^{3} - 3 x^{2} - 8 x - 6}

The limit is an indeterminate form of the type LaTeX: \displaystyle \frac{\infty}{\infty} . Using L'Hospitial's rule 3 times gives: LaTeX: \lim_{x \to -\infty}\frac{- x^{3} + 8 x^{2} + 8 x - 1}{3 x^{3} - 3 x^{2} - 8 x - 6} = \lim_{x \to -\infty}\frac{- 3 x^{2} + 16 x + 8}{9 x^{2} - 6 x - 8} = \lim_{x \to -\infty}\frac{2 \left(8 - 3 x\right)}{6 \left(3 x - 1\right)} = \lim_{x \to -\infty}\frac{-6}{18} = - \frac{1}{3}