Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 8 x^{3} - 9 x^{2} - 5 x - 1}{8 x^{3} + 6 x^{2} + 2 x + 2}

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{- 8 x^{3} - 9 x^{2} - 5 x - 1}{8 x^{3} + 6 x^{2} + 2 x + 2} = \lim_{x \to -\infty}\frac{- 24 x^{2} - 18 x - 5}{24 x^{2} + 12 x + 2} = \lim_{x \to -\infty}\frac{- 6 \left(8 x + 3\right)}{12 \left(4 x + 1\right)} = \lim_{x \to -\infty}\frac{-48}{48} = -1