Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 8 x^{3} + 9 x^{2} + 6 x + 9}{8 x^{3} + 7 x^{2} + 2 x + 4}

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} + 6 x + 9}{8 x^{3} + 7 x^{2} + 2 x + 4} = \lim_{x \to -\infty}\frac{- 24 x^{2} + 18 x + 6}{24 x^{2} + 14 x + 2} = \lim_{x \to -\infty}\frac{6 \left(3 - 8 x\right)}{2 \left(24 x + 7\right)} = \lim_{x \to -\infty}\frac{-48}{48} = -1