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

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} - 3 x^{2} + 3 x - 6}{6 x^{3} + 3 x^{2} + 5 x - 9} = \lim_{x \to -\infty}\frac{24 x^{2} - 6 x + 3}{18 x^{2} + 6 x + 5} = \lim_{x \to -\infty}\frac{6 \left(8 x - 1\right)}{6 \left(6 x + 1\right)} = \lim_{x \to -\infty}\frac{48}{36} = \frac{4}{3}