Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{9 x^{3} - 5 x^{2} + 4 x - 3}{- 8 x^{3} + 3 x^{2} - 8 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{9 x^{3} - 5 x^{2} + 4 x - 3}{- 8 x^{3} + 3 x^{2} - 8 x - 9} = \lim_{x \to -\infty}\frac{27 x^{2} - 10 x + 4}{- 24 x^{2} + 6 x - 8} = \lim_{x \to -\infty}\frac{2 \left(27 x - 5\right)}{6 \left(1 - 8 x\right)} = \lim_{x \to -\infty}\frac{54}{-48} = - \frac{9}{8}