Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{2 x^{3} - 7 x^{2} - 4 x - 8}{- 9 x^{3} - 8 x^{2} - 8 x - 5}

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{2 x^{3} - 7 x^{2} - 4 x - 8}{- 9 x^{3} - 8 x^{2} - 8 x - 5} = \lim_{x \to -\infty}\frac{6 x^{2} - 14 x - 4}{- 27 x^{2} - 16 x - 8} = \lim_{x \to -\infty}\frac{2 \left(6 x - 7\right)}{- 2 \left(27 x + 8\right)} = \lim_{x \to -\infty}\frac{12}{-54} = - \frac{2}{9}