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

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{6 x^{3} - 7 x^{2} - 2 x + 2}{9 x^{3} - 3 x^{2} - 8 x + 7} = \lim_{x \to -\infty}\frac{18 x^{2} - 14 x - 2}{27 x^{2} - 6 x - 8} = \lim_{x \to -\infty}\frac{2 \left(18 x - 7\right)}{6 \left(9 x - 1\right)} = \lim_{x \to -\infty}\frac{36}{54} = \frac{2}{3}