Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{2 x^{3} - 8 x^{2} - 7 x - 7}{5 x^{3} + 3 x^{2} - 7 x - 6}

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} - 8 x^{2} - 7 x - 7}{5 x^{3} + 3 x^{2} - 7 x - 6} = \lim_{x \to -\infty}\frac{6 x^{2} - 16 x - 7}{15 x^{2} + 6 x - 7} = \lim_{x \to -\infty}\frac{4 \left(3 x - 4\right)}{6 \left(5 x + 1\right)} = \lim_{x \to -\infty}\frac{12}{30} = \frac{2}{5}