Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{5 x^{3} + 6 x^{2} + 8 x - 1}{- x^{3} + 8 x^{2} - 6 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{5 x^{3} + 6 x^{2} + 8 x - 1}{- x^{3} + 8 x^{2} - 6 x - 6} = \lim_{x \to -\infty}\frac{15 x^{2} + 12 x + 8}{- 3 x^{2} + 16 x - 6} = \lim_{x \to -\infty}\frac{6 \left(5 x + 2\right)}{2 \left(8 - 3 x\right)} = \lim_{x \to -\infty}\frac{30}{-6} = -5