Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{8 x^{3} + 2 x^{2} - x + 2}{- 2 x^{3} + 3 x^{2} - 7 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{8 x^{3} + 2 x^{2} - x + 2}{- 2 x^{3} + 3 x^{2} - 7 x + 7} = \lim_{x \to -\infty}\frac{24 x^{2} + 4 x - 1}{- 6 x^{2} + 6 x - 7} = \lim_{x \to -\infty}\frac{4 \left(12 x + 1\right)}{6 \left(1 - 2 x\right)} = \lim_{x \to -\infty}\frac{48}{-12} = -4