Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 6 x^{3} + 4 x^{2} - x + 6}{- 8 x^{3} + 4 x^{2} - 7 x + 1}

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} + 4 x^{2} - x + 6}{- 8 x^{3} + 4 x^{2} - 7 x + 1} = \lim_{x \to -\infty}\frac{- 18 x^{2} + 8 x - 1}{- 24 x^{2} + 8 x - 7} = \lim_{x \to -\infty}\frac{4 \left(2 - 9 x\right)}{8 \left(1 - 6 x\right)} = \lim_{x \to -\infty}\frac{-36}{-48} = \frac{3}{4}