Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 7 x^{3} + 7 x^{2} - 3 x + 5}{- 6 x^{3} + x^{2} - 2 x - 4}

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{- 7 x^{3} + 7 x^{2} - 3 x + 5}{- 6 x^{3} + x^{2} - 2 x - 4} = \lim_{x \to -\infty}\frac{- 21 x^{2} + 14 x - 3}{- 18 x^{2} + 2 x - 2} = \lim_{x \to -\infty}\frac{14 \left(1 - 3 x\right)}{2 \left(1 - 18 x\right)} = \lim_{x \to -\infty}\frac{-42}{-36} = \frac{7}{6}