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

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