Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 6 x^{3} + 2 x^{2} - 6 x + 6}{- 6 x^{3} + 2 x^{2} + 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{- 6 x^{3} + 2 x^{2} - 6 x + 6}{- 6 x^{3} + 2 x^{2} + x + 6} = \lim_{x \to -\infty}\frac{- 18 x^{2} + 4 x - 6}{- 18 x^{2} + 4 x + 1} = \lim_{x \to -\infty}\frac{4 \left(1 - 9 x\right)}{4 \left(1 - 9 x\right)} = \lim_{x \to -\infty}\frac{-36}{-36} = 1