Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 7 x^{3} - x^{2} + x + 1}{7 x^{3} - x^{2} - 8 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{- 7 x^{3} - x^{2} + x + 1}{7 x^{3} - x^{2} - 8 x + 6} = \lim_{x \to -\infty}\frac{- 21 x^{2} - 2 x + 1}{21 x^{2} - 2 x - 8} = \lim_{x \to -\infty}\frac{- 2 \left(21 x + 1\right)}{2 \left(21 x - 1\right)} = \lim_{x \to -\infty}\frac{-42}{42} = -1