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

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{- 2 x^{3} - 5 x^{2} + 7 x + 4}{7 x^{3} - 6 x^{2} - 5 x + 5} = \lim_{x \to -\infty}\frac{- 6 x^{2} - 10 x + 7}{21 x^{2} - 12 x - 5} = \lim_{x \to -\infty}\frac{- 2 \left(6 x + 5\right)}{6 \left(7 x - 2\right)} = \lim_{x \to -\infty}\frac{-12}{42} = - \frac{2}{7}