Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 9 x^{3} + 4 x^{2} + 9 x + 4}{7 x^{3} - 9 x^{2} - x + 9}

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{- 9 x^{3} + 4 x^{2} + 9 x + 4}{7 x^{3} - 9 x^{2} - x + 9} = \lim_{x \to -\infty}\frac{- 27 x^{2} + 8 x + 9}{21 x^{2} - 18 x - 1} = \lim_{x \to -\infty}\frac{2 \left(4 - 27 x\right)}{6 \left(7 x - 3\right)} = \lim_{x \to -\infty}\frac{-54}{42} = - \frac{9}{7}