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

The limit is an indeterminate form of the type LaTeX: \displaystyle \frac{\infty}{\infty} . Using L'Hospitial's rule 2 times gives: LaTeX: \lim_{x \to -\infty}\frac{- 3 x^{2} + x - 3}{- 9 x^{2} - 7 x - 4} = \lim_{x \to -\infty}\frac{1 - 6 x}{- 18 x - 7} = \lim_{x \to -\infty}\frac{-6}{-18} = \frac{1}{3}