Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{- 2 x^{2} + 6 x + 9}{- 9 x^{2} - 3 x + 2}

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{- 2 x^{2} + 6 x + 9}{- 9 x^{2} - 3 x + 2} = \lim_{x \to \infty}\frac{6 - 4 x}{- 18 x - 3} = \lim_{x \to \infty}\frac{-4}{-18} = \frac{2}{9}