Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{- 9 x^{2} + 9 x + 5}{2 x^{2} + 7 x - 7}

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{- 9 x^{2} + 9 x + 5}{2 x^{2} + 7 x - 7} = \lim_{x \to \infty}\frac{9 - 18 x}{4 x + 7} = \lim_{x \to \infty}\frac{-18}{4} = - \frac{9}{2}