Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{- 9 x^{2} + 4 x + 1}{8 x^{2} - 6 x + 6}

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} + 4 x + 1}{8 x^{2} - 6 x + 6} = \lim_{x \to \infty}\frac{4 - 18 x}{16 x - 6} = \lim_{x \to \infty}\frac{-18}{16} = - \frac{9}{8}