Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{- 4 x^{2} - 6 x + 6}{8 x^{2} + 9 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{- 4 x^{2} - 6 x + 6}{8 x^{2} + 9 x - 7} = \lim_{x \to \infty}\frac{- 8 x - 6}{16 x + 9} = \lim_{x \to \infty}\frac{-8}{16} = - \frac{1}{2}