Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{- 5 x^{2} + 8 x - 7}{8 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{- 5 x^{2} + 8 x - 7}{8 x^{2} - 7 x + 7} = \lim_{x \to \infty}\frac{8 - 10 x}{16 x - 7} = \lim_{x \to \infty}\frac{-10}{16} = - \frac{5}{8}