Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{- 7 x^{2} - 3 x - 2}{- 8 x^{2} + 8 x + 5}

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{- 7 x^{2} - 3 x - 2}{- 8 x^{2} + 8 x + 5} = \lim_{x \to \infty}\frac{- 14 x - 3}{8 - 16 x} = \lim_{x \to \infty}\frac{-14}{-16} = \frac{7}{8}