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

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{- 8 x^{2} + 7 x + 3}{3 x^{2} - 7 x - 2} = \lim_{x \to \infty}\frac{7 - 16 x}{6 x - 7} = \lim_{x \to \infty}\frac{-16}{6} = - \frac{8}{3}