Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{7 x^{2} + 5 x - 7}{- 8 x^{2} + 8 x + 9}

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} + 5 x - 7}{- 8 x^{2} + 8 x + 9} = \lim_{x \to \infty}\frac{14 x + 5}{8 - 16 x} = \lim_{x \to \infty}\frac{14}{-16} = - \frac{7}{8}