Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{- 5 x^{2} - 7 x + 5}{- 9 x^{2} + 2 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{- 5 x^{2} - 7 x + 5}{- 9 x^{2} + 2 x - 5} = \lim_{x \to \infty}\frac{- 10 x - 7}{2 - 18 x} = \lim_{x \to \infty}\frac{-10}{-18} = \frac{5}{9}