Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{- x^{2} + 5 x - 3}{- 3 x^{2} + 9 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{- x^{2} + 5 x - 3}{- 3 x^{2} + 9 x - 7} = \lim_{x \to \infty}\frac{5 - 2 x}{9 - 6 x} = \lim_{x \to \infty}\frac{-2}{-6} = \frac{1}{3}