Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{7 x^{2} - 2 x - 9}{9 x^{2} - 3 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{7 x^{2} - 2 x - 9}{9 x^{2} - 3 x + 2} = \lim_{x \to \infty}\frac{14 x - 2}{18 x - 3} = \lim_{x \to \infty}\frac{14}{18} = \frac{7}{9}