Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{5 x^{2} - 4 x - 1}{6 x^{2} - 4 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{5 x^{2} - 4 x - 1}{6 x^{2} - 4 x - 7} = \lim_{x \to \infty}\frac{10 x - 4}{12 x - 4} = \lim_{x \to \infty}\frac{10}{12} = \frac{5}{6}