Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{7 x^{2} - x + 7}{- 6 x^{2} - 7 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{7 x^{2} - x + 7}{- 6 x^{2} - 7 x + 5} = \lim_{x \to \infty}\frac{14 x - 1}{- 12 x - 7} = \lim_{x \to \infty}\frac{14}{-12} = - \frac{7}{6}