Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{- 7 x^{2} - 3 x + 4}{- 6 x^{2} - 4 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} - 3 x + 4}{- 6 x^{2} - 4 x + 2} = \lim_{x \to \infty}\frac{- 14 x - 3}{- 12 x - 4} = \lim_{x \to \infty}\frac{-14}{-12} = \frac{7}{6}