Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{4 x^{2} - x + 2}{- 7 x^{2} - 7 x - 8}

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{4 x^{2} - x + 2}{- 7 x^{2} - 7 x - 8} = \lim_{x \to \infty}\frac{8 x - 1}{- 14 x - 7} = \lim_{x \to \infty}\frac{8}{-14} = - \frac{4}{7}