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

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