Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{2 x^{2} - 7 x - 1}{8 x^{2} - 7 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{2 x^{2} - 7 x - 1}{8 x^{2} - 7 x - 2} = \lim_{x \to \infty}\frac{4 x - 7}{16 x - 7} = \lim_{x \to \infty}\frac{4}{16} = \frac{1}{4}