Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{3 x^{2} - 7 x - 8}{7 x^{2} + 8 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{3 x^{2} - 7 x - 8}{7 x^{2} + 8 x - 5} = \lim_{x \to \infty}\frac{6 x - 7}{14 x + 8} = \lim_{x \to \infty}\frac{6}{14} = \frac{3}{7}