Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{3 x^{2} + 3 x + 8}{x^{2} + 7 x + 1}

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} + 3 x + 8}{x^{2} + 7 x + 1} = \lim_{x \to \infty}\frac{6 x + 3}{2 x + 7} = \lim_{x \to \infty}\frac{6}{2} = 3