Evaluate the limit $LaTeX: \displaystyle \lim_{x \to \infty}\frac{2 x^{2} - 3 x - 2}{2 x^{2} - 2 x - 6}$

The limit is an indeterminate form of the type $LaTeX: \displaystyle \frac{\infty}{\infty}$ . Using L'Hospitial's rule 2 times gives: $LaTeX: \lim_{x \to \infty}\frac{2 x^{2} - 3 x - 2}{2 x^{2} - 2 x - 6} = \lim_{x \to \infty}\frac{4 x - 3}{4 x - 2} = \lim_{x \to \infty}\frac{4}{4} = 1$