What is the limit of (x^2-1)/(2x^2-x-1) as x goes to infinity?

Oct 17, 2015

$\frac{1}{2}$

Explanation:

Since the quadratic terms dominate the function at infinity, we may write this limit as :

${\lim}_{x \to \infty} \frac{{x}^{2} - 1}{2 {x}^{2} - x - 1} = {\lim}_{x \to \infty} {x}^{2} / \left(2 {x}^{2}\right) = \frac{1}{2}$