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

Question

6877 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-17T18:39:17

$1/2$

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

$lim_(x->oo)(x^2-1)/(2x^2-x-1)=lim_(x->oo)x^2/(2x^2)=1/2$

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