# Thread: Finding the limit for x->∞

1. ## Finding the limit for x->∞

How do I find the limit of

(root(9x^2 + x)) - 3x when x -> ∞?

2. Originally Posted by sweetadam
How do I find the limit of

(root(9x^2 + x)) - 3x when x -> ∞?
$\lim_{x\to\infty}\sqrt{9x^2+x}-3x$

= $\lim_{x\to\infty}(\sqrt{9x^2+x}-3x)\frac{\sqrt{9x^2+x}+3x}{\sqrt{9x^2+x}+3x}$

= $\lim_{x\to\infty}\frac{x}{\sqrt{9x^2+x}+3x}$

= $\lim_{x\to\infty}\frac{1}{\sqrt{9+\frac{1}{x}}+3}$

= $\frac{1}{\sqrt{9+0}+3}$

= $\frac{1}{6}$