Existence of limit of the sequence $x_n=\sqrt{n^2+1}-n$

Question

I need to find the limit of the following sequence

$x_n=\sqrt{n^2+1}-n$.

I am having trouble on where to start for this question. Any help would be appreciated.

Answer 1

Hint: Multiply and divide by $\sqrt{n^2+1} + n$

Answer 2

Multiply the expression by $\frac{\sqrt{n^2+1}+n}{\sqrt{n^2+1}+n} $.

Nothing original here - move along now.