# Math Help - Limit xsin(1/x), x->0

1. ## Limit xsin(1/x), x->0

Hi
Can anyone help me prove this?
The limit of xsin(1/x) as x tends to 0 is 0.
Ta very much

2. ## Re: Limit xsin(1/x), x->0

Originally Posted by liv205
Hi
Can anyone help me prove this?
The limit of xsin(1/x) as x tends to 0 is 0.
Ta very much
I think it is more transparant to start by defining y = 1/x. Then your limit is of the form
$\lim_{y \to \infty} \frac{sin(y)}{y}$

Can you take it from here?

-Dan