# Math Help - Show that x*sin(1/x) is continuous. Help~

1. ## Show that x*sin(1/x) is continuous. Help~

Well, the problem is...
how do I show that f(x)= x*sin(1/x) for 0<x<=1 and f(0)=0 is continuous on [0,1]?
Can anyone help me with this problem?

2. ## Re: Show that x*sin(1/x) is continuous. Help~

Originally Posted by Rita
Well, the problem is...
how do I show that f(x)= x*sin(1/x) for 0<x<=1 and f(0)=0 is continuous on [0,1]?
All you need is to show that ${\lim _{x \to {0^ + }}}x\sin \left( {\frac{1}{x}} \right) = 0$

3. ## Re: Show that x*sin(1/x) is continuous. Help~

I'm sorry, but why is that?

4. ## Re: Show that x*sin(1/x) is continuous. Help~

Originally Posted by Rita
I'm sorry, but why is that?
Do you have any idea what it means for $f$ to be continuous of $[0,1]~?$