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

• Oct 12th 2013, 09:11 AM
Rita
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?
• Oct 12th 2013, 09:20 AM
Plato
Re: Show that x*sin(1/x) is continuous. Help~
Quote:

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 ${\lim _{x \to {0^ + }}}x\sin \left( {\frac{1}{x}} \right) = 0$
• Oct 12th 2013, 09:58 AM
Rita
Re: Show that x*sin(1/x) is continuous. Help~
I'm sorry, but why is that?
• Oct 12th 2013, 10:07 AM
Plato
Re: Show that x*sin(1/x) is continuous. Help~
Quote:

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 $[0,1]~?$