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?
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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 $\displaystyle {\lim _{x \to {0^ + }}}x\sin \left( {\frac{1}{x}} \right) = 0$
I'm sorry, but why is that?
Originally Posted by Rita I'm sorry, but why is that? Do you have any idea what it means for $\displaystyle f$ to be continuous of $\displaystyle [0,1]~?$
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