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Is $\sqrt x \sin⁡\frac{1}{x}$ continuous at $0$?

I found the limit of the function which is $0$, but the function is not defined at $0$. Is it continuous then?

Magdiragdag
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sky
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  • It helps to typeset with MathJaX - makes the problem readable. What are your thoughts? – gt6989b Dec 10 '13 at 22:51
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    It is not defined at $0$ but you probably wanted to ask: Can we extend that function to define it at $0$ so that it is continuous at $0$. – xavierm02 Dec 10 '13 at 22:52

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If the function is undefined, it cannot be continuous. However, if the limit exists, you can define $g(x)$ to be $\sqrt{x} \sin(1/x)$ for $x \neq 0$ and let $g(0)=0$. Then $g$ would be continuous (provided you took the limit correctly).

gt6989b
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