I have to decide if the function $f(x)=x\cdot \ln(x)$ in the interval $(0,3]$ is uniformly continuous but I don't know how to start.
In general I have problems with this kind of proof. Please can someone make me understand?
2026-03-27 18:34:40.1774636480
$f(x)=x\cdot \ln(x)$ uniformly continuous in $(0,3]$?
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Extend $f$ to $0$ by putting $f(0)=0$. Since $\lim_{x\to0}x\ln(x)=0$, this extension is continuous. And every continuous function whose domain is closed and bounded is uniformly continuous.