How to prove that $x\cos(nx)$ is equicontinuous on $[0;1]$? I proved that it is equicontinuous on 0, however I cannot prove either it is equicontinuous on[0;1] or not. I also tried to do something with $1$, like $\cos n - (1-\frac{1}{n})\cos(n(1-\frac{1}{n})))$ = $\cos(n) - \cos ((n-1)) +\frac{1}{n}\cos(n-1)$ = [ with $n\to\ \infty$] = $\cos(n)-\cos(n-1)$. But it seems that it isn't something helpful. What should I do?
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