# For the test of LaTeX typesetting

(It is an easy problem for the sake of testing. )
How to prove $f(x)=x\cdot sin(x)$ is not uniformly continuous?
By sequential criterion all we need to do is to find two sequences $(x_n)$ and $(y_n)$ such that given $\epsilon >0$, $lim|x_n-y_n|=0$, $|f(x_n)-f(y_n)|\geq \epsilon$.
Now we take $x_n=2\pi n+\frac{1}{n}$ and $y_n=2\pi n$, it can be easily verified that the two sequences will generate the desired results (simply making use of the fact that $\lim_{x\to 0} \frac{sin(x)}{x}=1$).
Good day;)
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