I'm trying to prove my sequence of functions $(f_n) = \frac{n}{n+1}\cos(x^2)$ on (0,1) is pointwise equicontinuous, uniformly continuous, but not uniformly equicontinuous. But, I'm having a lot of trouble with showing it's not uniformly equicontinuous.
I've tried numericals, but I can't seem to find and $\epsilon$>0 s.t. $\forall \delta >0$, $|x-y|<\delta$ and $|f_n(x) - f_m(y)|< \epsilon$. And I'm not sure how to start this proof. But I know that $\frac{n}{n+1} \cos(x^2)$ is not uniformly continuous because its derivative is unbounded.
Any help would be greatly appreciated.