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- Homework Statement
- Show ##f(x)=\sum_{k=1}^\infty \frac{\arctan (kx)}{k^2}## is not differentiable at ##x=0##.

- Relevant Equations
- Unsure.

I have previously shown that the function series is differentiable at ##x\neq 0##. The series converges uniformly (thus pointwise) on ##\mathbb R## and the term wise differentiated series is uniformly convergent on any interval ##d\leq |x|##, where ##d>0##. Moreover, the terms are continuously differentiable. So from all that, we can conclude that ##f(x)## is differentiable on ##\mathbb{R}\setminus \{0\}##, however, I am unsure how to show it is

**not**differentiable at ##x=0##. How would you do that?
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