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October 8th, 2017, 05:09 AM   #1
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Arctan continuous, differentiable?

Hi!
Can someone help me with this? I saw some examples with a sine-function but I have no idea how to do it with arctan?

Let f be the function given by:

f(x)=sum(arctan(kx)/k^2)
(k=1, infinity)
for any x ∈ R

a) Show that f is continuous for x ∈ R
b) Show that f is differentiable for x not equal to 0
c) Show that f is not differentiable for x = 0

Last edited by skipjack; October 8th, 2017 at 08:02 AM.
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