Thursday, 28 March 2019

sequences and series - Does the limit of f(x)=sumlimits+inftyn=1frac(1)nsinfracxnn exist?

Consider the function f:[0;+]R given by the formula f(x)=+n=1(1)nsinxnn


Does limx0f(x) exist? If yes, find it's value.
Is f differantiable? If yes, check if f(0)>0.



Any ideas how to do that? I assume this is about functions series, it's pointwise convergent I think, does that mean that this limit exists?



Thanks a lot for your help!

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