Is a following function periodic f(x) =\tan x +\tan (\sqrt{2}x)

misangela4gi

misangela4gi

Answered question

2022-04-21

Is a following function periodic f(x)=tanx+tan(2x)

Answer & Explanation

elseptimopc7

elseptimopc7

Beginner2022-04-22Added 14 answers

It's easy to show that a differentiable function f is periodic only if f' is periodic.
So
f(x)=1+tan2(x)+2+2tan2(2x)
If f' has a period T>0 then
1+2=1+tan2(T)+2+2tan2(2T)
This implies that tanT and tan(2T) are both 0, which is impossible for the same reason as for cos

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