- #1
jianxu
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Homework Statement
Hi and thank you for reading this!
Let [tex]\left.f(x) = cos(x) + cos\left(\pi x\right)[/tex]
a) show that the equation f(x)=2 has a unique solution.
b) conclude from part a that f is not periodic. Does this contradict withe the previous exercise that states if:
[tex]\left.f_{}1,f_{}2,f_{}3...f_{}n[/tex] are T-perioidc functions, then:
[tex]\left.a_{}1f_{}1+a_{}2f_{}2+...+a_{}nf_{}[/tex] is also T-periodic?
Homework Equations
The Attempt at a Solution
So for part a, I did:
[tex]\left.\int^{T}_{0}2 dx = 2T[/tex]
no idea if I approached this problem correctly...
but for part b) I took the integral of:
[tex]\left.\int^{T}_{0}cos(x) + cos\left(\pi x\right)+2 dx = -sin(T)+2T[/tex]
but the only other thing I can say is that f is not periodic, this is relatively obvious seeing how the problem at the end says, the function f is called almost periodic.
Please let me know what's wrong and what should be the correct way of approaching this question
Thanks!