Problem 15 Consider the function of with period 4 and geven on the interval [-2₁2] hy x f(x) = 3₁ if if -15x²1 The Fourier Semes of f is of 15x28 if -22×2-1 ( (-2² conit + 4 omnil) pm ni x 2 π7²n² n=1 a) can you use the Fouver series off to cleduce the Fouver series of f'? explais use the Fouer series of f to deduce the termer series of 6) Can you the anti derivative F(x) = √² ft) dt 7 c) Find the Founess seves of F. 2 Ans: Fl=+(+²) (²2₂) EX es 6 ทะ 4 om

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Problem 15
Consider the function of with perod 4 and geven on the interval
[-2₁ 2] hy
x
if -15x41
f(x) = 31 of 15x28
if -22×2-1
The Fourier Series of f is
2 (-2/ Lone + comer) non Nex
4 pm nil
πT²n²
pm
2
n=1
a) can you use the Fourier series off to deduce the Fouver series of f'?
explain
6) Can you use the Fouren series of f to deduce the Former series of
the anti derivative
x
F(x) = √² ft) dt
C) Find the Fouriess seves of F.
M DIT) (-2=-) e DTZ
пітх
7
om nit
F(x) = ² + 2 ( = // Cen! + + +
A4: Ex
Ans:
6
2
ทะ
Transcribed Image Text:Problem 15 Consider the function of with perod 4 and geven on the interval [-2₁ 2] hy x if -15x41 f(x) = 31 of 15x28 if -22×2-1 The Fourier Series of f is 2 (-2/ Lone + comer) non Nex 4 pm nil πT²n² pm 2 n=1 a) can you use the Fourier series off to deduce the Fouver series of f'? explain 6) Can you use the Fouren series of f to deduce the Former series of the anti derivative x F(x) = √² ft) dt C) Find the Fouriess seves of F. M DIT) (-2=-) e DTZ пітх 7 om nit F(x) = ² + 2 ( = // Cen! + + + A4: Ex Ans: 6 2 ทะ
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