Consider the function f : [-L, L] → R given by (x+L, if – L
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![Consider the function f : [-L, L] → R given by
(x +L, if – L <r< -
if – L< x < –
if - :< x < 0
L
2
L
L
f (x) =
2
x2,
if 0 < x < L.
Find the value to which the Fourier series of f at x converges when
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(b) х —
-L
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L
-
2
(c) x
(d) х
- L.
2
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- 5) a) Construct a Fourier Series for f(x) (x2 . 12x)for 12 < x < 3t b) Briefly explain the application of half - the range Fourier series in your SpecializationIf f is the Fourier series of g(x) = = f(x) = 32(-1)"+1 n²-² [16-r², What does f(-4) equal? f(-4) What does f(-2) equal? f(-2)= What does f(0) equal? f(0) n² What does f(1) equal? f(1) What does f(4) equal? ƒ(4) FIT 4 -4< <0 0Prove that f(x)={-3x if -pi<x<0, 3x if 0<x<pi is an even function using fourier series expansion.4. Express the f(x)=1+x function as a Fourier series in the interval of -T(b) Using the answer to Part (a) and without using Theorem 2.2.4, find the real Fourier series of the function f(x) = -2x 2r-8 if 0 < x < 2 if 2 < x < 4 and f(x+4)=f(x).If f(x) = (n - x)2, find the Fourier series of period 2n in the interval (0,27) and hence evaluate+ %3D 122. Show that the Fourier series function defined by f(x) below is an even function. Hence determine the Fourier series for the function: f(t)= 1-1, 1+1, when - <1 <0 when 0 <11. Express f(x) by the Fourier series where f(x)= {, 2, -7Let f(x) = x, where - 2< x< 2 %3D determine the number to which the full fourier series of f converges at x = 2 -2 1. -4Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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