Find the Fourier series for the function defined by (a) f(x) = –a, –π ≤ x < 0 and f(x) = a, 0 ≤ x ≤ π (a is a positive number); (d) f(x) = –1,–π ≤ x < 0 and f(x) = 2, 0 ≤ x ≤ π;
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Find the Fourier series for the function defined by
(a) f(x) = –a, –π ≤ x < 0 and f(x) = a, 0 ≤ x ≤ π (a is a positive number);
(d) f(x) = –1,–π ≤ x < 0 and f(x) = 2, 0 ≤ x ≤ π;
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- Show that the Fourier series for f (x) = x, –n (-1)n+1 n n-1Consider the function. f(x) = { -25 x+1, -7 < x < 0 1-x, 0≤x <7' (a) Sketch the graph of f(x) for three periods fx -20 -10 f(x)= [Choose one f(x+14) = f(x) -5 10 M (b) Find the Fourier series of f(x) 15 20 25 85. Find the Fourier Series of the function: S0, -TFind the Fourier series for f(x) in [-π, π] where f(x) = π + x, if − π1. Expand f(x) = -X X if - < x < 0, if 0 < x < π, in a Fourier series.Q1: Find the fourier expension of the periodic function whose defination in one period is: 0Compute the Fourier series for the following functions. (a) F(t) = sin³ t (b) F(t) = os³ = cos (c) F(t) = t² (d) F(t) = t|t| 3 (-π < t <π) (-π < t <π)WHAT IS THE FOURIER EXPANSION OF THE PERIODIC FUNCTION WHOSE DEFINITION IN ONE PERIOD IS : F(t) = for -II need help with this question and show your workFind the trigonometric Fourier series for the function f(x): [-T/2, π/2] → R given by the expression: ƒ(2) - {0 = O о O O cos 2x if x = [-π/2, 0] 0 if x = (0, π/2] O ∞ FS(x) = -2 cos(2x) + 1 n=1 FS(x) = −cos(2x) + Σ2 FS(x) = −sin(2x) + Σn=2 FS(x) = cos(2x) + Σn=0 FS(x) = cos(2x) + Ex-1 - n² cos² (n²-1)π 2n cos² n cos² (=) 2 n cos² (n²-1)T (+) 2 2(n²-1)π NE (+) (n.²-1) 2n cos² * ( =) 2 (n²+1)π -sin(2nx). -sin(2nx). -sin(nx). sin(2nx). -sin(2nx).(2) Find the full Fourier series for the periodic function f : R → R defined by f(x) = 1+ |x| on the interval (-1,1) and then extended using f(x+ 2) = f(x) for all r.1)Determine S[f] (Fourier series) if: d) f(x)=ex+x ,x∈ [-1, 1] such that f(x) = f(x + 2)SEE MORE QUESTIONSRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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