Question

Find Fourier series of f(x)= 0 if -35 x<0 and f(x)= 1 if 0 < x <3 which f(x) is defined on [-3,3)

Answer 1

Here we simply find the peroid 'L' for expansion of Fourier series and then we find Fourier coefficients and finally we write the required answer.

Here given fox) = 0 , -35% <0 -1, OS X < 3 The period 1, is given by 2= 6 the Foumen series SOOD f(x) = A + [an Cos nie & bn din nix ] i [1-Trgo A = 20 3 O -3 Now we will find the Fourien coefficients, where we have že ſ fra che ricors - 1 & S Forsche che + So 1. dhe = 5:3 = 2 A - 2 nice (วัดจาก จาเราย พกาน อาคาร An= t I Fox) cos ni ax = + J & fox) cas uz de [s oo Dorto di ti -l l wo 0 o. Cos ntx dat S 1. Co niti z dose 3 = 3 ar 3 -Sin Tx nIT 3 Ś[0-o] O 0 o an bn = 12 5l Fox) sin ninte de s f(x) sinntir de 3 cut -3

. 3 1/3 So sin nitx 3 O. Sin TTx + 1. Sin TTR 3 3 € dhe 3 cs -Cos na & goro sramot 3 3 η Γ' 3 [.Com [Coant - 1 o oro & [ 17 (-18 ] NT Lovas ant Too Costa =com] :. fræ) = + Ž [I-En] Sin intie nyt 3 [from 1 [oco lo 20] n=1 sito. I sin nix от со [L-Eign 3 = + n=1 = 1 + 1 [ 2 sin Tx + 2 Sin 37 x + 2 / 2 sin 5x...] It is the required fournies semes. [Ans] sob 3 aC [ sbr.