Question

please help in any of these in diff eq in Trigonometric Fourier Sine Series and Trigonometric Cosine Series

Homework Problems for Handout Sheet 25 In Problems 1 to 4, determine the Fourier Sine Series that converges to the given function at each of its points of continuity 0 when 0x<1/2 1. f(x)=when 1/2<x<1' flx+2)= f(x). 0 when 4<x<-2 2. f(x)={2 when 0<x<1 , f(x+8)= f(x). 1 when 1<x<2 3. f(x) 2-x when 0<x<27, f(x+47)=f(x) 4. f(x) 7-x when 0<x<47, f(x+87)= f(x)

Answer 1

period This meanS Founer sine senes ftx) ニ 2T - 1とラ×ラ0 2代 (21-x) Sin nx dz 2JT Bn= 2 L where 1(art-7 2L- it) 2 It 2TL 20 oSn 2 2. 2. JtJ n Jt 2TC 2 sinnx 2X2 2 OP Bnsin nJOX series Sine D -Ams 4 Sinnx 2 sinz) Na founer tosine series 2IT 2IT 2 A o 2JT 2 TC L 2元 -T = JT 2T元 L An- 2fa) (2T 2元 COS 2

2 TC 2Tt TINSINNX dx Jt sim nx sin ntz 2 JT 2 2. 21T = 0-0 +IX2 11 Jt n2 cosNt tcoso 2 2 or oS n cosine series = Jt t 22 (1+G) 2. =1 2t