Question

Please show detailed solution 1.Find the fourier cosine series for f(x)=x2 in the interval 0 < x <T 2. Find the fourier series of the odd extension of f(x)=x-2,0 < x < 2

Answer 1

OST is the fourier cosine series of of be 2 + E Cn los nzy Here LT So I en cas (na) -na where & MENO fa Ca 2+ " fa costa de 1 5 ) Cos (0:2) in nr de 2 7/7 [33] Nub} Coo 2 IT S. TT 2. 173 3 21 nto. Cn 2 2 "T S" x casual da 6 2 Tr in sinna 2a sinna 틔 2/4 2 w x sin na da Conn n TT casna da h h 1 S [sinn1" } T cant ht ht - 0 w

odd a { cn Gna) com.com function fed defined on 10. 2] the extension off) is the function to az fa) for onel for a lenco and the Fourier series become La fola)= I bn sin (1/2) , bet ne for an alte the hai Here 122. and ffn) 22. ent 5 hy bn Sin (nt 3 54 sn (Da 1 2-2.) sau (na) dhe Is anyagok x sin 2 in Cos (min) + Cais M hTT 2 da & 2 Cos ng 22 HT 2 2 - 2 cognT) + 297 Sin II Y 17 + 2 nit (Ces ht - 1) n+1 61) 4 + 0 ha + nIT Whena niseren 4 4 When irodd. TIT

So the serie fifa) = 2 Sin T haq