Question

3. A function f(t) defined on an interval 0 <t<L is given. Find the Fourier cosine and sine series off. f(t) = 6t(11 – t), 0 <t<n

Answer 1

Solutions tourin Serire Jourin sin ben #(1) = 6+ (-+) , OctCTI a = 7 - 8 Add an= 3 4 5 (A) (as (nt) ft) Sain $ 10) Sn (n) dt 4) dx S (677-6tJcht 22 [ 3714-27] :*372-373) To Sunty a = ? ZT T 2T a = T2 an= 2 4 5 1 674-643 (as in the =[(03-60% Castuess - Slen_129 ) sandpa) de 3 =[677-64?)X[o-o] -S(67–121) Sin(ne) JA

T --> [S16-18) Sinfusion *[1741215 anyone else [(T423) (03/04)" + 12+ [su(na)]." - 2 / 2 - Seng -12) Cas(14) dt re 6 +2 ! 2 2 (12t-6 TR 1 - Cornti L O [ 1-cesnim T² 2 12T1-6TT TX ² [l-cm] So the tourin Cariri rein of Ht) - Ht) a got a cor (nt) ha (A) T & 2 [1-6,7 ] 67 (19) T2 Then - bon = 3.5"(674-64') Su (nt) odt [604-6496 50 pande + SleT+124) Gay po ㅠ b = 2

7T d+- o = * {694-68Castru) + (67429) Cspan Sing sangat 3 [64672) 616ne) + 0 +12 X3 [carna?" 3 [lor_672)6907–1) + {12}(6967-) T 0 - T 24 Tins [l-cant So that tourin. Sin ruis of 1)- Mt) { bor fin (nt) om farlino 116) no 2Ě 24 no h3 [1- GANT] Sulit) This is the above function show that farin carins and rime sein of (A).