Find the Fourier cosine series for f over the given interval. Use symmetry whenever possible to help with the calculations. f(x) = ez; [-1, 1]. The Fourier series is + sin(mTa)+ cos (mix) m = 1, 2, 3, ...\f\ffourri Cosine Souls . H(x) = 3X towe've succes of fundion (1x) on the interval -LEX21 is defined as 7 () = Ao + 2 An . Cos (NITX ) + 5 Bn. ain (21) Ao = 1 ( fix)dx 2 L An = - ( fix) cos / nox jax ; no - L Bn = (flex) sin / nox Jax in20 +(xx)= 3x - L= 1 AD = 1 ( 3 x dx An = 38 Gos ( 1721 ) dx nix jax Bn = = 3x dx + 2 + 32 cos ( max )ax cos ( 2 . 1 Co + M 3xsin ( DR 3 ) doc sin 203 we know 3 xdx = 0 : since fix) is an odd function, 1 3 x cos ( nATX Jax= 0; since flux ) is an odd function - 1 1 3 x sin ( DAX ) ax = - 6 ( - 1 ) " - 12 . 1 O 8 Wil - . 0. Cos / nox ) ( - 6(-1)? sin nie 2 - 6 ( - 1) sin ( NTIAL ) n= 1 nn