Consider the function

f

defined on the interval

-4,4

as follows,\

f(x)={(-(1)/(2)x,xin[-4,0),),((1)/(2)x,xin[0,4].):}

\ Denote by

f_(F)

the Fourier series expansion of

f

on

-4,4

,\

f_(F)(x)=(a_(0))/(2)+\\\\sum_(n=1)^(\\\\infty ) [a_(n)cos((n\\\\pi x)/(L))+b_(n)sin((n\\\\pi x)/(L))].

\ Find the coefficients

a_(0),a_(n)

, and

b_(n)

, with

n>=1

.\

a_(0)=\ a_(n)=\ b_(n)=

Consider the function f defined on the interval [4,4] as follows, f(x)=21x,21x,x[4,0),x[0,4]. Denote by fF the Fourier series expansion of f on [4,4], fF(x)=2a0+n=1[ancos(Lnx)+bnsin(Lnx)]. Find the coefficients a0,an, and bn, with n1. a0=an=bn=