Check whether the function is piecewise smooth. If it is, state the value for which its Fourier series converges at each point x in the interval and at the end points.

a) f(x)= |x|+x, -1

Question

Check whether the function is piecewise smooth.  If it is, state the value for which its Fourier series converges at each point x in the interval and at the end points.

a) f(x)= |x|+x, -1<x<1
b) f(x)=xcosx, (-pi/2)<x<(pi/2)

experimentx · Answer

first looks piece wise smooth ... the value should converge to it's functional value where it is continuous ... (i guess)

experimentx · Answer

b) looks continuous everywhere http://www.wolframalpha.com/input/?i=plot+x*+cos+x+from+-pi%2F2+to+pi%2F2