I'm working on a problem at the moment and I just can't figure it out, here goes:

with l > 0 and f(x) differentiable on the interval [-l,l]

Things that come to mind are Riemann-Lebesgue Lemma -- from Wolfram MathWorld Riemann's lemma which states that any limit of n to infinity of an integral of a function on -l to l of the function times sin(nx) or cos(nx) tends to 0.

And ofcourse that

Does anyone have any ideas on how I can proceed?