U(x) = Sigma^infinity_k = -infinity u^(k) e^i k x U^(k) = 1/2 pi integral^infinity_infinity u(x) e^I k x dx} 0 lessthanorequalto x lessthanorequalto 2 pi Show that u^(1) (x) = Sigma^infinity_k = -infinity (ik) u^(k) e^I k x U(x) = sin(x), then 0