Let g is a Lebesgue integrable function (i.e., the Lebesgue integral exists and is finite) in R. Define for a E R G(a) = J_g(x) sin(ax) dx. Show that the following hold: (a) G is continuous at a = 0. (b) S_ lag(x) |dx = G'(0) exists. Note for the tutor: All integrals are Lebesgue integrals. Hint: A derivative is nothing but a limit. To show (b), we need to show the interchangeability of an integral and a limit