3. Let f em. All Taylor series referred to below are centered at O. (a) Recall that f' (x) f Prove this by showlng that the derivative of the Taylor series for f is equal to the Taylor series for f (b) Recall that the antiderivative Of f (x) is f -k C. Prove this by showing that the antiderivative of the Taylor series for f (x) is equal to the Taylor series for f (x) plus an additive constant. (c) Find the Taylor series for dr. 1 1 (d) Use your answer to (c) to prove that + -+ 1