(1) Find the Taylor series of f(x) = sin x centered at a = (2) (a) Find the Taylor series of f(x) = cos x at a = (b) Show that this series is equal to cos x for every real number x. (c) Deduce the identity sin(x) = = cos(x). (3) Use the Maclaurin series to compute the following limits: (a) lim sin x-x x→0 x3 1-cos x (b) lim 1+x-ex x→0 (c) lim x→0 2 cos x-2+x2 x4