Convergence Write the remainder term Rn(x) for the Taylor series for the following functions centered at the given point a Then show that for all x in the given interval. f(x) - sin x, a = 0, -< x

Solution 38REStep 1 of 2:In this problem we need to find the remainder term in the taylor series expansion of at center a = 0 , and we have to prove that = 0. Thus the Taylor series of with center 0 is as follows; Given : f(x) = , then f(0) = = 0 , since = = cos(x), then = cos(0) = 1 = = , then = = 0 = = , then = = -1 …………………….sin(x) or cos(x) 0r sin(+x) and …………(1) Therefore , the Taylor series of with center 0 is as follows; ……. = - + -........