Consider the following function. f(x) = ex Exercise (a) a=0, n=3, 0 x 0.2 Approximate f by a Taylor polynomial with degree n at the number a. Step 1 The Taylor polynomial with degree n = 3 is T(x) = f(a) + f'(a)(x a) + "(a) (x a) + (a) (x a). The function f(x) = e e2+2 f'(x)= 4x has derivatives 31 Step 2 4r Ar Jex f'(x) = 16x2 +4 16x+4 and . f(x) = 643 +48x 64x +48x f'(0) = = f"(0) = and ""(0) = 0. With a 0, f(0) = Submit Skip (you cannot come back) Exercise (b) Use Taylor's Inequality to estimate the accuracy of the approximation fx Tn(x) when x lies in the given interval. Step 1 If (4)(x) s M, then we know that M IR(x)|