The following infinite series can be used to approximate ex(a)Prove that this Maclaurin se...

The following infinite series can be used to approximate ex

(a)Prove that this Maclaurin series expansion is a special case of the Taylor series expansion (Eq. 4.13) with xi = 0 and h = x.

(b)Use the Taylor series to estimate f(x) = e–x at xi+1 = 1 for xi = 0.2. Employ the zero-, first-, second-, and third- order versions and compute the |ɛt| for each case.