The following infinite series can be used to approximate e^x?:

(a) Prove that this Maclaurin series expansion is a special case of the Taylor series expansion [(Eq. (4.7)] with x_i?= 0 and h = x

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

Transcribed Image Text:

et =l+x+ 3! 2 п!