1. Textbook problem 2.26.
(Textbook may have a typo labeling this as problem 20.26, see page 53)
3.a. The following infinite series can be used to approximate ex:
(i) Prove that this Maclaurin series expansion is a special case of the Taylor series expansion(Eq. (4.7) in text) with xi = 0 and h = x.
(ii) Use a Taylor series to estimate f(x) = e−x at xi+1 = 2 for xi = 1.5. Employ the zero-, first-, second-, and third-order versions and compute |εt| for each case. 3.b. Use zero- through third-order Taylor series expansions to predict f(1) for
f(x) = 20x3 − 5x2 + 7x − 80
using a base point at x = −1. Compute the true percent relative error εt for each approximation.
