Question

Use the following information to complete parts a and b below. f(x) = (1 + x)*?; approximate 1.092 a. Find the first four nonzero terms of the Taylor series centered at 0 for the given function. The first term is (Simplify your answer. Use integers or fractions for any numbers in the expression.) The second term is (Use integers or fractions for any numbers in the expression.) The third term is (Use integers or fractions for any numbers in the expression.) The fourth term is (Use integers or fractions for any numbers in the expression.) b. Use the first four terms of the series to approximate the given quantity. (Round to three decimal places as needed.) 1.092

Please provide detailed steps and methods that were used to derive the answers to the given questions

Answer 1

Centred at o سے (1+2)-2, (10) f first ferm (a) f(o) isor ill fersh Jesen (b) pred f'(o) f'(m), -2 (1+20)-3 f(0) = -2 9 gecond deren 3nd ferm (0) 6 (?+*) -4 f"(0) (wut (out 3 C ferm is 13 yn flom (d)

{"!(0) 31 A(n)- - 24 (1+x)-5 {"160) -24 4 fourth Segm the is 1-4 (b) Afbreximahe Chore using first ferme. four fol" Rr (0) 1-20 + 3x² - 4x3. i put x = 0.09. = (1+x)-2 (1+0) / Ry (0.09) (7.09 1 - (0.09) + 3 (0,09) 2 420.09) 3 0.84 138 4 (0.841