00 f(x) = x³ at z = 4 as Cn (x – 4)". E Cn (x - 4)". n=0

↑ Use the following information to complete parts a. and b. below. 3 f(x) = -, a = 1 a. Find the first four nonzero terms of the Taylor series for the given function centered at a. OA. The first four terms are −3+3(x-1)-3(x-1)² +3(x-1)³. OB. The first four terms are 3-3(x-1)+3(x-1)²-3(x-1)³. OC. The first four terms are 3-3(x-1) + 6(x-1)²-9(x-1)³. OD. The first four terms are -3+3(x-1)-6(x-1)² +9(x-1)³. b. Write the power series using summation notation. 3(-1)+1 k=0 (x-1) k 00 Oc. Σ 31-1)*(x-1) k=0 00 OA. OCCER 00 OB. 3(-1)+¹(x-1)* k=0 00 OD. Σ 3(-1)k k=0 (x-1)^ į OWD W

Write the Taylor series for f(x) = x³ about x = -2 as Find the first five coefficients. CO= C1= C2= C3= C4= Σen(x + 2)". n=0

6 Use substitution to find the Taylor series at x = 0 of the function 1- 4x ... What is the general expression for the kth term for the Taylor series at x= 0 for 1- 4x 00 k = 0 8 W