Question

Use the following information to complete parts a. and b. below. P(x) = 1 = 1 ; a = 1 a. Find the first four nonzero terms of the Taylor series for the given function centered at a. O A. The first four terms are - 3 + 3(x-1)-3(x - 1)2 + 3(x - 1) OB. The first four terms are - 3+3(x - 1) - 6(x - 1)2 + 9(x - 1)3. OC. The first four terms are 3 -3(x-1)+3(x - 1)2 - 3(x - 1)3 OD. The first four terms are 3-3(x-1) + 6(x - 1)2-9(x-13. b. Write the power series using summation notation. 0 31-1 +1 3(-1)+1(x - 1) k=0 k=0 (x - 1) IM: M8 c. 13(-1k 31-1)*(x-1) k=0 K=O (X- 1k

Answer 1

for- rasi 1 Taylor's f(x) = formulain f(a) + (x-4) ficas. (x-aj² f"(a) + (x-a13 ficas 2 f. 121 31 ahoat x=a +(x) = f'(X) = -3 f(1) = 3 PCI= - -> f"(x) 6 - f"() = 6 23 f(x) = -18 "(1) = -18 put in obnove Cormilaran 412f"(1) + f(x) = f(+ (x-1) f'(o) + (x-1)2 f'(o) = 3 + (x-1) (-3) + 1 ! (x-1)² 6 + (x-1} (-18) 31 = 3 - 3(x-1) + 3(x-1)2 - 3(x-1)+..

f(x) = 3 - 3 (x-1) + 3 (x-172 – 3 (x-17 3 + ... sight is charging Alternatively .] 50 4x) = 31-(x-1) + (x-1)² – (x-194 Acx) - 3 1 (-17 * (x-10k ko 4.x) = Keo