About x = 0 f(r) = sin(x)

Find the Taylor Series for the following functions:

Use the following information to complete parts a. and b. below. f(x) = 13 Inx, a = 4 a. Find the first four nonzero terms of the Taylor series for the given function centered at a. 13 O A. The first four nonzero terms are 13 In 4+ 13 13 4(x-4)- -(x-4) + (x-4)³. 32 192 13 O B. The first four nonzero terms are 13 In 4-- 13 13 4 (x-4)- -(x-4)². 16 32 (x-4)³ 13 13 O C. The first four nonzero terms are 13 2 (x-4). (x-4)² + 4 32 -(x-4)³. 192 13 13 O D. The first four nonzero terms are 13 4 32 (x-4). 32 (x-4)²+. b. Write the power series using summation notation. 13(-1)+1(x-4) Ο A. 13In 4+ Σ 4k k=1 OB. 13 In 4+ (-1). k=0 13(-1)k+1 O C. 13 In 4+ k=0 4²(x-4) k OD. 13 In 4+ (−1)k+1.. =(x-4) k 13 k.4k k=1 13 4*(x-4)k + + 13 1024 64(x-4)³ 39 2

Use the following information to complete parts a. and b. below. f(x)= 3/x; a= 3