Please solve the attached question, and please show all work that is needed to get the answer. I am trying to better understand the process/the question.

Thank you. =)

Use the following information to complete parts a. and b. below. f(x) = 5 Inx, a =4 a. Find the first four nonzero terms of the Taylor series for the given function centered at a. 5 5 5 O A. The first four nonzero terms are 5 In 4- -(x - 4) - - 16 (X - 4) 37 (x - 4)3 5 5 5 O B. The first four nonzero terms are 5 In 4 + -(x - 4)- 37 (x - 4)2 + 197 ( x - 4)3 5 5 5 15 O C. The first four nonzero terms are A + 37 (X - 4) - 7( x - 4)-+ 64 (X - 4)3 5 5 5 5 O D. The first four nonzero terms are 4 + 32 (x - 4) - 197 (x - 4)2 + 1024 (X -4)3 b. Write the power series using summation notation. O A. 5In 4+ S 5( - 1)* + 1(x -4)k Ak k = 1 5 O B. 5In 4+ > (-1)k k =0 4K (x - 4)k O c. 5In 4+ 5 5(-1)*+1 k=0 4"(x-4)k O D. 5In 4+ > (-1)k+1. 5 k. k (x - 4) k K = 1 Q5