Taylor series centered at a ? 0a. Find the first four nonzero terms of the Taylor series for the given function centered at a.b. Write the power series using summation notation.f(x) = In x, a= 3

Solution 21EStep 1:a) In this problem we need to find first four nonzero terms of the taylor series for the function f(x) = ln(x) , centered at a = 3 .We know that , the taylor series of the function centered at ‘a’ is : f(x) = f(a) + (x-a)++Given ; f(x) = ln(x), centered at a = 3. f(x) = , then f(3) = ln(3) , then , since (ln(x)) = , then , since = , then = , then ………………Therefore , the taylor series of the function f(x) = ln(x), centered at a = 3is ; f(x) = ln(x) = f(3) +(x-3)++ = ln(3)+ (x-3)++ = ln(3) +(x-3)-+Therefore , the first four nonzero terms of the taylor series centered at ‘3’ for the function ’ are ln(3) +(x-3) -+That is , ln(3) ,(x-3) , -,First term = ln(3)Second term = (x-3)Third term = -Fourth term =