Find a power series representation for the function. (Give your power series representation centered at x = 0.) f ( x ) = - X 7x- + 1 f ( x ) = n = 0 Determine the interval of convergence. (Enter your answer using interval notation.)(a) Use differentiation to find a power series representation for f ( x ) = - 1 (2+ x) 2 . A(x ) = n = 0 What is the radius of convergence, R? R = (b) Use part (a) to find a power series for 1 f ( x ) = = (2 + x)s f( x ) = > n = 0 What is the radius of convergence, R? R = (c) Use part (b) to find a power series for f ( x) = - x2 (2+ x)3 F(x ) = E n = 2 What is the radius of convergence, R? R =This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Find a power series representation for the function. Determine the radius of convergence, R. (Give your power series representation centered at x = 0.) f(x) = In(10 - x) Step 1 We must first recognize that f(x) = In(10 - x) is an anti-derivative of a more familiar function. To find this function, we find - In(10 - x) = Submit Skip_(you cannot come back)Find a power series representation for the function. f(x) = x2 tan -1 (X F(x ) - E n=0 Determine the radius of convergence, R. R =