4. (15 points) In this problem we will use the integral test to investigate the 10 2 arctann nature of the series Lin=1 1+n (a) Consider the function f(x) = 2arctan defined for all x > 1. It can be shown that f' (x) = 2(1-2x arctan x) (1 + 20 2 ) 2 which is negative for all x 2 1. What does this imply about f(x)? Also, what is lime-> f(x)? Are the conditions of the integral test satisfied in this situation? Briefly explain. (Recall that lime- arctan x = 1 /2.) (b) Compute the indefinite integral S f(x) dx and then the improper integral i f(x) dx. Recall that arctan 1 = T/4. What does the integral test tell us about the series , 2arctann? Briefly explain