1. The problem statement, all variables and given/known data Prove that if y>=x>=0: a) [tex] y^2 arctan y - x^2 arctan x >= (y^2 - x^2) arctan x [/tex] b) [tex] \ | \ y^2 arctan y - x^2 arctan x \ | \ >= (y^2 - x^2) arctan x [/tex] c) use (b) to prove that x^2 arctan(x) isn't UC in R. 2. Relevant equations 3. The attempt at a solution a) We have to prove that [tex] y^2 ( arctan y - arctan x ) >= 0 [/tex] And since arctan(y) - arctan(x) >= 0 for all y>=x and y^2 > 0 this is true. b)Since [tex] y^2 arctan y - x^2 arctan x >= 0 [/tex] for all y>=x>=0 then this is obviously true from a. c)If we choose Epsilon (E) = 1/2 , Lambda (L) > 0 and y = x+L then (y^2 - x^2)arctan(x) = (2xL - L^2)arctanx and the limit of that at infinity is infinity. So we can find N>0 so that for every x>N (y^2 - x^2)arctan(x) = |y^2 arctan(y) - x^2 arctan(x)| > E Now my questions are: 1) a & b seemed too trivial -are those the right are answers? 2)Is (c) right? Thanks.