1. (10 points) Let f be defined on an open interval (a, b). Consider the two statements (a) lim If(x th) - f(x)| = 0 (b) lim |f(x +h) - f(x - h)| =0 h-0 h-0 Prove that (a) always implies (b), and given an example in which (b) holds but (a) does not