Let f be a continuous, positive function defined on [1, co) such that lim f(x) exists (i.e. the x-+00 limit is finite). .OO (a) Give an example of such a function f such that (f (x)) dax converges but f(x) dx diverges. .OO (b) Prove that if f(x) dx converges, then (f (x))'dx converges. 1