1. If |f(x)|<=|g(x)| for all x in [0,inf), and the integral int(0-->inf)g(x)dx converges so the ntegral int(0-->inf)f(x)dx converges.

(I think its not true...)

2. If ntegral int(0-->inf)g(x)dx converges so integral int(0-->inf)g(x)*sin(x)dx converges.

(Maybe with using Dirichelet?)

3. If ntegral int(0-->inf)g(x)dx converges so integral int(0-->inf)g(x)*e^-x^2dx converges.

(Abel test?)

Thank you!!!