On both, look at the long term behaviour of each. For the first
and the second .
So we need inequalities that are integrable. For the first
isn't true since
isn't true because isn't true, so we need little more to have something true for all . Try
so
so or . We see that if then which is true.
Same for the second problem.
isn't true so we try
and find an a where this is true.