Is this homework? If so, what have you done so far?
yes, and i realize that we want the integral to converge when we take the inverse transform. so in order to do that, i'm guessing the denominator has to have a power > 1, which is why we have that condition on a. so it will fail the second time, i guess. but i can't formalize my argument (and i'm clueless about the third one).