I won't give the right answers here. If you want to know the right answers, come to see me.
9.1.02. Surprisingly, a lot of you had problem with this one. You goal is to find a C and an X, such that for all x>X, x^n < Ce^x. The simplest way to go is to use the fact that lim {x^n/e^x} = 0 when x goes infinity. Yes, you can use the fact (or you can use L'Hospital's rule). But you have to find the C and X given the limit.
9.1.04. The simple way is to say the left hand side is less than n*n^2. You can use the identity that \sum_i {i^2}=..., too.
9.2.*. I don't ask for exact numbers, but you should get to the vicinity.
10.2.*. You need some facility to deal with large integers. There is a Perl module can do that. So to compute 58^32, you can say something like the following: