For each pair of functions determine if f(n) (g(n)) or f(n) (g(n)) or f(n) O(g(n)) and provide a proof as specified.

For each of the following, give a proof using limits.

1. f(n) =2^(2n), g(n) = 3^n

2. f(n) =2n + log (n), g(n) = log^2 (50n)

3. f(n)=n^3+45n^2,g(n)=n^3*logn

4. f(n) = 2^n, g(n) = 32n

5. f(n)=n^2,g(n)=n^(logn)