Solved : Algorithm analysis

For each of the following pairs of functions f(n) and g(n), state whether f is bigoh(g); whether f is teta(g); and whether f is

omega(g). (More than one of there can be true for a single pair.) Justify your answers

a. f(n) = n^10; g(n) = 2^(n/2)

b. f(n) = n^(3/2); g(n) = nlg^2(n)

c. f(n) = lg(n^3); g(n) = lg(n)

d. f(n) = lg(3^n); g(n) = lg(2^n)

e. f(n) = 2^n; g(n) = 2^(n/2)

I think my approach to the problem is very time consuming where i will use L'hopital's rule to solve the problem. I am pretty scared that i will take too much time doing such a tedious process in exam. Does anyone

has a better way of doing the questions listed above other than using a graph software or calculator. Please enlighten me.

Thanks in advance.