Please explain the reasoning behind the answer, I'm having a hard time with this subject. Also, for part (a) can you also help me understand the difference between O, omega, theta, little o, and little omega?

(a) Find the best possible relationship using one of the notations: O, , , o, w, for the following pairs of functions: n. 7n1.5 - 3 and 0.5 1.1 an each answer. (b) Function f(n) = n' 5000n-60000 when n 50 and f(n) = nlog n+ 100n for n 50. Write f(n) in asymptotic notation in the simplest possible form