Problem 3: Give asymptotic estimates, using the -notation, for the following functions:

(a) 3n^3 + 5n^2 2n + 4

(b) 3n^2 log n + 2n + n^3

(c) 3n + n^2/log n + n log^3 n

(d) 7 n^4 + n^3 log^2 n + 3^n

(e) log^9 n + n^3*4^n + 5^n

Justify your answer. For part (a), use the definition of the -notation. For parts (b) - (e), use asymptotic relations between the basic reference functions: nb, log n, and cn. 2