Question

3N4 - 7N2lgN = Ω(N2lgN) True or False. Justify your answer using limits.

Answer 1

Lets take
f(n) = 3N4 - 7N2lgN

Definition of Big-Omega:
-----------------------
f(n) = Ω (g(n)) means there are positive constants c and k,
such that 0 ≤ cg(n) ≤ f(n) for all n ≥ k.
The values of c and k must be fixed for the function f and must not depend on n.


f(n) >= N^2LhN
Where c = 1 and N0>0 then g(n) = N^2LhN

So, From the definition of Big-Omega
we can say that
f(n) = Ω (g(n))

3N4 - 7N2lgN = Ω(N2lgN) 

True