I have a problem about question #4. I know that statement is true and I used limit techniques. I know that according to limit tech. if lim x-gt;...

4) Prove or disprove: 2n is in O(3n)

The claim is true. I need to prove:

∃c ∈ R+, ∃B ∈ N, ∀n ∈ N, n ≥ B ⇒ 2n ≤ c 3n

Pick c = and c ∈ R+
Pick B = 1 and B ∈ N
Assume n ∈ N and n ≥ B.
Then # if x < 1.
Then 2n ∈ O(3n). # according to limit techniques if
Then 2n ≤ c 3n = ≤ c #n ≥ 1 and c =
Conclude, ∀n ∈ N, n ≥ B ⇒ 2n ≤ c 3n
Then ∃c ∈ R+, ∃B ∈ N, ∀n ∈ N, n ≥ B ⇒ 2n ≤ c 3n
So, 2n is in O(3n).