√ 3n2 + 5 ∈ Θ(n lg n) Formally prove or disprove the claim using limits

Question

Question

√ 3n2 + 5 ∈ Θ(n lg n)

Formally prove or disprove the claim using limits

engineering Computer-Science

Answer 1

Answer #1

`Hey,

Note: Brother if you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

Let f(n)=sqrt(3*n^2+5) and g(n)=n*log(n)

So,

for f=theta(g) we need to prove that f/g=c for n tending inf

So,

f/g=sqrt(3*n^2+5)/(n*log(n))=sqrt(3+5/n^2)/log(n)

So, for n tending inf

f/g=0

So, the statement is false hence f is not theta of g

Kindly revert for any queries

Thanks.

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Answer 2

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