Asymptotic behavior of polynomials LetLetwhere ad > 0, be a degree-d polynomial in n, a...

Asymptotic behavior of polynomials Let

Let

where ad > 0, be a degree-d polynomial in n, and let k be a constant. Use the definitions of the asymptotic notations to prove the following properties.

a.If k ≤ d, then p(n) = O(nk).

b. If k=d, then p(n)= Ω(nk).

c.If k>d, then p(n) = Θ(nk).

d.If k>d, then p(n) = o(nk).

e.If k<d, then p(n) = ω(nk).