3-1 Asymptotic behavior of polynomials¶
Let
where ad > 0, be a degree-d polynomial in n, and let k be a constant. Use the deûnitions of the asymptotic notations to prove the following properties. a. If k d , then p.n/ D O.nk /. b. If k හ d , then p.n/ D �.nk /. c. If k D d , then p.n/ D ‚.nk /. d. If k > d , then p.n/ D o.nk /. e. If k < d , then p.n/ D !.nk /.