Problem

Relative asymptotic growthsIndicate, for each pair of expressions (A, B) in the table belo...

Relative asymptotic growths

Indicate, for each pair of expressions (A, B) in the table below, whether A is O, o, Ω, ω, or Θ of B. Assume that k 1, ∈ > 0, and c > 1 are constants. Your answer should be in the form of the table with “yes” or “no” written in each box.

 

A

B

O

o

Ω

ω

Θ

a.

lgk n

n

 

 

 

 

 

b.

nk

cn

 

 

 

 

 

c.

nsin n

 

 

 

 

 

d.

2n

2n/2

 

 

 

 

 

e.

nlgc

clgn

 

 

 

 

 

f.

lg(n!)

lg(nn)

 

 

 

 

 

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Solutions For Problems in Chapter 3.P