For the following pairs of functions, first decide whether f(n) dominates g(n), or g(n) dominates f(n); then decide whether f = O(g), or f = Ω(g), or f = Θ(g), and briefly explains. i....

For the following pairs of functions, first decide whether f(n) dominates g(n), or g(n) dominates f(n); then decide whether f = O(g), or f = Ω(g), or f = Θ(g), and briefly explains.

i. f(n)=n2,g(n)=1000n+30

√1 ii. f(n) = n, g(n) = n3

iii. f(n) = 10 log2 n, g(n) = log10(n3)

iv. f(n)=n

100 n ,g(n)=1.2 .

4

nn

v. f(n)=2 ,g(n)=2.01 .