- #1

- 800

- 8

## Homework Statement

Given that:

f(n) = n^(1.01) + n(log(n))^5

g(n) = n^(1.01)

Show that:

a) f(n) ∈ O(g(n))

b) f(n) ∈ Ω(g(n))

c) f(n) ∈ Θ(g(n))

## Homework Equations

Any method as long as it's correct. It doesn't have to be strictly by using the definition of the big O notation but it could be using limits or any other correct method.

## The Attempt at a Solution

I can see how b is true. Also, given that I know the answer to a is true because the "solution" my teacher gave states it, I can automatically conclude that c is true because if both a and b are true, then c must also be true.

I tried plugging in n = 1,000,000 and n(log(n))^5 grows larger than n^(1.01) which makes intuitive sense but seems to contradict a.

Any help in showing that a is in fact true would be greatly appreciated!

Thanks in advance!