2. Asymptotic Notations

For each pair of the following functions f (n) and g(n), check if

1. f(n)=(g(n))?

2. f(n)=O(g(n))?

3. f(n)=(g(n))?

4. f(n)=o(g(n)) little o?

5. f(n)=(g(n)) little omega?

Functions f (n) and g(n) are:nn

1. f(n)=(128)(n/4) vs. g(n)=(512)(n/8)

2. f(n) =. n^64 2^n vs. g(n)= lg(n) 2^n + 4^n + n^32

3. f(n) = n^1024 vs. g(n) = 2 ^ (lg(n)lg(n))

You do not need to provide formal proofs. Describe your justifications in text form.

Image of the above is provided below for further clarity:

1. f(n) = (g(n)) ? 2. f(n) = O(g(n)) ? 3. f(n) = N(g(n)) ? 4. f(n) = 0(g(n)) little o? 5. f(n) = w(g(n)) little omega? Functions f(n) and g(n) are: 1. f(n) = (128)(*) vs. g(n) = (512)() 2. f(n) = n64 21 vs. g(n) = 1g(n) x 21 +41 + 132 3. f(n) = n1024 vs. g(n) = 2g(n)xlg(n)