Use the formal definition to show that Upload a file with yo

Use the formal definition to show that

Upload a file with your solution.

Solution

Answer :

Question is prove that 5n^4 + n^2 - 100 = omega (n^3)

Proof :

We know the capital omega definition ... f(n) = omega(g(n) if f(n) > = c xg(n) , where c is any constant and c > 0

Now , place the value in the definition, we get

f(n) = 5n^4 + n^2 - 100 , g(n) = n^3

=> 5n^4 + n^2 - 100 >= c x n^3

Now, let us put n = 5 and c = 1 in above , we get

5(5)^4 + (5)^2 - 100 > = 5^3

=> 625 + 25 - 100 > = 125

=> 650 - 100 > = 125

550 >= 125

Therefore f(n) > g(n), thus we proved that 5n^4 + n^2 - 100 = omega(n^3 ).