Use the formal definition to show that 5n2 100n 800 on3 A

Use the formal definition to show that

5n² - 100n + 800 = o(n³)

Any explanations appreciated!

Solution

Answer:

We have given , f(n) = 5n^2 + 100n + 800 , g(n) = n^3 , now f by small o notation we have :

f(n) < c1 * g(n)

5n^2 + 100n + 800 < c1 * n^3

Let c1 = 1000 , n = 1

5(1)^2 + 100(1) + 800 < 1000 * (1)^3

910 < 3000

There fore it is proved here that f(n) < c1 * g(n)

= > 5n^2 + 100n + 800 = o(n^3).