#204 Prove that (each one 0.25pt.)

Prove that (each one 0.25pt.) - Computer Science

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Free Chegg Question

Prove that (each one 0.25pt.)

a) 3n2+2n+4 is: O(n?)

b) (n3+ n2) is: O(n)

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Free Chegg Answer

Big-Oh definition:
f(n) = O(g(n)) means there are positive constants c and k, such that 0 ≤ f(n) ≤ cg(n) for all n ≥ k.
 
a)
Given f(n) = 3n^2 + 2n + 4
0 <= f(n) <= 9n^2
Where c=9, n>0 and g(n)=n^2
So, from the definition of Big-Oh we can say that
f(n) = O(g(n)
3n^2 + 2n + 4 = O(n^2)


b)
Given f(n) = n^3 + n^2
0 <= f(n) <= 2n^3
Where c=2, n>0 and g(n)=n^3
So, from the definition of Big-Oh we can say that
f(n) = O(g(n)
n^3 + n^2 = O(n^3)