Write a proof for the determined Big-O notation of the following:
SHOW EACH STEP CLEARLY
B) f(n) = sqrt(2n) + 30log(4n)^2 + 27n - 3
NOTE: I know it is O(n) notation. I just can not figure out the proof. Please add as much detail as possible I am trying to learn.
The Big-O Asymptotic Notation gives us the Upper Bound Idea, mathematically described below:
f(n) = O(g(n)) if there exists a positive integer n0 and a positive constant c, such that f(n) <= c.g(n) ∀ n >= n0
For c = 58 and n >= 2, we have
0 <= sqrt(2n) + 30log(4n)^2 + 27n - 3 <= n + 30n + 27n - 3 <= 58n
Hence, f(n) = O(n)
Write a proof for the determined Big-O notation of the following: SHOW EACH STEP CLEARLY B)...