Hello everyone I don't really understand the question.
I approached the given problem by carefully examining the provided sequence of inequalities, aiming to understand the growth rates of various functions. Breaking down the given function (f(n) = 9n^n + 8n! + \sqrt{5n} + n \log_4(n)), I compared each term against the established inequalities. I successfully identified the dominant terms as (n^n) and (n!), and through subsequent analysis, determined that (n^n) dominates over (n!). Utilizing the given inequalities, particularly (n^n > n!), I concluded that the closest upper boundary for (f(n)) is (O(9n^n)). While I feel confident in this assessment, there might be additional nuances or insights to consider, and I would appreciate any feedback or further discussion on the approach I've taken.
1 < log2(n) < √n < n <nlog2(n) < n2 < n3 < … < 2n < n! < nn
Use the inequalities above to find the closest upper boundary function for
f(n)=9nn + 8n! + sqrt(5n) + nlog4(n)
the answers as follows
nn
1
n2
n4
n3
log4(n)
n!
n log4(n)
n
2n
√n
n5