To check which function is not bounded by O(n^2)
well
option 1,4 are exponent functions and can never be bounded by n^2 for large inputs
option 2 n^1.98 is bounded by n^2
option 3 n^3/sqrt(n) ==> n^2.5 is also not bounded by n^2
So option 1,3,4 are not bounded whereas option 2 is bounded.
Am I right?
Not quite. Options 1 and 4 are an+b, where a and b are constants. Remember, we drop lower-order terms and constant coefficients: O(an+b) = O(n), which is bounded by O(n^2).
You correctly identified option 2 as bounded by O(n^2) and option 3 as not bounded by O(n^2).
This leaves option 3 as the correct answer.
15^10 is a huge value for any test case.
O(n) is not very relevant.
For example for inputs like 10^5 we cannot write O(n^2) equivalent to O(n) saying O(n^2)=O(10^5 n) =O(n) since 10^5 is a constant.
It is all relative to n. One amongst these is the very relevant answer, but two of them are not wrong either.
