Question

i'm trying to determine if n^1/2 logn^1/2 is O(n). where do i start?

Answer 1

use basic Big O notation:
f(n) = O g(n)
if and only if
\[0\le f(n)\le c1 g(n) \]
where c1 is an arbitrary constant.

Answer 2

here,
\[f(n)=n ^{\frac{ 1 }{ 2 }}\log n ^{\frac{ 1 }{ 2 }}\]
and g(n)=O(n).
now find some constant c1 which fits the above equation
if it exists then you can say that f(n)=O g(n)
otherwise not.