Can someone please explain how I would approach this question, other thanplugging in numbers and trying to figure it out from there?
Is the last one the biggest ?
thank you.
You need a lot of experience with these functions.
For example, the first is an increasing sequence bounded above by $\displaystyle e^2$ its limit.
You need to know that for $\displaystyle F>1$ then $\displaystyle \log(F)< F$.
So $\displaystyle \log(n^{2^{-1}}\log(n))< n^{2^{-1}}\log(n)$
Here is a hint on the last one: $\displaystyle \frac{n!}{n^n}\le 1~.$ WHY?