Calculate big O notation I'm a bit unsure how to determine the big O notation of the following terms: 
$\sqrt n\ $ + $\log n\ $
Is the big O notation O($\sqrt n\ $) or O ($\sqrt n\ $ + $\log n\ $)? 
It's clear that $\sqrt n\ $ grows faster than $\log n\ $ but I'm uncertain, if it's enough to express that with O($\sqrt n\ $). 
Thanks in advance!

It's enough to say $\sqrt{n} + \log n = O(\sqrt{n})$. Notice that $\log n \le \sqrt{n}$ then $\sqrt{n} + \log n \le 2 \sqrt{n}$. More generally, if you have a sum $a_n + b_n$ and $\frac{a_n}{b_n} \to 0$ when $n \to \infty$ then $a_n + b_n = O(b_n)$. You can think of this as the largest asymptotic term wins.
