174 questions linked to/from Sorting functions by asymptotic growth
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### asymptotic growth of n^log log n [duplicate]

I'm ordering functions by their asymptotic growth for an assignment and I have verified I have the correct order by using limits, but I'm trying to understand why $n^{log\ log\ n}$ is between $n^3$ ...
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### Big O Asymptotic complexity [duplicate]

I am trying to rank $\log n$, $\log_{10} n$, $n \log n$, $n \log n^2$, $n^{0.8}$, $\sqrt{n}$ in increasing asymptotic complexity. $\log n$ has base 2 unless specified otherwise. The answer I ...
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### Extra space of MergeSort [duplicate]

Here is my implementation of mergeSort. I need n extra space for the helper array. But what about recursive calls? I call sort ...
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### Which one grows faster asymptotically: $\log(\log^an)$ or $\log^a(\log n)$ [duplicate]

Could someone explain to me which function grows faster? $f(n)=\log(\log^an)$ or $g(n)=\log^a(\log n)$
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### Show that 6n^2 + 12n is O(n^2) [duplicate]

I understand how I would do this if the problem were as such $8n + 5$ is $O(n)$ $c>0$ and an integer constant $n(not 0) \geq 1$ such that $8n + 5 \leq cn$ for every integer $n \geq n(not 0)$ we ...
How would I tackle this equation? $$10n^3 +3n = \Theta(n^3)$$ I know I have to solve Big $O$ and Big $\Omega$ but have no idea how to do this. I got as far as $$10n^3+3n \leq c_1n^3$$ 0 \leq ...