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I want to find out how to check, if the following relationships are true or false.

f(n) = nlog(n!); g(n) = nlog(2n^3n); Check, if f(n) = O(g(n)) and/or f(n) = Ω(g(n)) true/false;

f(n) = 3n^2; g(n) = 9^(base3-logn); Check, if f(n) = O(g(n)) and/or f(n) = Ω(g(n)) true/false;

I am very new to this topic, so i would be very grateful, if someone could explain it to me. If something is not understandable, don't hesitate and ask me.

Thank you in advance.

roeas
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1 Answers1

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In second example if you have $f(n)=3n^2$ and $g(n)=n^2$, then, of course $f(n)=\Theta(g(n))$.

For first enough to note, that $n! < (2n)^{3n}$.

zkutch
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