tlimato / asymptotics-tlimato

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The O, Omega, and Theta

Each row in the table below specifies two functions $f(n)$ and $g(n)$. Fill in the number from this list that best describes their relationship:

1. $f(n)\in O(g(n))$, but $f(n)\not \in \Omega(g(n))$
2. $f(n)\in \Omega(g(n))$, but $f(n)\not \in O(g(n))$
3. $f(n)\not\in O(g(n))$, and $f(n)\not \in \Omega(g(n))$
4. $f(n)\in \Theta (g(n))$

I have done the first one for you, as an example.

$f(n)=\ldots$	compared to	$g(n)=\ldots$
$f(n)=n$	1	$g(n)=2n^2 + n$
$f(n)= 10n + 3\log_{15} n$	4	$g(n)= 4n - 2\log_2 n$
$f(n) = 2n^5$	2	$g(n) = 5n^2$
$f(n)=\log_{10} \left(n^{10}\right)$	1	$g(n)=n$
$f(n)= 4n^5 $	2	$g(n)= 5n^4$
$f(n) = 10^{256}$	1	$g(n) = \log n$
$f(n)= n^2 $	1	$g(n)= 2^n$