0
$\begingroup$

The question is: A simple example of a function that is $o(n)$ is $\ln(n)$. Give another example of a non-negative, non-constant function that is $o(n)$.

I thought about using $f(n) = 10n - n\ln(n)$ but I am not sure if it's a good enough answer since, for extremely large values of n, $lim_{nā†’āˆž}\frac{f(n)}{g(n)} < 0$

Any suggestions?

  • 0
    what about $\sqrt{n}$ ā€“ 2017-02-03
  • 1
    $f(n)$ is negative for $n > e^{10}$, so it doesn't meet one of the requirements. ā€“ 2017-02-03

1 Answers 1

1

You could use any $|n|^z$ where $z<0$. Or you could use $e^{-\sqrt{n}}$; there are many functions that could work.