I was wondering if $f(x)=O(x^{c+a})$ for all $a>0$ then is it necessarily true that $f(x)=O(x^c\log x)$? I suspect it's not true but want to know why. (I know the converse is true.)
Any help is much appreciated, Thank you.
I was wondering if $f(x)=O(x^{c+a})$ for all $a>0$ then is it necessarily true that $f(x)=O(x^c\log x)$? I suspect it's not true but want to know why. (I know the converse is true.)
Any help is much appreciated, Thank you.