find $f(n)$ that isn't little $o(n^2)$ and isn't $w(n)$

Question

im having a problem with a question that tells me to find $f(n)$ so that
$f(n) neq o(n^2)$ meaning also that $lim_{rightarrowinfty} frac{f(n)}{n^2} neq 0$
and $f(n) neq w(n)$ meaning also that $lim_{nrightarrowinfty} frac{f(n)}{n} neq infty$
I have tried solving each part and
the first equation tells me that if $f(n) = x^q$ then $2leq q$
and the second tells me that $qleq 1$.
is there even a solution to this problem?

quasi · Answer

A function which oscillates back and forth between $x$ and $x^2$ will work.

Explicitly, consider the function $f$ given by $f(x)=x,sin^2(x)+x^2,cos^2(x)$.

find $f(n)$ that isn't little $o(n^2)$ and isn't $w(n)$

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