how to bound this function above

how to bound above the following sequence

$\displaystyle f_{n}(x)=\Bigl(1-\frac{x}{n}\Bigr)^{n}\ln(x)$

since $\displaystyle \displaystyle\lim_{n\to\infty}\Bigl(1-\frac{x}{n}\Bigr)^{n}=e^{-x}$ we should probably bound above by the exponential function.

Someone knows how to do that?

Re: how to bound this function above

Hey rayman.

If you need to bound above by a function, you have want to consider that a*log(x) = log(x^a). With regards to the bounding case, you will want to know if the function approaches the asymptotic limit from below or above. If it approaches from below then you can use your limit, but if it approaches from above, then you will need to modify your boundary case.