The limit n->infinity I have to compute is:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\frac{n\cdot \log ^{5}(n)}{n^{2}}[/itex]

Should I use L'hopital's rule? If I do, I have a problem:

First I simplify and get:

[itex]\frac{ \log ^{5}(n)}{n}[/itex]

Taking the derivative of the top, and the bottom leads to:

[itex]\frac{\frac{ 5\log ^{4}(n)}{n}}{1}[/itex]

At this point, we can see that the numerator is approaching 0, as n increases.

There 0/1 = 0

Is this correct?

Thanks

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# Homework Help: Limit problem / l'hopital's rule

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