show limit of e^(1/n) / n = 0

**buckeye1973** · February 3rd 2010, 03:49 PM

Hi all again,

I know that this limit = 0, but I'm blanking on how to show it..

$\lim_{n\to\infty} \frac{e^{1/n}}{n} = 0$

I'm trying to manipulate it into an acceptable form for l'Hospital, but it isn't coming to me. Thanks for any help!

Brian

**Calculus26** · February 3rd 2010, 03:56 PM

don't need L'Hopital as directly you get e^(0)/inf = 1/inf = 0

**buckeye1973** · February 3rd 2010, 05:19 PM

Originally Posted by Calculus26

don't need L'Hopital as directly you get e^(0)/inf = 1/inf = 0

Oh! Of course...duh..

heh, thanks.

**Drexel28** · February 3rd 2010, 05:31 PM

Originally Posted by buckeye1973

Hi all again,

I know that this limit = 0, but I'm blanking on how to show it..

$\lim_{n\to\infty} \frac{e^{1/n}}{n} = 0$

I'm trying to manipulate it into an acceptable form for l'Hospital, but it isn't coming to me. Thanks for any help!

Brian

Originally Posted by Calculus26

don't need L'Hopital as directly you get e^(0)/inf = 1/inf = 0

A little more rigorously note that $\left|\frac{e^{\frac{1}{n}}}{n}\right|\leqslant\fr ac{1}{n}$

**TWiX** · February 3rd 2010, 05:45 PM

Originally Posted by Drexel28

A little more rigorously note that $\left|\frac{e^{\frac{1}{n}}}{n}\right|\leqslant\fr ac{1}{n}$

So we will apply the sandwich theorem, right ?

**Drexel28** · February 3rd 2010, 05:47 PM

Originally Posted by TWiX

So we will apply the sandwich theorem, right ?

True dat.

Thread: show limit of e^(1/n) / n = 0

LinkBack

Thread Tools

Display

show limit of e^(1/n) / n = 0

Similar Math Help Forum Discussions

show that limit exist

Is there a way to show my work for this limit?

show the limit is b

How to show there's no limit at a jump

show limit approaches 0

Search Tags