Hey everyone,

Got this problem from a math packet. No idea how to evaluate this limit. I assume L'hopital's rule is involved.

Attachment 28945

No matter how hard I try, I am unable to manipulate this limit in such a way as to evaluate it.

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- Aug 6th 2013, 02:07 PMShadowKnight8702Evaluate a limit
Hey everyone,

Got this problem from a math packet. No idea how to evaluate this limit. I assume L'hopital's rule is involved.

Attachment 28945

No matter how hard I try, I am unable to manipulate this limit in such a way as to evaluate it. - Aug 6th 2013, 02:11 PMMarkFLRe: Evaluate a limit
Have you tried taking the natural log, so that you get the form 0/0?

- Aug 6th 2013, 04:13 PMHallsofIvyRe: Evaluate a limit
First obvious step is to factor out . I would then factor out so this becomes .

Now, do you know the limit definition of "e"? - Aug 6th 2013, 04:18 PMMarkFLRe: Evaluate a limit
- Aug 6th 2013, 06:41 PMPlatoRe: Evaluate a limit
That is correct. It cannot be factored in that way.

[URL="[QUOTE=HallsofIvy;794322]First obvious step is to factor out . I would then factor out so this becomes . Now, do you know the limit definition of "e"?[/QUOTE]"

Look at this link.

http://www.wolframalpha.com/input/?i...9%2F%28x%29%29 - Aug 21st 2013, 07:28 AMx3bnmRe: Evaluate a limit
- Aug 21st 2013, 07:49 AMPlatoRe: Evaluate a limit
- Aug 21st 2013, 11:03 AMBobPRe: Evaluate a limit
This is a bit rough and ready, but I think that the result is okay.

Suppose that then

as

(since and the resulting

Notice btw that if then

(or ). - Aug 21st 2013, 02:17 PMPlatoRe: Evaluate a limit
Please look at this page.

NOTE you have

On the wolfram page l'Hospitial's rule gives - Aug 21st 2013, 03:27 PMx3bnmRe: Evaluate a limit
- Aug 21st 2013, 03:35 PMShadowKnight8702Re: Evaluate a limit
thanks x3bnm. The final step actually tursn the answer to sqrt(a)*sqrt(b) rather than ab-e^2, the process helped a lot.

- Aug 21st 2013, 03:43 PMPlatoRe: Evaluate a limit
- Aug 22nd 2013, 01:11 AMBobPRe: Evaluate a limit
Hi Plato

Regarding your comment to my post #8, your post #9, somewhat sheepishly I have to admit that, (have just noticed that), I was calculating the wrong limit, rather than

Apologies to all.