I already evaluated the limit, and got the answer, but I want to see if you guys can come up with an easier way to solve it (Sun):

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- May 9th 2008, 09:07 PMChris L T521An Interesting Limit...
I already evaluated the limit, and got the answer, but I want to see if you guys can come up with an easier way to solve it (Sun):

. - May 9th 2008, 10:43 PMmr fantastic
- May 9th 2008, 10:44 PMwingless

Now we know that converges because it's always greater than zero and the limit of is 1. So the limit is in indeterminate form . We can use L'hopital later.

Define .

Now it's .

Use L'hopital:

- May 9th 2008, 11:00 PMCaptainBlack
- May 9th 2008, 11:01 PMmr fantastic
- May 9th 2008, 11:07 PMCaptainBlack
- May 9th 2008, 11:12 PMmr fantastic
- May 11th 2008, 01:35 PMKrizalid
Let's make this more generally:

If - May 11th 2008, 02:29 PMThePerfectHacker
- May 11th 2008, 02:46 PMThePerfectHacker
Here is a solution without L'Hopital's rule.

Note that, for all .

Thus, .

This gives us, .

Dividing by gives, .

Since it follows by the Squeeze theorem that .