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- Jun 2nd 2010, 03:26 AMbigliCaculation a limit ?
How do I show ?

- Jun 2nd 2010, 03:48 AMtonio
- Jun 2nd 2010, 04:00 AMbigli
It doesn't work.Is there any easier way?

- Jun 2nd 2010, 08:55 AMtonio
- Jun 2nd 2010, 12:41 PMRandom Variable
According to Maple, the series expansion of about is (EDIT: You can derive it by starting with the Taylor series for centered at and using long division.)

Since we're integrating over values close to 1, is approximately .

so

- Jun 2nd 2010, 02:23 PMtonio
- Jun 2nd 2010, 02:32 PMRandom Variable
As approaches from the right, is much greater than . You can include it if you want. You'll still get the same answer.

- Jun 4th 2010, 10:57 PMDrexel28
It is fairly easy to verify that for we have that and so . It follows that . Note though that the LHS is just and . The conclusion follows from the Squeeze Theorem.

- Jun 5th 2010, 08:07 PMbigli
Thanks DREXEL28. Every thing is OK!. But only, your inequalities should be strictly and they are correct for .