. Show that:

I used integration by parts. I've come across a limit part, what's that value? . <-- Is that just zero, if so why?

Printable View

- Jan 10th 2009, 09:12 AMSimplicityReduction Formula
. Show that:

I used integration by parts. I've come across a limit part, what's that value? . <-- Is that just zero, if so why? - Jan 10th 2009, 09:32 AMJester
Yes, it's zero. As for a proof, consider

So handwaving - exponentials grow much facter than powers. If you look at a power series for the exponetial

so

and you can always go out far enough in the power series so that the powers in the denominator are larger than that in the numerator.

Do you know about L'Hopitals rule? - Jan 10th 2009, 09:56 AMSimplicity
L'Hopitals rule is valid when limits put into the numerator and denominator give zero. We keep differentiating till numberator and denominator have a different value.

But if we apply L'Hopitals rule then wouldn't we get a number other than zero unless numerator gives zero. However, isn't the numerator, Because greater the value, then greater it's power will increase it by. - Jan 10th 2009, 10:23 AMJester
- Jan 11th 2009, 01:17 AMMoo
Hello,

The first limit is easy since goes to 1 and since , goes to 0.

For the second one, you can ideed use l'Hospital's rule if you haven't learnt an other way, implying the comparison of increasing "speeds"..