. 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?
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?
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.