Hi guys,

please can someone here help me to prove that:

Assume that:

this implies that:

thanks in advance

Printable View

- Dec 17th 2006, 10:33 AMmiss_lolittaUrgent and important??! integral inequality
Hi guys,

please can someone here help me to prove that:

Assume that:

this implies that:

thanks in advance - Dec 17th 2006, 01:30 PMThePerfectHacker
- Dec 17th 2006, 01:57 PMmiss_lolitta
hi..ThePerfectHacker

right..c(x) is a decreasing function and continous:o

thanks:) so much - Dec 17th 2006, 03:05 PMThePerfectHacker
Then it is simple.

Otherwise the expression is undefined.

Now, if is decreasing function and continous then,

is decreasing.

And we are told that,

Converges.

That means, by the integral test,

Converges.

But that means that,

.

Thus,

We now that,

*)

This is a L'Hopital rule problem.

(But then we need to know that the function is differenciable).

*)I am not sure about this. Perhaps this statement works only the other way.