Let

Show that

and that

where , for some constant C.

I got everything except I don't know where to get the r(x) part at all...

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- Dec 10th 2009, 05:34 PMtediiIntergral
Let

Show that

and that

where , for some constant C.

I got everything except I don't know where to get the r(x) part at all... - Dec 11th 2009, 02:36 AMShanks
by letting , we have:

Thus

where y belongs to the interval (x, x+1).

From the above computation,I think, it should be bounded by a constant C, not Ce^{-x}. are you sure it is Ce^{-x}? I guess This boundry is too strong . - Dec 11th 2009, 12:31 PMtedii
It does say that in Rudin, if you have it chapter 6 problem 14. But what you did helped. I went about proving the the <2 part a bit incorrectly. Thank you for your help though.

- Dec 11th 2009, 09:21 PMShanks
I saw the probelm, maybe you are right, we need a tighter and better boundry.

- Dec 12th 2009, 02:36 AMShanks
by using integration by parts twice, you will get the result.