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Topic: Does this imply that lim x --> oo f'(x) = 0?
Replies: 18   Last Post: May 26, 2013 1:28 AM

 Messages: [ Previous | Next ]
 Bacle H Posts: 283 Registered: 4/8/12
Re: Does this imply that lim x --> oo f'(x) = 0?
Posted: May 26, 2013 1:25 AM

On Friday, May 24, 2013 8:28:07 PM UTC-7, Graham Cooper wrote:
> On May 25, 12:50 pm, William Elliot <ma...@panix.com> wrote:
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> > On Fri, 24 May 2013, baclesb...@gmail.com wrote:
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> > > On Friday, May 24, 2013 3:28:09 AM UTC-4, William Elliot wrote:
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> > > > > > Suppose f:[0, oo) --> R is increasing, differentiable and has a
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> > > > > > finite limit as x --> oo. Then, must we have lim x --> oo f'(x) =
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> > > > > > 0?  I guess not, but couldn't find a counter example.
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> > >  How about this: with the same lay out as before: f(n+1)-f(n)=f'(cn).
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> >
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> > Give it up, counter examples have been presented.

Maybe you should check your counterexamples more carefully.
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> I think this one works..
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> -1/(5+sin(x))/x/x
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> http://www.wolframalpha.com/input/?i=-1%2F%285%2Bsin%28x%29%29%2Fx%2Fx
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> Herc
>
> --
>
> www.BLoCKPROLOG.com

Date Subject Author
5/23/13 steinerartur@gmail.com
5/23/13 Robin Chapman
5/23/13 David C. Ullrich
5/23/13 Bart Goddard
5/23/13 steinerartur@gmail.com
5/23/13 William Elliot
5/24/13 steinerartur@gmail.com
5/24/13 Bacle H
5/24/13 William Elliot
5/24/13 Bacle H
5/24/13 William Elliot
5/24/13 Graham Cooper
5/24/13 Graham Cooper
5/25/13 steinerartur@gmail.com
5/25/13 Graham Cooper
5/26/13 Bacle H
5/26/13 Bacle H
5/24/13 William Elliot
5/24/13 Graham Cooper