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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

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Graham Cooper

Posts: 4,348
Registered: 5/20/10
Re: Does this imply that lim x --> oo f'(x) = 0?
Posted: May 24, 2013 11:33 PM
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On May 25, 1:28 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On May 25, 12:50 pm, William Elliot <ma...@panix.com> wrote:
>

> > On Fri, 24 May 2013, baclesb...@gmail.com wrote:
> > > On Friday, May 24, 2013 3:28:09 AM UTC-4, William Elliot wrote:
> > > > > > Suppose f:[0, oo) --> R is increasing, differentiable and has a
> > > > > > finite limit as x --> oo. Then, must we have lim x --> oo f'(x) =
> > > > > > 0?  I guess not, but couldn't find a counter example.

> > >  How about this: with the same lay out as before: f(n+1)-f(n)=f'(cn).
>
> > Give it up, counter examples have been presented.
>
> I think this one works..
>
> -1/(5+sin(x))/x/x
>
> http://www.wolframalpha.com/input/?i=-1%2F%285%2Bsin%28x%29%29%2Fx%2Fx



Close, but no cigar?


Herc



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