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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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William Elliot

Posts: 2,637
Registered: 1/8/12
Re: Does this imply that lim x --> oo f'(x) = 0?
Posted: May 24, 2013 10:50 PM
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On Fri, 24 May 2013, 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.

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