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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: 2,383
Registered: 1/8/12
Re: Does this imply that lim x --> oo f'(x) = 0?
Posted: May 23, 2013 11:10 PM
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On Thu, 23 May 2013, steinerartur@gmail.com wrote:

> Suppose f:[0, oo) --> R is increasing, differentiable and has a finit
> limit as x --> oo. Then, must we have lim x --> oo f'(x) = 0?

Most likely. What would happen if lim(x->oo) f'(x) /= 0?
What would happen if the limit was infinite or didn't exist.

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