Re: limit of a limit

In article <1134589103.378861.41010@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<gaya.patel@xxxxxxxxx> wrote:

>How about the following (is it true?):
>
>lim f ' (x) = f ' (a)
>x->a

It is true that if f is continuous at a and lim_{x -> a} f'(x) exists
then it is f'(a).
This follows easily from the Mean Value Theorem.

On the other hand, as George Ivey noted in his reply, if you
just assume that f is differentiable on an interval containing a
the limit might not exist.

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada

.