If domain(log) = (0,inf), then limit(log(x),x,0) = -inf is
correct. This is agrees with the limit definition in T. Apostal, for
example. And it agrees, I think with
http://functions.wolfram.com/ElementaryFunctions/Log/03/02/
Now if domain(log) = complex - {0}, the correct value is complex
infinity (infinity in Maxima); see the section "Complex
analysis" in http://en.wikipedia.org/wiki/Infinity
Of course, largely the problem is that limits are defined for
functions, not their formulae. We have limit(n in Z |--> sin(n),
infinity) = 0, but limit(n in R |--> sin(n), infinity) is undefined
(here Z = set of integers and R = set of reals).
Barton
maxima-bounces at math.utexas.edu wrote on 01/26/2010 12:49:28 PM:
> [image removed]
>
> [Maxima] limit(log(x),x,0)?
>
> Raymond Toy
>
> to:
>
> Maxima List
>
> 01/26/2010 12:49 PM
>
> Sent by:
>
> maxima-bounces at math.utexas.edu
>
> What is limit(log(x),x,0)? Maxima currently returns infinity. I
> suppose that's correct, but with a default domain of real, shouldn't
> this be undefined?
>
> Ray
>
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