limit(log(x),x,0)?



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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