- labels: --> Lisp Core - Limit
Maxima 5.5/Windows/gcl
limit(abs(log(x)),x,0)
Error: The tag LIMIT is undefined.
Should of course be INF.
More controversially, perhaps, limit(log(x),x,0) gives
UND -- I believe it should give INFINITY; after all, limit(log
(x),x,0,minus) gives INFINITY.
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The error no longer occurs in current CVS. It returns UND,
after asking if x is positive or negative.
Why should the answer be INF? log(x) is undefined for
negative real x.
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re limit(abs(log(x)),x,0)
If we're working over real x and the complex log function,
then if x>0, it should clearly be inf. If x<0, log(x) is not
real, but abs(log(x)) is, and sure enough
limit(abs(log(x)),x,0,minus) gives inf. This is I believe
correct. And it's all consistent with limit(abs(log(x)),x,0)
=> inf.
If on the other hand you take the position that limit
operates on real functions, then negative x are not part of
the domain of log(x), so we should look only at the limit
for x>0, which also gives us the result inf. But limit is
actually happy to return imaginary results, e.g.
limit(sqrt(x),x,-1) => %i.
By the way, currently, limit(log(x),x,0,minus) gives
minf+%i*%pi, which makes some sort of intuitive sense, but
isn't really a valid expression -- it should be infinity.
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As of limit.lisp rev 1.56:
(%i6) limit(log(x), x, 0, minus);
(%o6) minf+%i*%pi
(%i7) limit(log(x), x, 0, plus);
(%o7) minf
(%i8) limit(abs(log(x)), x, 0, minus);
(%o8) inf
(%i9) limit(abs(log(x)), x, 0, plus);
(%o9) inf
(%i10) limit(abs(log(x)), x, 0);
(%o10) inf
(%i11) limit(1/x, x, 0, minus);
(%o11) minf
(%i12) limit(1/x, x, 0, plus);
(%o12) inf
(%i13) limit(1/x, x, 0);
(%o13) infinity
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