Il 30/10/2010 08:23, Mike Hansen ha scritto:
Thank for your answer. I didn't knew about dir="plus" option in the limit !
(sorry for my late answer)
Laurent
On Fri, Oct 29, 2010 at 11:06 PM, Laurent<[email protected]> wrote:
sage: f(x)=sqrt(x)/( sqrt(4-x)-sqrt(4+x) )
sage: f.limit(x=0)
Infinity
sage: limit(f,x=0)
Infinity
sage: f(0.0001)
-199.999999983591
A computation by hand shows that the limit is actually -Infinity. Why does
Sage say Infinity ?
"Infinity" in Sage represents the unsigned "complex" infinity, while
"+Infinity" and "-Infinity" represent the real signed infinities. The
limit is -Infinity only as you approach 0 from the positive side of
the real axis:
sage: limit(f, x=0, dir='plus')
-Infinity
As, you approach from the negative side of the real axis, you get
complex infinity
sage: f(-0.0001)
1.22464679904688e-14 + 199.999999983591*I
sage: limit(f, x=0, dir='minus')
Infinity
Therefore, Sage (Maxima) says that the limit is complex infinity.
--Mike
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