STACK/MAXIMA limit of a function

STACK/MAXIMA limit of a function

by Hendrikje Schmidtpott -
Number of replies: 4

I've got a small problem with the lim function, in one of our questions Students were asked to find the limit of a function with l'hospital. Now in some of the caseses the limit is infinity. And now STACK/MAXIMA claims the limit is either inf or infinity depending on whether a trig function is involved or not.

I copied some of the cases from the questiontests to wxMaxima, so it seems to be a maxima thing. We already have a workaround in our feedbackvariables, so that the input of the students is correct either way, but maybe there is some sort of option, that would fix this in a more elegant way?

Attachment inf infinity.PNG
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In reply to Hendrikje Schmidtpott

Re: STACK/MAXIMA limit of a function

by Christopher Sangwin -
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Could you please separate out if this is the result of Maxima's design decision or something we've done in STACK? E.g. try using WxMaxima on the desktop to evaluate these limits. The Maxima community are very responsive and helpful in explaining their design decisions (and the limitations). I don't recall us modifying the limit function as part of STACK, although we have needed to provide more options to teachers in other areas.

Chris
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In reply to Christopher Sangwin

Re: STACK/MAXIMA limit of a function

by Hendrikje Schmidtpott -

Seems to be Maxima, I copied the variables from Questiontests and they also yield to inf or infinity and both are not equal according to wxMaxima.

Attachment inf infinity2.PNG
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In reply to Hendrikje Schmidtpott

Re: STACK/MAXIMA limit of a function

by Hendrikje Schmidtpott -
Just a short update, my version of wxMaxima is 20.06.6. I asked a collegue to run my exaples using a 22 version, there this problem is resolved.
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In reply to Hendrikje Schmidtpott

Re: STACK/MAXIMA limit of a function

by Andreas Steiger -
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In case this is still open, or someone finds this later on and needs an answer:

The difference is described in the maxima manual on `limit`: https://maxima.sourceforge.io/docs/manual/maxima_93.html

"infinity (complex infinity) is returned when the limit of the absolute value of the expression is positive infinity, but the limit of the expression itself is not positive infinity or negative infinity. This includes cases where the limit of the complex argument is a constant, as in limit(log(x), x, minf), cases where the complex argument oscillates, as in limit((-2)^x, x, inf), and cases where the complex argument is different for either side of a two-sided limit, as in limit(1/x, x, 0) and limit(log(x), x, 0)."

The cosine limit is different for the two sides, whereas the cubic limit is not.
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