# [Maxima] limit(1/x, x, 0) => infinity

Mon Dec 22 09:40:10 CST 2008

```Robert Dodier wrote:
> On 12/22/08, Dan Gildea <dgildea at users.sourceforge.net> wrote:

Hi,

>> That was Stravros's reasoning in the bug report.  Maxima still
>>  has some problems distinguishing und from infinity - for example,
>>  limit(log(x), x, 0) and limit(exp(x*%i)*x,x,inf) currently return
>>  und but technically should return infinity.
>
> OK, good. Let's let it stand.
>
> Robert
>

Well, according to the documentation:

Maxima 5.17.1 http://maxima.sourceforge.net
Using Lisp CLISP 2.46 (2008-07-02)
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) ? und

-- Constant: und
`und' represents an undefined result.

Example:

(%i1) limit (1/x, x, 0);
(%o1)                          und

There are also some inexact matches for `und'.
Try `?? und' to see them.

(%o1)                                true
(%i2) ? infinity

-- Constant: infinity
`infinity' represents complex infinity.

There are also some inexact matches for `infinity'.
Try `?? infinity' to see them.

(%o2)                                true

So

(a) the documentation for "und" needs to be updated one way or the other

(b) it makes me mathematically very uncomfortable that the limit of
1/x at 0 is infinity since the limit IMHO clearly does not exist. While
the definition of "infinity" is different internally in Maxima
(according to Robert) a calculus student would consider the result
incorrect IMHO.

By the way: The following is reproducible on clisp 2.46+Maxima 5.17.1
while it worked on 2.46 + Maxima 5.16.3:

[mabshoff at eno sage-3.2.2-eno]\$ maxima
Maxima 5.17.1 http://maxima.sourceforge.net
Using Lisp CLISP 2.46 (2008-07-02)
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) limit(x,x,infinity);

*** - Lisp stack overflow. RESET

[eval.d:573] reset() found no driver frame (sp=0x4b91a5e0-0x4b917cb0)
Exiting on signal 6
Aborted

Not sure why this happens, but if I would have to guess I would blame
clisp :)

Cheers,

Michael
```