Just for the record. At work I have Maxima 5.28 available and this is
what I observe.
Example 1)
(%i2) limit((exp(x+h)-exp(x))/h,h,0);
Is x an ?integer?
n;
(%o2) %e^x
Example 2)
(%i3) limit((log(y+h)-log(y))/h,h,0);
(%o3) infinity
(%i4) assume(y>0);
(%o4) [y > 0]
(%i5) limit((log(y+h)-log(y))/h,h,0);
(%o5) 1/y
Example 3)
(%i6) limit((exp(q*x)-exp(x))/(q*x-x),q,1);
Is x an ?integer?
n;
(%o6) %e^x
Volker van Nek
2013/3/1 Reinhard Oldenburg <roldenburg at gmx.de>:
> Dear Maxima list members,
>
> the limit command (maxima 5.29, but this does not depend much on the
> version) shows strange behaviour in several cases.
> We discovered them when we asked students to calculate derivatives using the
> limit command.
>
> Example 1)
> limit((exp(x+h)-exp(x))/h,h,0);
> Asks if x is an integer, but the (correct) result %e^x does not depend on
> the answer given.
> This problem would not appear if L'Hopitals rules was used.
> The very same behavious shows limit((exp(q*x)-exp(x))/(q*x-x),q,1);
>
> Example 2)
> limit((log(y+h)-log(y))/h,h,0);
> This gives infinity. However, after saying assume(x>0), or alternatively
> assume(x<0) or even assume(equal(x,0)) the result 1/x is produced.
>
> Example 3)
> limit((exp(q*x)-exp(x))/(q*x-x),q,1);
> This gives division by zero
>
> Any ideas?
>
> Reinhard Oldenburg
>
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