# [Maxima] Learning that limit is 0 from above

Paul Smith phhs80 at gmail.com
Thu Nov 1 19:52:03 CDT 2007

```On 11/1/07, Jaime Villate <villate at fe.up.pt> wrote:
> > I do not know which one of the following sentences is wrong:
> >
> > 1. Maxima is wrong;
> >
> > 2. The Taylor series method does not apply here;
> >
> > 3. Maple is wrong
>
> It seems to me that the limit is 0+ and not 0- as the Maxima result
> wrongly suggests:
>
> (%i11) k: 0.75\$
> (%i12) a:1\$
> (%i13) assume(b>1)\$
> (%i14) e : (1/(b-a))*integrate((1-k)*((2*t-a)/k)^(k/(k-1)),t,a,b)\$
> (%i15) plot2d(e,[b,2,100]);

Thanks, Jaime. Maxima is able to calculate the limits for your example:

(%i53) k: 0.75\$
(%i54) a:1\$
(%i55) assume(b>1)\$
(%i56) e : (1/(b-a))*integrate((1-k)*((2*t-a)/k)^(k/(k-1)),t,a,b)-(1-k)*((b+a)/(2*k))^(k/(k-1))\$
(%i57) limit(e,b,inf);
(%o57)                                 0
(%i58) limit(1/e,b,inf);
(%o58)                                inf

This results is the opposite of the result obtained by Barton.

Paul
```