## #2525 limit( (sin(x)-x)/x³, x, 0) should be -1/6, returns 0

None
closed
nobody
5
2013-01-06
2012-12-28
Hache
No

Hello, I'm using maxima as a help to study and got what I believe is a wrong result.

limit( (sin(x)-x)/x³, x, 0);
=> 0

AFAIU, it should return -1/6:

lim x-> 0 (sinx - x)/x³
= lim x->0 (cosx - 1)/3x² (L'Hopital)
= lim x->0 (-sinx)/6x (L'Hopital)
= -1/6 (as lim x->0 sinx/x = 1)

I've checked it on WolframAlpha and it returns -1/6.

Thanks,
H

## Discussion

• Robert Dodier
2012-12-28

Maxima 5.29.1: limit((sin(x) - x)/x^3, x, 0) => -1/6 as expected.

What version of Maxima are you using?

• Robert Dodier
2012-12-29

• labels: --> Lisp Core - Limit
• status: open --> closed

• Robert Dodier
2012-12-29

Can't reproduce the reported behavior. I'm guessing it's a bug which is already fixed. Closing this report in the absence of further information from the original poster.

• Hache
2013-01-06

I'm sorry I didn't checked that I was using the newest version. I was using maxima 5.27.0-3 from Ubuntu. I've just upgraded to 5.29.1 and now it works as it should. Thanks!