# Limit Error - Mathematica

1. Aug 30, 2011

### you878

I was using Mathematica to find the limit of the equation:
(x^3*Floor[x - 3])/(x - 3)
As x approaches 3.

Mathematica gave the answer as 0, but when I checked by hand, I did not get that.

As the function approaches 3 from the left side, it goes to positive infinity. As the function approaches 3 from the right side, it goes to 0. Since the two one-sided limits do not equal each other, shouldn't the limit at 3 not exist?

(The Floor[x-3] function I used was to represent the Step-function [[x-3]])

2. Aug 30, 2011

### HallsofIvy

Staff Emeritus
Yes, for x close to but less than 3, "floor[x- 3]" is -1 so the limit, as x goes to 3, is the same as [itex]\lim_{x\to 3}x^3/(x- 3)[/tex] which does not exit. The limit itself does not exist.

I don't use Mathematica so I can't speak for how it tried to find that limit.

3. Aug 30, 2011

### jackmell

Tell you what, place your cursor over the Limit word (in Mathematica) and hit F1 to get help on the matter. Read that help carefully, then answer your own question.

Last edited: Aug 30, 2011