Limit of a Step Function in Mathematica

[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]])

 

[HallsofIvy]

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.

 

[jackmell]

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]])

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.