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Calculus/limits at infinity


I don't understand why the limit of the function xsin(x)=infinity as x approaches infinity !?
I would really appreciate your help :)
Thank You in advance.

The limit is really undefined.

Lets start by saying that f(x) = x*sin(x).

The limit(x->infinity)[f(x)] is undefined.
Given any y0 value, no matter what x0 is chosen,
an x value can be found such that f(x0) = y0.

This is because sin(x) always varies between -1 and 1.
This means the limit always varies between -x and x.
As x goes to infinity, the function then varies between -infinity and infinity.'


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