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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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