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## Main Question or Discussion Point

I came across something I'd never seen before, the use of |x| instead of just ‘x’ in limits.

What is the difference between [itex]\displaystyle\lim_{|x|\to\infty}x\sin\frac{1}{x}[/itex] and [itex]\displaystyle\lim_{x\to\infty}x\sin\frac{1}{x}[/itex] ?

Is there any difference when evaluating them? Is that notation used only with infinity?

Thanks.

What is the difference between [itex]\displaystyle\lim_{|x|\to\infty}x\sin\frac{1}{x}[/itex] and [itex]\displaystyle\lim_{x\to\infty}x\sin\frac{1}{x}[/itex] ?

Is there any difference when evaluating them? Is that notation used only with infinity?

Thanks.