(adsbygoogle = window.adsbygoogle || []).push({}); How to show lim sin(1/x) DNE as x-->0

Hello,

I am trying to see how lim sin(1/x) does not exist as x-->0. It is obvious from a graph.

I think one way to do this is to pick two sequences converging to 0 and show that the limit of these sequences do not equal each other. For example, I can pick a sequence where sin gives me +1 and another one where sin gives me -1. I think this would work. Can someone confirm that this strategy is sound?

Also, I would also like to see how to show this using epsilon-delta argument at well.

Thanks in advance.

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# How to show lim sin(1/x) DNE as x->0

**Physics Forums | Science Articles, Homework Help, Discussion**