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.