# How do you show the limit does not exist #lim_(x->oo)sin(x)# ?

It does not exist because it is an oscillating function.

If you want to be more precise, you would have to do a proof by contradiction with the precise definition of a limit. However, I don't think this is what your instructor is looking for.

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The limit does not exist for lim_(x->oo)sin(x).

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