Show that doesn't exist by using the squeeze theorem.

Thanks in advance.

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- April 12th 2009, 04:49 PMBiscaim\lim_{x\rightarrow 0} sin (\frac{1}{x})
Show that doesn't exist by using the squeeze theorem.

Thanks in advance. - April 12th 2009, 05:10 PMTheEmptySet
I don't see how the squeeze theorem will help but here is a method.

By using the sequental char of limits all we need to do is find two different sequences that converge to 0 that have different function limits.

note that both of these go to zero and n goes to infinity, but

and

There for the limit does not exists at 0