Maybe the first thing that a calculus student when studying the sine and cosine function is that these are the first that he knows and do not have a limit as .
But how about the sequence and ? do they have a limit ?
A method to prove that does not have a limit is as follow :
Assume that it has a limit then it should be a real number since is bounded.
Since , we get and : .
we have :
But the limit of the right side is :
Which means that which is absurd.
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