Question: Limit does not give correct answer


I try to calculate the limit of the function, 

sin(x*sin(1/x))/(x*sin(1/x))  at point x=0,maple gives answer:1

However,actually it does not have a limit at x=0,because for the limit to exist at a point,there needs to exist a neighbourhood at the point so that all x in the neighbour have definition.

It means f(x) should have have definition at point x=0's negihbourhood,however small the neighbourhood is.If I choose x=1/(n*Pi), n belongs to integers,the function doesn't have definition.As n increase,there doesn't exist such a neighbourhood.So is it something maple should correct?


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