SOLUTION: Lim Sin (1/x)
X-0
Algebra.Com
Question 238695: Lim Sin (1/x)
X-0
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
)
As 
approaches 0, 
increases without bound. Thus in any open interval containing 0 there will be values of such that is a multiple of 
, values of such that is 
more than a multiple of , and values of such that is 
more than a multiple of . The sine of these values of will be 0, 1 and -1 respectively.
)
oscillates "an infinite number of times" between 1 and -1 in any neighbourhood of 
. Therefore the limit doesn't exist.
John
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