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Question

Find the limit: limx0sinxx.


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Solution

Compute the required limit:

For x<0,x=-x

limx0-sinxxlimx0-sin-xxlimx0--sinxx-1 {Since, sin(-x)=-sin(x) and limx0sinxx=1}

For x>0,x=x

limx0+sinxxlimx0-sinxx1

Since, the two limits from the left and from the right are different.

Therefore the above limit does not exist.


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