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Question

If α is a root of the equation sinx+1=x then limx[min(sinx,{x})x1] is
Where [.] denotes greatest integer function
{x} fractional part of x.

A
1
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B
Does not exist
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C
-1
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Solution

The correct option is B Does not exist

LHL
limxα[min(sinx,x[x])(x1)]When 1<x<α{x}=x1<sinxmin{sinx,x1}=x1Required limit=limx[x1x1]=1xα+sinx<x1sinxx1<1RHL:limxα+[sinxx1]=0Hence LHLRHLLimit does not exist[sinxx1]=0

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