`lim_(xto0) [(1-e^(x))(sinx)/(|x|)]` is (where `[.]` represents the greatest integer function )
`lim_(xto0) [(1-e^(x))(sinx)/(|x|)]` is (where `[.]` represents the greatest integer function )
A. 1
B. 2
C. 3
D. none of these
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Correct Answer - A
`underset(xto0^(+))lim[(1-e^(x))(sinx)/(|x|)]=underset(xto0^(+))lim[(0^(-))(sinx)/(x)]=[0^(-)]=-1.`
`underset(xto0^(-))lim[(1-e^(x))(sinx)/(|x|)]=underset(xto0^(-))lim[(0^(+))(sinx)/(-x)]=[0^(-)]=-1`
Hence, `underset(xto0)lim[(1-e^(x))(sinx)/(|x|)]=-1.`
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