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.`