\displaystyle\lim_{{{x}\to{0}}}{\left[{\left({1}-{e}^{{x}}\right)}\frac{{{\sin{{x}}}}}{{{\left|{x}\right|}}}\right]}{i}{s}{\left({w}{h}{e}{r}{e}{\left[{\dot}\right]}\right.} represents the greatest integer function). (a)$-1$ (b) $1$ (c) $0$ (d) does not exist

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