The largest value of the non-negative integer \( a \) for which \( \lim _{x \rightarrow 1}\left\...

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The largest value of the non-negative integer \( a \) for which \( \lim _{x \rightarrow 1}\left\{\frac{-a x+\sin (x-1)+a}{x+\sin (x-1)-1}\right\}^{\frac{1-x}{1-\sqrt{x}}}=\frac{1}{4} \), is
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