For each \( t \in R \), let \( [t] \) be the greatest integer less than or equal to \( t \). The...

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For each \( t \in R \), let \( [t] \) be the greatest integer less than or equal to \( t \). Then ,
\[
\lim _{x \rightarrow 1+} \frac{(1-|x|+\sin |1-x|) \sin \left(\frac{\pi}{2}[1-x]\right)}{|1-x|[1-x]}
\]
\( \mathrm{P} \)
(1) does not exist
(2) equals 1
(3) equals \( -1 \)
(4) equals 0
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