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

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


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