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

$\underset{x\to 1+}{\lim }\frac{\left(1-\left|x\right|+\sin \left|1-x\right|\right)\sin \left(\frac{\pi }{2}\left[1-x\right]\right)}{\left|1-x\right|\left[1-x\right]}$