A) equals 1
B) equals 0
C) equals\[-1\]
D) does not exist
Correct Answer: B
Solution :
\[\underset{x\to 1+}{\mathop{\lim }}\,\frac{(1-\left| x \right|+\sin \left| 1-x \right|)\sin \left( [1-x]\frac{\pi }{2} \right)}{\left| 1-x \right|[1-x]}\] |
\[=\underset{x\to {{1}^{-}}}{\mathop{\lim }}\,\frac{(1-x+\sin (x-1)\sin \left( -\frac{\pi }{2} \right)}{(x-1)(-1)}\] |
\[=\underset{x\to {{1}^{-}}}{\mathop{\lim }}\,\frac{-(x-1)+\sin (x-1)}{(x-1)}=-1+1=0.\] |
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