A) \[-\,\sin 1\]
B) 0
C) 1
D) sin1
Correct Answer: A
Solution :
\[\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,\frac{x\,([x]+\left| x \right|)sin[x]}{\left| x \right|}\] \[x\to 0\,-\] \[\left. \begin{align} & [x]=-1 \\ & \left| x \right|=-x \\ \end{align} \right\}\Rightarrow \underset{x\to \,0{{\,}^{-}}}{\mathop{\lim }}\,\frac{x\,(-x-1)\sin (-1)}{-x}=-\sin 1.\]You need to login to perform this action.
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