For each $x \in \mathbb{R}$,let $[x]$ be the greatest integer less than or equal to $x$. Then $\lim_{x \to 0^+} \frac{x([x] + |x|) \sin [x]}{|x|}$ is equal to

  • A
    $-\sin 1$
  • B
    $0$
  • C
    $1$
  • D
    $\sin 1$

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