limx→3 ([x−3]+[3−x]−x) where [·]denotes the greatest integer function, is equal to 

limx→3 ([x−3]+[3−x]−x) where [·]denotes the greatest integer function, is equal to 

  1. A

    4

  2. B

    -4

  3. C

    0

  4. D

    none of these

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    Solution:

    We have,

    x+3+[3−x]=[x−3]+[−(x−3)]=[x−3]−[x−3]−1=−1∴ limx→3 ([x−3]+[3−x]−x)=limx→3 (−1−x)=−4

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