If f(x)=sin⁡(1+[x])[x] for [x]≠00 for [x]=0denotes the greatest integer not exceeding x, then limx→0− f(x)=

If f(x)=sin(1+[x])[x] for [x]00 for [x]=0

denotes the greatest integer not exceeding x, then limx0f(x)=

  1. A

    -1

  2. B

    0

  3. C

    1

  4. D

    2

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    Solution:

    We have,

    f(x)=sin(1+[x])[x] for  x[0,1)0 for  x[0,1)limx0f(x)=limx0sin(1+[x])[x]=limx0sin(11)1=01=0

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