limx→∞ log⁡x[x] where [·] denotes the greatest integer function, is

limxlogx[x] where [·] denotes the greatest integer function, is

  1. A

    0

  2. B

    1

  3. C

    -1

  4. D

    non-of these 

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    Solution:

    We have,

    x1<[x]x for all xR1x1[x]<1x1 for ail xR{0,1}logxxlogx[x]<logxx1 [logx>0 as xx]limxlogxxlimxlogx[x]<limxlogxx1limxlogx[x]=0 limxlogxx=limxlogxx1=i

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