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AP EAMCET202125 Aug 2021Evening ShiftMathematicsLimitsActual

If [.] here denotes the greatest integer function, _ x 0 x^7 [ 1 x^3 ] is equal to

Options

  1. A1
  2. B0
  3. C-1
  4. Ddoes not exist

Correct answer

B. 0

Step-by-step solution

_ x 0 x^7 [ 1 x^3 ] RHL Let x=0+h , where h 0 _ h 0 h^7 [ 1 (0+h)^3 ]=0 aligned & LHL Let x=0-h where h 0 & _ h 0 (-h)^7 [ 1 (0-h)^3 ] & _ h 0 -h^7 (-1)=0 aligned aligned & LHL = RHL =0 & _ x 0 x^7 [ 1 x^3 ]=0 aligned

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