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MHT CET202416 May 2024Morning ShiftMathematicsLimitsActual

The value of _ x 0 (( x)^ 1 x + ( 1 x )^ x ) , where x 0 is

Options

  1. A0
  2. B-1
  3. C1
  4. D2

Correct answer

C. 1

Step-by-step solution

aligned & _ x 0^0 ( x)^ 1 x + ( 1 x )^ x & = _ x 0 ( x)^ 1 x + _ x 0 ( 1 x )^ x & =0+ _ x 0 ( 1 x )^ x & = _ x 0 ( 1 x )^ x aligned Let l= _ x 0 ( 1 x )^ x . Then, aligned & l= _ x 0 ( 1 x )^ x & l= _ x 0 (- x x) & l=- _ x 0 x cosec x & l=- _ x 0 1 x - cosec x x = _ x 0 ^2 x x x & l= _ x 0 x x x=1 0=0 & l= e ^0=1 aligned

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