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JEE Main202522 Jan 2025Evening ShiftMathematicsLimitsActual

If _ x ( ( e 1- e ) ( 1 e - x 1+x ) )^x= , then the value of _ e 1+ _ e equals :

Options

  1. Ae⁻¹
  2. Be ^2
  3. Ce⁻²
  4. De

Correct answer

D. e

Step-by-step solution

aligned & = _ x ( ( e 1- e ) ( 1 e - x 1+ x ) )^ x (1^ form ) & = e ^ L & Where L = _ x x ( ( e 1- e ) ( 1 e - x 1+ x )-1 ) & L = _ x ( e 1- e ) x ( 1 e - x 1+ x - ( 1- e e ) ) & L = e 1- e _ x x (1- x 1+ x ) & L = e 1- e _ x x x +1 & ~L = e 1- e 1 & ~L = e 1- e & = e ^ e 1- e = e 1- e & Required value = e 1- e 1+ e 1- e = e aligned

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