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
- Ae⁻¹
- Be ^2
- Ce⁻²
- 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