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JEE Advanced2024MathematicsLimitsActual

Let S be the set of all ( , ) R R such that _ x (x^2 ) ( _e x )^ ( 1 x^2 ) x^ ( _e(1+x) )^ =0 . Then which of the following is (are) correct?

Options

  1. A(-1,3) S
  2. B(-1,1) S
  3. C(1,-1) S
  4. D(1,-2) S

Correct answer

B. (-1,1) S

Step-by-step solution

aligned & _ x x^2 ( _e x )^ 1 x^2 x^ ( _e(1+x) )^ =0 & _ x ( _e x )^ ( _e(x+1) )^ x^ +2 =0 aligned aligned & _ x ( _e x _e(x+1) )^ ( _e x )^ - x^ +2 =0 & _ x ( _e x )^ - x^ +2 =0 Put _e x=t & _ t t^ - (e^t )^ +2 =0 aligned As we know _ x x e^x =0 +2>0 >-2

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