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JEE Main2013MathematicsLimitsActual

The value of _ x 0 1 x [ ⁻¹ ( x+1 2 x+1 )- 4 ] is :

Options

  1. A1
  2. B- 1 2
  3. C2
  4. D0

Correct answer

B. - 1 2

Step-by-step solution

_ x 0 ( 1 x ) [ ⁻¹ ( x+1 2 x+1 )- 4 ]= _ x 0 ( 1 x ) [ ⁻¹ ( x+1 2 x+1 )- ⁻¹(1) ]= _ x 0 ( 1 x ) ⁻¹ ( x+1 2 x+1 -1 1+ x+1 2 x+1 )= _ x 0 1 x ⁻¹ ( -x 3 x+2 )=- _ x 0 [ ⁻¹ ( x 3 x+2 ) x 3 x+2 1 3 x+2 ]=- 1 2

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