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JEE Advanced2011MathematicsLimitsActual

If _ x 0 [1+x (1+b^2 ) ]^ 1 / x =2 b ^2 b>0 and (- , ] , then the value of is

Options

  1. A4
  2. B3
  3. C6
  4. D2

Correct answer

D. 2

Step-by-step solution

Here, _ x 0 1+x (1+b^2 ) ^ 1 / x aligned & Given, [1^ from ] & e^ _ x 0 x (1+b^2 ) 1 x & e^ (1+b^2 ) =(1+b)^2 & _ x 0 1+x (1+b^2 ) ^ 1 / x =2 b ^2 & (1+b^2 )=2 b ^2 & ^2 = 1+b^2 2 b (ii) aligned By A M G M , b+ 1 b 2 (b 1 b )^ 1 / 2 b^2+1 2 b 1 From Eqs. (ii) and (iii), we get ^2 =1 = 2 as (- , ]

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