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JEE Main2007MathematicsLimitsActual

The function f:R 0 R given by f(x)= 1 x - 2 e^ 2 x -1 can be made continuous at x=0 by defining f(0) as

Options

  1. A2
  2. B-1
  3. C0
  4. D1

Correct answer

D. 1

Step-by-step solution

_ x 0 1 x - 2 e^ 2 x -1 _ x 0 e^ 2 x -1-2 x x (e^ 2 x -1 ) _ x 0 2 e^ 2 x -2 (e^ 2 x -1 )+2 x e^ 2 x _ x 0 4 e^ 2 x 4 e^ 2 x +4 x e^ 2 x =1 .

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