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Black Book Advanced Problems in MathematicsMathematicsContinuity and Differentiability

Suppose a function f(x) satisfies the following conditions f(x+y) = f(x) + f(y) 1 + f(x) f(y) , x, y R and f'(0) = 1 Also -1 < f(x) < 1 , x R The value of the limit _ x (f(x))^x is :

Options

  1. A0
  2. B1
  3. Ce
  4. De^2

Correct answer

B. 1

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