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Black Book Advanced Problems in MathematicsMathematicsContinuity and Differentiability

Let f(x) = x + (1-x)x^2 + (1-x)(1-x^2)x^3 + + (1-x)(1-x^2) (1-x^ n-1 )x^n ; (n 4) then :

Options

  1. Af(x) = - _ r=1 ^n (1-x^r)
  2. Bf(x) = 1 - _ r=1 ^n (1-x^r)
  3. Cf'(x) = (1-f(x)) ( _ r=1 ^n rx^ r-1 (1-x^r) )
  4. Df'(x) = f(x) ( _ r=1 ^n rx^ r-1 (1-x^r) )

Correct answer

B. f(x) = 1 - _ r=1 ^n (1-x^r)

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