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MHT CET202615 April 2026Morning ShiftMathematicsContinuity and DifferentiabilityActual

If the function f is continuous at x = 1 , where f(x) = 1 + ( x) (1-x)^2 , for x 1 , then the value of f(1) is....

Options

  1. A2
  2. B4
  3. C6
  4. D9

Correct answer

A. 2

Step-by-step solution

Since f(x) is continuous at x = 1 , f(1) = _ x 1 f(x) . f(1) = _ x 1 1 + ( x) (1-x)^2 This is a 0 0 form. Applying L'Hospital's rule: f(1) = _ x 1 - ( x) -2 (1-x) f(1) = _ x 1 ( x) 2(1-x) This is again a 0 0 form. Applying L'Hospital's rule once more: f(1) = _ x 1 ( x) -2 Substituting x = 1 : f(1) = ( ) -2 = (-1) -2 = 2 Answer: 2

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