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MHT CET202311 May 2023Morning ShiftMathematicsContinuity and DifferentiabilityActual

If f (x)= array ll 1+ m x - 1- m x x & ,-1 x < 0 2 x+1 x-2 & , 0 x 1 array . is continuous in the interval [-1,1] , then m is equal to

Options

  1. A1 2
  2. B- 1 2
  3. C-1
  4. D- 1 4

Correct answer

B. - 1 2

Step-by-step solution

Since f (x) is continuous in [-1,1] , it is continuous at x=0 . aligned & _ x 0⁻ f (x)= _ x 0⁺ f (x) & _ x 0 1+ m x - 1- m x x = _ x 0 2 x+1 x-2 & _ x 0 (1+ m x-1+ m x) x( 1+ m x + 1- m x ) = 2(0)+1 0-2 & 2 ~m 1+1 = 1 -2 & m = -1 2 aligned

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