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MHT CET20239 May 2023Evening ShiftMathematicsContinuity and DifferentiabilityActual

f (x)= array ll 1- k x x^2 , & if x 0 x 16+ x -4 , & if x>0 array . is continuous at x=0 , then the value of k is

Options

  1. A4
  2. B2
  3. C-1
  4. D-3

Correct answer

A. 4

Step-by-step solution

f (x) is continuous at x=0 aligned L.H.L. & = _ x 0 1- k x x^2 & = _ x 0 2 ^2 k x 2 x^2 & =2 _ x 0 ^2 k x 2 k ^2 x^2 4 4 k ^2 & = 1 2 k ^2 _ x 0 ( k x 2 k x 2 )^2 L.H.L. & = 1 2 k ^2 aligned aligned R.H.L. & = _ x 0 x 16+ x -4 & = _ x 0 ( x )( 16+ x +4) ( 16+ x -4)( 16+ x +4) & = _ x 0 x ( 16+ x +4) 16+ x -16 & = 16+ 0 +4 aligned R.H.L. =8 f (x) is continuous at x=0 ... [Given] array ll & L.H.L. = R.H.L & 1 2 k ^2=8 & k ^2=16 k = 4 array

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