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MHT CET20226 Aug 2022Morning ShiftMathematicsContinuity and DifferentiabilityActual

The function defined by f(x)= array cc x-4 |x-4| +a & if x 4 array . is continuous at x=4 , are

Options

  1. Aa=0, b=1
  2. Ba =1, ~b =0
  3. Ca =1, ~b =-1
  4. Da =-1, ~b =0

Correct answer

C. a =1, ~b =-1

Step-by-step solution

L.H.L at x=4 _ h 0 4-h-4 |4-h-4| +a= _ h 0 -h |-h| +a= _ h 0 -h h +a=-1+a R.H.L at x=4 _ h 0 4+h-4 |4+h-4| +b= _ h 0 h |h| +b= _ h 0 h h +b=1+b For continuity at x =4-1+ a = a + b =1+ b a =1 and b =-1

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