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COMEDK2024Morning ShiftMathematicsContinuity and DifferentiabilityActual

If f(x)= array cc 1- x ( -2 x)^2 & , if x 2 , & if x= 2 array . Then f(x) will be continues function at x= 2 , then =

Options

  1. A1 4
  2. B1 8
  3. C- 1 8
  4. D1

Correct answer

B. 1 8

Step-by-step solution

For f(x) to be continuous at x = 2 , we must have = _ x /2 f(x) . Let x = 2 + h . As x 2 , h 0 . Substituting this into the expression for f(x) : _ h 0 1 - ( /2 + h) ( - 2( /2 + h))^2 = _ h 0 1 - h ( - - 2h)^2 = _ h 0 1 - h (-2h)^2 = _ h 0 1 - h 4h^2 Using the standard limit _ h 0 1 - h h^2 = 1 2 : = 1 4 1 2 = 1 8 . Answer: 1 8

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