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AP EAMCET20226 Jul 2022Morning ShiftMathematicsContinuity and DifferentiabilityActual

If f(x)= (1- x) (1+ ^2-4 x+4 x^2 ) is continuous at x= 2 , then f ( 2 )=

Options

  1. A1 4
  2. B1 8
  3. C1 16
  4. D1 32

Correct answer

B. 1 8

Step-by-step solution

f ( x ) is continous at x = 2 aligned & _ x 2 f(x)=f ( 2 ) & f ( 2 )= _ x 2 1- x (1+ ^2-4 x+4 x^2 ) & f ( 2 )= _ x 2 ( - x (1+ ^2-4 x+4 x^2 ) ) (-4 +8 x) & f ( 2 )=- _ x 2 ( x) (1+ ^2-4 x+4 x^2 ) (-4 +8 x) & f ( 2 )= _ x 2 ( x)(-4 +8 x)+ (1+ ^2-4 x+4 x^2 )(- x) 8 & f ( 8 2 )= _ x 2 (1+2 ^2-2 ^2 ) 8 = 1 8 & f ( 2 )= _ x 2 (1+ ^2-4 2 +4 ^2 4 )(+1) 8 aligned

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