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AP EAMCET202123 Aug 2021Evening ShiftMathematicsLimitsActual

_ x 0 8 x^8 [ array l 1- ( x^2 2 )- ( x^2 4 ) + ( x^2 2 ) ( x^2 4 ) array ] is equal to

Options

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

Correct answer

D. 1 32

Step-by-step solution

_ x 0 8 x^8 (1- ( x^2 2 )- ( x^2 4 )+ ( x^2 2 ) ( x^2 4 ) ) _ x 0 8 x^8 1 (1- x^2 2 )- ( x^2 4 )^2 (1- ( x^2 2 ) ) _ x 0 8 x^8 (1- x^2 2 ) (1- ( x^2 4 ) ) [ (1- )=2 ^2 2 . _ x 0 8 x^8 (2 ^2 (x^2 / 4 ) ) (2 ^2 (x^2 / 8 ) .32 . _ x 0 1 x^8 ( ( x^2 4 ) x^2 4 )^2 x^4 16 ( (x^2 / 8 ) x^2 / 8 )^2 x^4 64 _ x 0 32 x^8 16 64 x^8 ( x^2 / 4 x^2 / 4 )^2 ( x^2 / 8 x^2 / 8 )^2= 1 32 1 1 _ x 0 x x =1 = 1 32

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