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AP EAMCET202421 May 2024Morning ShiftMathematicsLimitsActual

If _ x ( 2 x+1 + 2 x-1 )^8+( 2 x+1 - 2 x-1 )^8 (P x^4-16 ) (x+ x^2-2 )^8+ (x- x^2-2 )^8 =1 , then P=

Options

  1. A16
  2. B64
  3. C1 64
  4. D1 16

Correct answer

D. 1 16

Step-by-step solution

_ x [( 2 x+1 + 2 x-1 )^8+( 2 x+1 - 2 x-1 )^8 ] (P x^4-16 ) (x+ x^2-2 )^8+ (x- x^2-2 )^8 Dividing numerator and denominator by x^8 aligned & _ x [ ( 2+ 1 x + 2- 1 x )^8+ ( 2+ 1 x - 2- 1 x )^8 ] (P- 16 x^4 ) (1+ 1- 2 x^2 )^8+ (1- 1- 2 x^2 )^8 & =1 aligned Apply the limit aligned & [( 2+0 + 2-0 )^8+( 2 - 2 )^8 ] P (1+1)^8+(1-1)^8 =1 & 2^4 P =1 P = 1 16 aligned

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