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Highly selective Backlog Qs for JEE MainMathematicsLimits

( _ x 1- x / 2 ( x 2 ) ( x 4 - x 4 ) = )

Options

  1. A( 3 2 )
  2. B( -1 2 )
  3. C( 1 2 )
  4. D( 5 2 )

Correct answer

C. ( 1 2 )

Step-by-step solution

( _ x 1- x 2 ( x 2 ) ( x 4 - x 4 ) ) Let ( x= +h, x , h 0 ) ( gathered = _ x h 0 1- ( 2 + h 2 ) ( 2 + h 2 ) ( ( +h 4 )- ( +h 4 ) ) = _ h 0 1- h 2 - h 2 ( 4 h 4 - 4 h 4 - 4 h 4 - 4 h 4 ) gathered ) ( aligned & = _ h 0 2 (1- h 2 ) - h 2 h 4 - h 4 - h 4 - h 4 & = _ h 0 2 (1- h 2 ) h 2 (-2 h 4 ) & = _ h 0 2 2 ^2 h 4 2 h 2 h 4 & = _ h 0 2 h 4 h 2 = 2 _ h 0 h 4 4 ( h 4 ) 2(h / 2) h 2 & = 2 2 4 _ h 0 ( h 4 h 4 ) ( h 2 h 2 ) & = 2 2 4 1 1= 1 2 aligned )

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