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COMEDK2025MathematicsLimitsActual

_ x 4 ^2 x-2 x-1 =

Options

  1. A1
  2. B2
  3. C1 2
  4. D2

Correct answer

D. 2

Step-by-step solution

Given the limit L = _ x 4 ^2 x-2 x-1 . Using the identity ^2 x = 1 + ^2 x , the expression becomes: L = _ x 4 1 + ^2 x - 2 x - 1 L = _ x 4 ^2 x - 1 x - 1 Factoring the numerator as a difference of squares: L = _ x 4 ( x - 1)( x + 1) x - 1 Canceling the common term ( x - 1) for x 4 : L = _ x 4 ( x + 1) Substituting x = 4 : L = ( 4 ) + 1 = 1 + 1 = 2 . Answer: 2

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