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COMEDK2024MathematicsLimitsActual

The value of _ x 0 (a+x)- (a-x) x is

Options

  1. A1
  2. B2 a
  3. C0
  4. D2 a

Correct answer

B. 2 a

Step-by-step solution

The given limit is L = _ x 0 (a+x) - (a-x) x . Using the trigonometric identity C - D = 2 ( C+D 2 ) ( C-D 2 ) , we set C = a+x and D = a-x . Then C+D 2 = a+x+a-x 2 = a and C-D 2 = a+x-(a-x) 2 = x . Substituting these into the expression, we get L = _ x 0 2 a x x . Since _ x 0 x x = 1 , the expression simplifies to 2 a 1 = 2 a . Answer: 2 a

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