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COMEDK2023Morning ShiftMathematicsLimitsActual

The value of _ x 0 e^ a x -e^ b x 2 x is equal to

Options

  1. A0
  2. Be^ a b 2
  3. Ca+b 2
  4. Da-b 2

Correct answer

D. a-b 2

Step-by-step solution

The limit is given by L = _ x 0 e^ ax - e^ bx 2x . Since the limit is of the form 0 0 as x 0 , L'Hopital's rule can be applied by differentiating the numerator and the denominator with respect to x . L = _ x 0 d dx (e^ ax - e^ bx ) d dx (2x) L = _ x 0 ae^ ax - be^ bx 2 Substituting x = 0 into the expression: L = ae⁰ - be⁰ 2 = a - b 2 Answer: a-b 2

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