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JEE Main202126 Feb 2021Evening ShiftMathematicsLimitsActual

Let f x be a differentiable function at x = a with f ' a = 2 and f a = 4 . Then lim x → a x f a - a f x x - a equals:

Options

  1. Aa + 4
  2. B2 a - 4
  3. C4 - 2 a
  4. D2 a + 4

Correct answer

C. 4 - 2 a

Step-by-step solution

f ' a = 2 , f a = 4 lim x → a x f a - a f x x - a ⇒ lim x → a f a - a f ' x 1 (L'Hospitals rule) = f a - a f ' a = 4 - 2 a

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