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99 Percentile Qs Bank for JEE MainMathematicsDifferentiation

If f ( x ) has a derivative at x = a , then l i m x → a x f a - a f x x - a is equal to

Options

  1. Af a - a f ′ a
  2. Ba f a - f ′ a
  3. Cf a + f ′ a
  4. Da f a + f ′ a

Correct answer

A. f a - a f ′ a

Step-by-step solution

l i m x → a x f a - a f x x - a Add and subtract a f ( a ) = lim x → a x f a - a f a + a f a - a f x x - a = l i m x → a f a x - a - a f x - f a x - a Separate and solve = lim x → a f a x - a x - a - lim x → a a f x - f a x - a As f ' ( a ) = lim x → a f ( x ) - f ( a ) x - a (derivative of f ( x ) at x = a exist) = f a - a f ′ a

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