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For a differentiable function f x , if f ' 2 = 2 and f ' 3 = 1 , then the value of lim x → 0 f x 2 + x + 2 − f 2 f x 2 − x + 3 − f 3 is equal to

Options

  1. A2
  2. B1
  3. C- 2
  4. D- 1

Correct answer

C. - 2

Step-by-step solution

Given, lim x → 0 f x 2 + x + 2 − f 2 f x 2 − x + 3 − f 3 lim x → 0 f x 2 + x + 2 − f 2 x 2 + x + 2 - 2 × x 2 + x + 2 - 2 f x 2 − x + 3 − f 3 x 2 − x + 3 - 3 × x 2 − x + 3 - 3 = f ′ 2 f ′ 3 lim x → 0 x x + 1 x x − 1 = − 2 1 = − 2

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