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JEE Main202429 Jan 2024Morning ShiftMathematicsDifferentiationActual

Suppose f x = 2 x + 2 - x tan x tan - 1 x 2 - x + 1 7 x 2 + 3 x + 1 3 . Then the value of f ' 0 is equal to

Options

  1. Aπ
  2. B0
  3. Cπ
  4. Dπ 2

Correct answer

C. π

Step-by-step solution

Given: f x = 2 x + 2 - x tan x tan - 1 x 2 - x + 1 7 x 2 + 3 x + 1 3 We know that, f ' 0 = lim h → 0 f h - f 0 h ⇒ f ' 0 = lim h → 0 2 h + 2 - h tan h tan - 1 h 2 - h + 1 7 h 2 + 3 h + 1 3 - 2 0 + 2 0 tan 0 tan - 1 0 - 0 + 1 0 + 0 + 1 3 h ⇒ f ' 0 = lim h → 0 2 h + 2 - h tan h tan - 1 h 2 - h + 1 h 7 h 2 + 3 h + 1 3 ⇒ f ' 0 = lim h → 0 2 h + 2 - h tan - 1 h 2 - h + 1 7 h 2 + 3 h + 1 3 ⇒ f ' 0 = 2 0 + 2 0 tan - 1 1 0 + 1 3 ⇒ f ' 0 = 2 π 4 ⇒ f ' 0 = π

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