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NTA Abhyas JEE Main2020MathematicsDifferentiationPractice

If y = 2 + sin ⁡ x + 2 + sin ⁡ x + 2 + sin ⁡ x + … ∞ , then the value of d y d x at x = 0 is

Options

  1. A0
  2. B2
  3. C1 2
  4. D1 3

Correct answer

D. 1 3

Step-by-step solution

Given equation can be rewritten as y = 2 + sin ⁡ x + y ⇒ y - 2 2 = sin ⁡ x + y ⇒ y 2 - 4 y + 4 = sin ⁡ x + y … i Putting x = 0 in the equation i , we get, y 2 - 4 y + 4 = 0 + y ⇒ y 2 - 5 y + 4 = 0 ⇒ y - 1 y - 4 = 0 y = 1 or y = 4 ∵ y > 2 ⇒ y = 4 Now differentiating equation i with respect to x , we get, d y d x = cos ⁡ x 2 y - 5 Putting x = 0 , y = 4 d y d x = cos ⁡ 0 2 4 - 5 = 1 3

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