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The function f x = l i m n → ∞ x - 2 2 n - 1 x - 2 2 n + 1 ∀ n ∈ N is discontinuous at

Options

  1. Ax = 1 only
  2. Bx = 3 only
  3. Cx = 1 and 3
  4. Dx = 0,1 and 2

Correct answer

C. x = 1 and 3

Step-by-step solution

Given, f x = l i m n → ∞ x - 2 2 n - 1 x - 2 2 n + 1 ⇒ f x = l i m n → ∞ 1 - 1 x - 2 2 n 1 + 1 x - 2 2 n ⇒ f x = - 1 , 0 , 1 , 0 ≤ x - 2 2 < 1 x - 2 2 = 1 x - 2 2 > 1 ⇒ f x = 1 , x < 1 0 , x = 1 - 1 , 1 < x < 3 0 , x = 3 1 , x > 3 Thus, f x is discontinuous at x = 1,3

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