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If I n = ∫ 0 2 2 d x 1 - x n , then the value of lim n → ∞ ⁡ I n is equal to

Options

  1. A1
  2. B2
  3. C1 2
  4. D1 3

Correct answer

B. 2

Step-by-step solution

Ι n = ∫ 0 2 2 d x 1 - x n l i m n → ∞ Ι n = l i m n → ∞ ∫ 0 1 2 dx 1 - x n + l i m n → ∞ ∫ 1 2 2 dx 1 - x n lim n → ∞ I n = l i m n → ∞ 2 ∫ 0 1 d x 1 - 0 + 0 = 2 1 - 0 = 2

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