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Consider the set P = n 1 n , n ∈ N , then the largest element of set P is

Options

  1. A2 1 2
  2. B3 1 3
  3. Ce 1 e
  4. D7 1 7

Correct answer

B. 3 1 3

Step-by-step solution

Let f x = x 1 x ⇒ f ′ x = x 1 x 1 − ln x x 2 At x = e , f ′ x = 0 and sign change of derivative is from positive to negative, hence x = e is a point of local maxima of f x . Now 2 < e < 3 , hence f 2 or f 3 is the greatest element of set P Since 2 3 < 3 2 ⇒ 2 1 2 < 3 1 3 So, f 3 = 3 1 3 is the largest element of set P

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