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JEE Main202431 Jan 2024Evening ShiftMathematicsLimitsActual

Let f : → R → 0 , ∞ be strictly increasing function such that lim x → ∞ f 7 x f x = 1 . Then, the value of lim x → ∞ f 5 x f x − 1 is equal to

Options

  1. A4
  2. B0
  3. C7 5
  4. D1

Correct answer

B. 0

Step-by-step solution

Let, x be any poistive real number. ⇒ x < 5 x < 7 x ⇒ f x < f 5 x < f 7 x ⇒ f x f x < f 5 x f x < f 7 x f x ⇒ 1 < f 5 x f x < f 7 x f x ⇒ lim x → ∞ 1 < lim x → ∞ f 5 x f x < lim x → ∞ f 7 x f x It is given that, lim x → ∞ f 7 x f x = 1 So, by using Sandwich theorem, ⇒ lim x → ∞ f 5 x f x = 1 ⇒ lim x → ∞ f 5 x f x - 1 = 0

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