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99 Percentile Qs Bank for JEE MainMathematicsLimits

The value of l i m x → 0 sin ⁡ x 3 5 x is equal to (where, . represents the greatest integer function)

Options

  1. A1 3
  2. B0
  3. C5 3
  4. D1

Correct answer

C. 5 3

Step-by-step solution

5 x - 1 < 5 x ≤ 5 x sin ⁡ x 3 5 x - 1 ⏟ h x < sin ⁡ x 3 5 x ⏟ f x ≤ sin ⁡ x 3 5 x ⏟ g x by sandwich theorem ∵ l i m x → 0 g x = l i m x → 0 h x = 5 3 ∴ l i m x → 0 f x = 5 3

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