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JEE Main20199 Jan 2019Evening ShiftMathematicsLimitsActual

For each x ∈ R , let x be the greatest integer less than or equal to x . Then l i m x → 0 - x x + x sin ⁡ x x is equal to

Options

  1. A1
  2. B0
  3. C- sin ⁡ 1
  4. Dsin ⁡ 1

Correct answer

C. - sin ⁡ 1

Step-by-step solution

= lim x → 0 - ⁡ x   x + x sin ⁡ x x = l i m x → 0 - x - 1 - x sin ⁡ - 1 - x x = - 1 , ∀   x ∈ [ - 1 , 0 ) = l i m x → 0 - - 1 + x sin ⁡ 1 sin - θ = - sin θ = - sin ⁡ 1 .

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