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JEE Main202117 Mar 2021Morning ShiftMathematicsLimitsActual

The value of lim x → 0 + cos - 1 x - [ x ] 2 · sin - 1 x - [ x ] 2 x - x 3 , where x denotes the greatest integer ≤ x is:

Options

  1. Aπ
  2. B0
  3. Cπ 4
  4. Dπ 2

Correct answer

D. π 2

Step-by-step solution

Given L = lim x → 0 + cos - 1 x - [ x ] 2 · sin - 1 x - [ x ] 2 x - x 3 ∵   x ∈ [ 0 , 1 ) ⇒ x = 0 Then L = lim x → 0 + cos - 1 x 1 - x 2 × lim x → 0 + sin - 1 x x L = π 2 × lim x → 0 + 1 1 - x 2     Apply L'Hospital rule for  0 0  form L = π 2

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