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JEE Main202118 Mar 2021Morning ShiftMathematicsLimitsActual

If lim x → 0 sin - 1 x - tan - 1 x 3 x 3 is equal to L , then the value of ( 6 L + 1 ) is

Options

  1. A1 6
  2. B1 2
  3. C6
  4. D2

Correct answer

D. 2

Step-by-step solution

Given lim x → 0 sin - 1 x - tan - 1 x 3 x 3 ⇒ lim x → 0 x + x 3 3 ! … - x - x 3 3 … 3 x 3 ⇒ lim x → 0 1 + 3 x 2 3 ! … - 1 - 3 x 2 3 … 9 x 2 (Use L'Hospital rule 0 0 form) ⇒ lim x → 0 6 x 3 ! + … - - 6 x 3 + … 18 x (Use L'Hospital rule 0 0 form) ⇒ lim x → 0 6 3 ! + … - - 6 3 + … 18 = 1 + 2 18 = 1 6 Given that, lim x → 0 sin - 1 x - tan - 1 x 3 x 3 = L ∴   1 6 = L ⇒ 6 L = 1 So, 6 L + 1

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