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JEE Main2016MathematicsLimitsActual

lim x → 0 ⁡ 1 - cos ⁡ 2 x 2 2 x tan ⁡ x - x tan ⁡ 2 x is

Options

  1. A2
  2. B- 1 2
  3. C- 2
  4. D1 2

Correct answer

C. - 2

Step-by-step solution

lim x → 0 ⁡ 1 - cos ⁡ 2 x 2 2 x tan ⁡ x - x tan ⁡ 2 x =   lim x → 0 ⁡ 2 sin 2 ⁡ x 2 2 x x + x 3 3 + 2 x 5 15 + … - x 2 x + 2 3   x 3 3 + 2 2 5   x 5 15 + … =   lim x → 0 ⁡ 4 x - x 3 3 ! + x 5 5 ! - … . 4 x 4 2 3 - 8 3 + x 6 4 15 - 64 15 (dividing numerator and denominator by x 4 ) =   lim x → 0 ⁡ 4 1 - x 2 3 ! + x 4 5 ! - … . 4 - 2 + x 2 - 60 15 + … =   - 2

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