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NTA Abhyas JEE Main2020MathematicsLimitsPractice

The value of lim x → π 6 ⁡ 2 cos ⁡ x + π 3 1 - 3 tan ⁡ x is equal to

Options

  1. A1 2
  2. B3
  3. C3 4
  4. D3 2

Correct answer

D. 3 2

Step-by-step solution

Let x = π 6 - t Given limit is lim t → 0 ⁡ 2 cos ⁡ π 2 - t 1 - 3 tan ⁡ π 6 - t ⇒ lim t → 0 ⁡ 2 sin ⁡ t 1 - 3 1 - 3 tan t 3 + tan t = lim t → 0 ⁡ 2 sin ⁡ t 3 + tan t 4 tan t = 3 2

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