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NTA Abhyas JEE Main2020MathematicsLimitsPractice

The value of lim x → π 4 ⁡ sin ⁡ 2 x sec 2 ⁡ 2 x is equal to

Options

  1. A- 1 2
  2. B1 2
  3. Ce - 1 2
  4. De 1 2

Correct answer

C. e - 1 2

Step-by-step solution

lim x → π 4 ⁡ sin ⁡ 2 x sec 2 ⁡ 2 x = e lim x → π 4 ⁡ sec 2 ⁡ 2 x sin ⁡ 2 x - 1 = e lim x → π 4 ⁡ sin ⁡ 2 x - 1 cos 2 ⁡ 2 x Applying L'Hospital Rule, we get, = e lim x → π 4 ⁡ 2 cos 2 x 2 cos 2 x - 2 sin ⁡ 2 x = e lim x → π 4 ⁡ - 1 2 sin ⁡ 2 x = e - 1 2

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