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NTA Abhyas JEE Main2020MathematicsLimitsPractice

If L = lim x → π 4 1 − tan x 1 − sin 2 x 1 + tan x π − 4 x 3 , then the value of 40 L is equal to

Correct answer

1.25

Step-by-step solution

L = lim x → π 4 tan π 4 − x 1 − sin 2 x 4 π 4 − x π − 4 x 2 = l i m x → π 4 1 4 1 - sin ⁡ 2 x π - 4 x 2 = l i m x → π 4 1 4 - cos ⁡ 2 x ⋅ 2 2 π - 4 x - 4 (applying L-Hospital rule) = l i m x → π 4 1 16 c o s 2 x π - 4 x = l i m x → π 4 1 16 - sin ⁡ 2 x × 2 - 4 (again applying L-Hospital rule) = 1 16 - 1 - 4 × 2 ⇒ L = 1 32

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