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

Question

The value of lim x → π 4 ⁡ sin ⁡ 2 x sec 2 ⁡ 2 x is equal to, - 1 2, 1 2, e - 1 2, e 1 2

MARKS App · Accepted Answer

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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