The value of l i m x → π 3 2 - 3 sin ⁡ x - cos ⁡ x 3 x - π 2 is equal to the reciprocal of the number

Question

The value of l i m x → π 3 2 - 3 sin ⁡ x - cos ⁡ x 3 x - π 2 is equal to the reciprocal of the number,

MARKS App · Accepted Answer

l i m x → π 3 2 - 2 3 2 sin ⁡ x + 1 2 cos ⁡ x 3 x - π 2 ⇒ l i m x → π 3 2 - 2 c o s x - π 3 3 x - π 2 Let, x - π 3 = t ⇒ l i m t → 0 2 - 2 cos ⁡ t 3 t 2 = l i m t → 0 2 1 - cos ⁡ t 9 t 2 = 2 9 ⋅ 1 2 = 1 9

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