The value of lim n → ∞ ⁡ cos ⁡ x 2 cos ⁡ x 4 cos ⁡ x 8 … … . . . cos ⁡ x 2 n + 1 is equal to

Question

The value of lim n → ∞ ⁡ cos ⁡ x 2 cos ⁡ x 4 cos ⁡ x 8 … … . . . cos ⁡ x 2 n + 1 is equal to, x sin ⁡ x, sin ⁡ x x, 0, None of these

MARKS App · Accepted Answer

Let, L = lim n → ∞ ⁡ cos ⁡ x 2 cos ⁡ x 2 2 cos ⁡ x 2 3 … . . cos ⁡ x 2 n + 1 = lim n → ∞ ⁡ 1 2 sin ⁡ x 2 n + 1 cos ⁡ x 2 … … cos ⁡ x 2 n 2 sin ⁡ x 2 n + 1 cos ⁡ x 2 n + 1 = l i m n → ∞ 1 2 2 sin ⁡ x 2 n + 1 cos ⁡ x 2 … 2 cos ⁡ x 2 n sin ⁡ x 2 n = lim n → ∞ ⁡ 1 2 n + 1 sin ⁡ x 2 n + 1 2 cos ⁡ x 2 sin ⁡ x 2 = lim n → ∞ ⁡ sin ⁡ x 2 n + 1 sin ⁡ x 2 n + 1 = sin ⁡ x x lim n → ∞ ⁡ x 2 n + 1 sin ⁡ x 2 n + 1 = sin ⁡ x x

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