The value of l i m x → 0 1 - cos ⁡ 2 x x is equal to

Question

The value of l i m x → 0 1 - cos ⁡ 2 x x is equal to, 1 2, - 1 2, Does not exist, 1

MARKS App · Accepted Answer

l i m x → 0 1 - cos ⁡ 2 x x = l i m x → 0 1 - cos ⁡ 2 x x . 1 1 + cos ⁡ 2 x = l i m x → 0 2 | sin ⁡ x | x . 1 1 + cos ⁡ 2 x Now, we have L H L = l i m x → 0 - 2 sin ⁡ x x . 1 1 + cos ⁡ 2 x = - 2 . 1 2 = - 1 R H L = l i m x → 0 2 sin ⁡ x x . 1 1 + cos ⁡ 2 x = 2 . 1 2 = 1 ∵ L H L ≠ R H L Hence, limit does not exist.

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