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The value of lim x → 0 ⁡ 1 x 18 1 - cos ⁡ x 3 3 - cos ⁡ x 6 6 + cos ⁡ x 3 3 ⋅ cos ⁡ x 6 6 is λ 2 , then the value of 900 λ is equal to (here, λ > 0 )

Correct answer

25

Step-by-step solution

lim x → 0 ⁡ 1 - cos ⁡ x 3 3 - cos ⁡ x 6 6 1 - cos ⁡ x 3 3 ⋅ 1 x 18 lim x → 0 ⁡ 1 - cos ⁡ x 3 3 1 - cos ⁡ x 6 6 x 18 lim x → 0 ⁡ 1 - cos ⁡ x 3 3 x 3 3 2 x 6 9 ⋅ 1 - cos ⁡ x 6 6 x 6 6 2 ⋅ x 6 6 2 ⋅ 1 x 18 lim x → 0 ⁡ 1 2 × x 6 9 ⋅ 1 2 ⋅ x 12 36 ⋅ 1 x 18 = 1 36 2 ∴ λ = 1 36

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