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If l i m x → 0 sin ⁡ 2 x - a sin ⁡ x x 3 exists finitely, then the value of a is

Options

  1. A0
  2. B2
  3. C1
  4. D4

Correct answer

B. 2

Step-by-step solution

l i m x → 0 sin ⁡ x 2 cos ⁡ x - a x ⋅ x 2 = l i m x → 0 sin ⁡ x x 2 cos ⁡ x - a x 2 For this limit to exists finitely, l i m x → 0 2 cos ⁡ x - a x 2 = f i n i t e ∴ It must be 0 0 form ∴   2 cos ⁡ 0 - a = 0 ⇒ a = 2

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