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The value of l i m x → 0 c o s tan ⁡ x - cos ⁡ x 4 x 4 is equal to

Options

  1. A- 1 3
  2. B- 1 12
  3. C1 2
  4. D1

Correct answer

B. - 1 12

Step-by-step solution

c o s tan ⁡ x - cos ⁡ x = 2 s i n x + tan ⁡ x 2 s i n x - tan ⁡ x 2 ⇒ l i m x → 0 c o s tan ⁡ x - cos ⁡ x 4 x 4 = l i m x → 0 2 s i n x + tan ⁡ x 2 s i n x - tan ⁡ tan ⁡ x 2 4 x 4 = l i m x → 0 2 s i n x + tan ⁡ x 2 s i n x - tan ⁡ x 2 4 x 4 x + tan ⁡ x 2 x - tan ⁡ x 2 x 2 - t a n 2 x 4 = 1 8 l i m x → 0 x 2 - t a n 2 x x 4 = 1 8 l i m x → 0 x 2 - x + x 3 3 + 2 15 x 5 + . . . . 2 x 4 = 1 8 l i m x → 0 1 x 2 1 - 1 + x 2 3 + 2 15 x 4 + . . . . 2 = - 1 12

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