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The value of l i m x → 0 sec ⁡ x - sec ⁡ x s e c x 1 - sec ⁡ x + ln ⁡ sec ⁡ x is equal to

Options

  1. A0
  2. B1
  3. C2
  4. D- 1

Correct answer

C. 2

Step-by-step solution

Let, sec ⁡ x = t l i m t → 1 t - t t 1 - t + ln ⁡ t = l i m t → 1 1 - t t ( 1 + ln ⁡ t ) - 1 + 1 t by L-hospital rule = l i m t → 1 - t t 1 t - t t 1 + ln ⁡ t 2 - 1 / t 2 again by L-hospital rule = - 1 - 1 - 1 = 2

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