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Let f x = x 3 x - 1 1 - cos ⁡ x for x ≠ 0 . Then value of f 0 , which make f x continuous at x = 0, is

Options

  1. Alog ⁡ 3
  2. B1 2 log ⁡ 3
  3. C1 2 log ⁡ 3
  4. D2 log ⁡ 3

Correct answer

D. 2 log ⁡ 3

Step-by-step solution

lim x → 0 ⁡ f x = lim x → 0 ⁡ x 3 x - 1 1 - cos ⁡ x = lim x → 0 ⁡ 3 x - 1 x ⋅ x 2 1 - cos ⁡ x = log ⁡ 3 ⋅ 1 1 2 = 2 log ⁡ 3

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