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The value of f 0 , such that f x = 1 x 2 1 - c o s s i n x can be made continuous at x = 0 , is

Options

  1. A1 2
  2. B2
  3. C1 4
  4. D4

Correct answer

A. 1 2

Step-by-step solution

lim x → 0 ⁡ 1 - c o s s i n x x 2 = lim x → 0 ⁡ 2 sin 2 ⁡ s i n x 2 x 2 lim x → 0 2 . sin sin x 2 sin x 2 2 . sin x 2 x 2 = 1 2 ⁡ Thus, for continuity at x = 0 , f ( 0 ) = 1 2

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