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Let the function f x = x 2 sin ⁡ 1 x ∀ x ≠ 0 is continuous at x = 0 . Then, the value of the function at x = 0 is

Options

  1. A0
  2. B- 1
  3. C1
  4. Dindeterminate

Correct answer

A. 0

Step-by-step solution

For f x to be continuous at x = 0 , we must have f 0 = lim x → 0 ⁡ f x ⇒ f 0 = lim x → 0 ⁡ x 2 sin ⁡ 1 x = 0 × a finite quantity = 0 Hence, f 0 = 0 .

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