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If f x = x p cos ⁡ 1 x , x ≠ 0 0 , x = 0 is differentiable at x = 0 , then

Options

  1. Ap < 0
  2. B0 < p < 1
  3. Cp = 1
  4. Dp > 1

Correct answer

D. p > 1

Step-by-step solution

Given, f x = x p cos &#8289; 1 x , &#160; x &#8800; 0 &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; 0 , &#160; &#160; &#160; x = 0 Since, f ( x ) is differentiable at x = 0 , therefore it is continuous at x = 0 &#8756; &#160; l i m x &#8594; 0 &#160; f x = f 0 = 0 &#8658; &#160; l i m x &#8594; 0 &#160; &#160; x p cos &#8289; 1 x = 0 &#160; &#160; &#160; &#8658; &#160; &#160; &#160; &#160; p &#62; 0 As f x is differentiable at x = 0 &#8756; &#160; &#160; &#

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