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NDA2020MathematicsContinuity and DifferentiabilityActual

If f(x)= x x , where x R , is to be continuous at x=0 , then the value of the function at x=0

Options

  1. Ashould be 0
  2. Bshould be 1
  3. Cshould be 2
  4. Dcannot be determined

Correct answer

B. should be 1

Step-by-step solution

As the given function is continuous at x=0 , then LHL = RHL _ x 0⁻ f(x)= _ x 0⁻ x x = _ x 0⁻ [ x 1 ]=1 _ x 0⁺ f(x)= _ x 0⁺ x x = _ x 0⁺ [ x 1 ]=1 x x at x=0 , should be 1 .

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