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Manipal MET2016MathematicsContinuity and Differentiability

If the function f(x)= array cc ( x)^ 1 / x , & x 0 k, & x=0 array . is continuous at x=0 , then the value of k is

Options

  1. A8
  2. B1
  3. C-1
  4. DNone of these

Correct answer

B. 1

Step-by-step solution

For f(x) to be continuous at x=0 , we must have _ x 0 f(x)=f(0) _ x 0 ( x)^ 1 / x =k _ x 0 1+( x-1) ^ 1 / x =k e^ _ x 0 x-1 x =k e^ - _ x 0 2 ^2 x / 2 x =k array ll & e^0=k & k=1 array

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