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Manipal MET2016MathematicsContinuity and Differentiability

If f(x)= e^ 1 / x -1 e^ 1 / x +1 , x 0 and f(0)=0 , then f(x) is

Options

  1. Aleft continuous at 0
  2. Bright continuous at 0
  3. Cdiscontinuous at 0
  4. Dcontinuous at 0

Correct answer

C. discontinuous at 0

Step-by-step solution

f^ (0⁻ )= _ h 0 f(0-h) f^ (0⁻ )= _ h 0 e^ -1 / h -1 e^ 1 /-h +1 array ll & f^ (0⁻ )= 0-1 0+1 & f^ (0⁻ )=-1 array and f^ (0⁺ )= _ h 0 f(0+h)= _ h 0 e^ 1 / h -1 e^ 1 / h +1 f^ (0⁺ )= 1-0 1+0 =1

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