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If f(x)=(e^(1/x)-1)/(1+e^(1/x)) when x!=...

If `f(x)=(e^(1/x)-1)/(1+e^(1/x))` when `x!=0` `=0,` when `x=0` show that `f(x)` is discontinuous at `x=0`.

Answer

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Knowledge Check

  • If f(x)={((x)/(e^(1/x)+1),",","when" x != 0),(0,",","when"x = 0):} , then

    A
    `lim_(x to 0^(+)) f(x) = 1`
    B
    `lim_(x to 0^(-)) f(x) = 1`
    C
    f(x) is continuous at` x = 0`
    D
    f(x) is discontinuous at` x = 0`

  • If f(x)={:{((e^(1/x)-1)/(e^(1/x)+1)", for " x !=0),(1", for " x=0):} , then f is

    A
    continuous at `x=0`
    B
    discontinuous at `x=0`
    C
    continuous if `f(0)=-1`
    D
    discontinuous if `f(0)=-1`

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