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The function f(x)={((|x|(3e^(1//|x|)+4)...

The function
`f(x)={((|x|(3e^(1//|x|)+4))/(2-e^(1//|x|)),x ne 0),(0, x =0):}`

A

differentiable at x=0

B

non-differentiable at x=0

C

not continuous at x=0

D

Cannot be determined

Text Solution

Verified by Experts

The correct Answer is:
A
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Knowledge Check

  • Let f(x)=(|x|(3e^(1//|x|)+4))/(2-e^(1//|x|)),x ne 0 and f(0)=0 then

    A
    f is not continuous
    B
    f is continuous but not differentiable at x = 0
    C
    `f'(0)` exist
    D
    `f'(0+)=2`

  • On the interval [-2,2] the function: f(x) = {{:((x+1)e^(-{1/|x|+1/x}), x ne 0),(0, x =0):}

    A
    is continuous for all `x in Z`
    B
    is continuous for all `x in Z- {0}`
    C
    assumes all intermediate values from f(-2) to f(2)
    D
    has a maximum value equal to `3/e`.

  • Let f (x)= [{:((x(3e^(1//x)+4))/(2 -e^(1//x)),,,( x ne 0)),(0 ,,, x=0):} x ne (1)/(ln 2) which of the following statement (s) is/are correct ?

    A
    f (x) is continous `at x=0`
    B
    ` f (x)` is non-dervable at `x=0`
    C
    `f'(0^(+))=-3`
    D
    `f '(0^(-))` does not exist

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    For the function f(x) = f(x)={((e^(1//x)-1)//(e^(1//x)+1),xne0),(0,x=0):} x=0, which of the following is correct :

    For the function f(x) = f(x)={((e^(1//x)-1)//(e^(1//x)+1),xne0),(0,x=0):} x=0, which of the following is correct :

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