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If f(0) = 0 and f(x) =(1)/((1-e^(-1//x))...

If f(0) = 0 and `f(x) =(1)/((1-e^(-1//x))) " for " x ne 0.` Then, only one of the following statements on f(x) is true. That is f(x) is

A

continuous at x = 0

B

not continuous at x = 0

C

both continuous and differentiable at x = 0

D

not defined at x = 0

Text Solution

Verified by Experts

The correct Answer is:
B
`lim_(x to 0) (1)/(1-e^(-1//x))=lim_(x to 0) (1)/(1-(1)/(e^(1//x)))=(1)/(1-(1)/(e^(oo)))=1`
`and f(0)=0 rArr lim_(x to 0) (1)/(1-e^(-1//x)) ne f(0)`
`therefore` Function is not continuous at x = 0.
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