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

Options

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

Answer

B

Explanation

`underset(xto0)(lim)(1)/(1-e^(-1//x))`
`=underset(xto0)(lim)(1)/(1-e^(-1//0))=(1)/(1-(1)/(e^(oo)))=1`
and `f(0)=0`
`impliesunderset(xto0)(lim)(1)/(1-e^(-1//x))nef(0)`
`therefore` Function is not continuous at x=0.