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

At x = 0,
LHL `" "underset(hto0)lim(1)/(1-e^(-1(0-h)))`
`=underset(hto0)lim(1)/(1-e^(1//h))=0`
RHL `" "=underset(hto0)lim(1)/(1-e^(-1(0+h)))`
`=underset(hto0)lim(1)/(1-e^(-1//h))=1`
`:.` Function is not continuous at
`x=0`.