Question

$f\left(x\right)=1/(1-e^{-1/x}),x\ne 0$ If f is continuous at $x=0$ then, Find f(0)

Answer 1

$f\left(x\right)=\frac{1}{1-e^{-1/x}},x\ne 0$
If $f\left(x\right)$ is continuous at $x=0$ then
$f\left(0\right)=\underset{x\to 0}{lim}\frac{1}{1-e^{-1/x}}=\frac{1}{1-1/\infty }=1$