## avshvk Group Title f(x) = e^(1/x) / (1+ e^(1/x)) except x=0 and 0 if x=0 find whether f(x) is continuous one year ago one year ago

1. avshvk Group Title

$f(x) = \frac{e^{1/x}}{ 1+ e^{1/x} }, if x \neq 0$

2. Abhishek619 Group Title

check if the right and the left limit exists and are defined, and if the limits are equal tot he functional value at x=0, then it is continuous at x=0.

3. Abhishek619 Group Title

does the left limit exists?

4. avshvk Group Title

no idea if we apply limit for e^(1/x) then it will be e^infinity which is equal to inifinity but f(0)=0. Therefore f(0) neq to limit, hence it is discontinuous at x=0. Not sure whether my solution is correct or not??

5. Abhishek619 Group Title

left limit=0, right limit=1 hence both the limits exists, but are not equal. If at all there exists a functional value, it is of no use, because left limit is not equal to right limit to check the continuity of the function. hence, the function is discontinuous at x=0.