f(x) = e^(1/x) / (1+ e^(1/x)) except x=0
and 0 if x=0
find whether f(x) is continuous

Question

f(x) = e^(1/x) / (1+ e^(1/x)) except x=0
and 0 if x=0
find whether f(x) is continuous

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

does the left limit exists?

anonymous · Answer

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??

anonymous · Answer

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.