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

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avshvkBest ResponseYou've already chosen the best response.0
\[f(x) = \frac{e^{1/x}}{ 1+ e^{1/x} }, if x \neq 0\]
 10 months ago

Abhishek619Best ResponseYou've already chosen the best response.0
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.
 10 months ago

Abhishek619Best ResponseYou've already chosen the best response.0
does the left limit exists?
 10 months ago

avshvkBest ResponseYou've already chosen the best response.0
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??
 10 months ago

Abhishek619Best ResponseYou've already chosen the best response.0
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.
 10 months ago
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