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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0check 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
 3 years ago
Best ResponseYou've already chosen the best response.0does the left limit exists?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0no 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
 3 years ago
Best ResponseYou've already chosen the best response.0left 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.
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