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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

Calculus1
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\[f(x) = \frac{e^{1/x}}{ 1+ e^{1/x} }, if x \neq 0\]
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.
does the left limit exists?

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Other answers:

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??
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.

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