Answer
(a) 1
(b) 0
(c) does not exist
Work Step by Step
$f(x)=\dfrac{1}{1+2^{1/x}}$
The first step to take is to graph the function (image attached below).
(a) As x goes to 0 from the left hand side, y approaches 1.
Therefore, $\lim\limits_{x \to 0^-}f(x)=1$
(b) As x goes to 0 from the right hand side, y approaches 0. Therefore, $\lim\limits_{x \to 0^+}f(x)=0$
(c) $\lim\limits_{x \to 0}f(x)$ does not exist because $\lim\limits_{x \to 0^-}f(x)\ne\lim\limits_{x \to 0^+}f(x)$
