Single Variable Calculus, Chapter 2, 2.2, Section 2.2, Problem 11

State the value of each limit using the graph of the function $\displaystyle f(x) = \frac{1}{(1 + 2^{\frac{1}{x}})}$, if it exists. If it does not exist, explain why.


$
\begin{equation}
\begin{aligned}
a.)& \lim\limits_{x \rightarrow 0^-} f(x) \\
b.)& \lim\limits_{x \rightarrow 0^+} f(x)\\
c.)& \lim\limits_{x \rightarrow 0} f(x)
\end{aligned}
\end{equation}
$










a. According to the graph $\lim \limits_{x \to 0^-} f(x) = 1$

b. According to the graph $\lim \limits_{x \to 0^+} f(x) = 0$

c. According to the graph $\lim \limits_{x \to 0} f(x)$ does not exist because the left and the right limits are different.