Single Variable Calculus, Chapter 2, 2.2, Section 2.2, Problem 6

The graph function $h$ is given, state the value of each quantity, if it exists. If it does not exist, explain why.


$
\begin{equation}
\begin{aligned}
\text{a.) }& \lim\limits_{x \rightarrow -3^-} h(x) &
\text{b.) }& \lim\limits_{x \rightarrow -3^+} h(x)&
\text{c.) }& \lim\limits_{x \rightarrow -3} h(x)\\

\text{d.) }& h(-3) &
\text{e.) }& \lim\limits_{x \rightarrow 0^-} h(x) &
\text{f.) }& \lim\limits_{x \rightarrow 0^+} h(x) \\

\text{g.) }& \lim\limits_{x \rightarrow 0} h(x) &
\text{h.) }& h(0) &
\text{i.) }& \lim\limits_{x \rightarrow 2} h(x) \\

\text{j.) }& h(2)
\end{aligned}
\end{equation}
$






a. Referring to the graph given $\lim\limits_{x \rightarrow -3^-} h(x) = 4$

b. Referring to the graph given $\lim\limits_{x \rightarrow -3^+} h(x) = 4$

c. Referring to the graph given $\lim\limits_{x \rightarrow -3} h(x) = 4$

d. Referring to the graph given $h(-3)$ does not exist because the value at that point is not defined, it is an empty circle.

e. Referring to the graph given $\lim\limits_{x \rightarrow 0^-} h(x) = 1$

f. Referring to the graph given $\lim\limits_{x \rightarrow 0^+} h(x) = -1$

g. Referring to the graph given $\lim\limits_{x \rightarrow 0} h(x)$ does not exist because
$\lim\limits_{x \rightarrow 0^+} h(x)$ does not equal $\lim\limits_{x \rightarrow 0^-} h(x)$

h. Referring to the graph given $h(0) = 1$

i. Referring to the graph given $\lim\limits_{x \rightarrow 2} h(x) = 2$

j. Referring to the graph given $h(2)$ does not exist because the function is not defined at that point.