Single Variable Calculus, Chapter 2, 2.2, Section 2.2, Problem 7

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


$
\begin{equation}
\begin{aligned}
\text{a.) }& \lim\limits_{t \rightarrow 0^-} g(t) &
\text{b.) }& \lim\limits_{t \rightarrow 0^+} g(t) &
\text{c.) }& \lim\limits_{t \rightarrow 0} g(t)\\

\text{d.) }& \lim\limits_{t \rightarrow 2^-} g(t) &
\text{e.) }& \lim\limits_{t \rightarrow 2^+} g(t) &
\text{f.) }& \lim\limits_{t \rightarrow 2} g(t) \\

\text{g.) }& g(t) &
\text{h.) }& \lim\limits_{t \rightarrow 4} g(t)
\end{aligned}
\end{equation}
$





a. According to the graph given $\lim\limits_{t \rightarrow 0^-} g(t) = -1$

b. According to the graph given $\lim\limits_{t \rightarrow 0^+} g(t) = -2$

c. According to the graph given $\lim\limits_{t \rightarrow 0} g(t)$ does not exist because
$\lim\limits_{t \rightarrow 0^-} g(t)$ doest not equal $\lim\limits_{t \rightarrow 0^+} g(t)$

d. According to the graph given $\lim\limits_{t \rightarrow 2^-} g(t) = 2$

e. According to the graph given $\lim\limits_{t \rightarrow 2^+} g(t) = 0$

f. According to the graph given $\lim\limits_{t \rightarrow 2} g(t)$ does not exist because left and right limits are different.

g. According to the graph given $g(2) = 1$

h. According to the graph given $\lim\limits_{t \rightarrow 4} g(t) = 3$