Single Variable Calculus, Chapter 2, 2.2, Section 2.2, Problem 5

Find the value of each quantity if it exist by using the given graph of $f$. If it does not exist, explain why.


$
\begin{equation}
\begin{aligned}
\text{a.) }& \lim\limits_{x \rightarrow 1^-} f(x)\\
\text{b.) }& \lim\limits_{x \rightarrow 1^+} f(x)\\
\text{c.) }& \lim\limits_{x \rightarrow 1} f(x)\\
\text{d.) }& \lim\limits_{x \rightarrow 5} f(x) \\
\text{e.) }& f(5)
\end{aligned}
\end{equation}
$





a. Referring to the graph given $\lim\limits_{x \rightarrow 1^-}f(x) = 2$

b. Reffering to the graph given $\lim\limits_{x \rightarrow 1^+} f(x) = 3$

c. Reffering to the graph given $\lim\limits_{x \rightarrow 1} f(x)$ does not exist because left and right limit are different

d. Reffering to the graph given $\lim\limits_{x \rightarrow 5} f(x) = 4$

e.Reffering to the graph given $f(5)$ does not exist because the function is not defined at that point.