Single Variable Calculus, Chapter 2, 2.2, Section 2.2, Problem 4

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


$\begin{equation} \begin{aligned} \text{a.) }& \lim\limits_{x \rightarrow 0} f(x)\\ \text{b.) }& \lim\limits_{x \rightarrow 3^-} f(x)\\ \text{c.) }& \lim\limits_{x \rightarrow 3^+} f(x)\\ \text{d.) }& \lim\limits_{x \rightarrow 3} f(x) \\ \text{e.) }& f(3) \end{aligned} \end{equation}$





a. Referring to the graph given $\lim\limits_{x \rightarrow 0} f(x) = 3$

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

c. Referring to the graph given $\lim\limits_{x \rightarrow 3+}f(x) = 2$

d. Referring to the graph given $\lim\limits_{x \rightarrow 3}f(x)$ does not exist because left and right limits are different.

e. Referring to the graph given $f(3) = 3$