Question: Consider the function \[f(x)=\left\{ \begin{aligned} & x \\ & 1 \\ & 3 \\ \end{aligned} \right.\] \[\begin{matrix}

\text{if}\ x<3 \\

\begin{aligned} & \text{if}\ x=3 \\ & \text{if }x>3 \\ \end{aligned} \\

\end{matrix}\] whose graph is shown below. Find the value of each limit, if it exists.

(a) \[\underset{x\to {{3}^{+}}}{\mathop{\lim }}\,f(x)\]

(b) \[\underset{x\to {{3}^{-}}}{\mathop{\lim }}\,f(x)\]

(c) \[\underset{x\to 3}{\mathop{\lim }}\,f(x)\]