Determine the value for $c$ so that $\underset{x3}{lim}f(x)$ exists. $f(x)=\{\begin{array}{ccc}\frac{1}{3}x+c,& \text{f}\text{o}\text{r}& x<mn\; id="EditorElement\_3298140">3</mn>\\ -x+8,& \text{f}\text{o}\text{r}& x>3\end{array}$ The value of $c$ is