Let $f$ be the function whose graph is given below.

(a). Use this graph to find the largest number $\delta > 0$ such that $$\text{if} \qquad 0<\left|x-3\right| < \delta \qquad \text{then} \qquad \left| f(x) - 6 \right| < 3 \;.$$ (Enter dne if no such $\delta$ exists.)

$\delta =$

(b). Use the graph to find the largest number $\delta > 0$ such that $$\text{if} \qquad 0<\left|x-3\right| < \delta \qquad \text{then} \qquad \left| f(x) - 6 \right| < 0.5 \;.$$ (Enter dne if no such $\delta$ exists.)

$\delta =$