Answer
$\delta=0.1$
Work Step by Step
Find a $\delta\gt0$ such that for all $x$ $$0\lt (x-5)\lt\delta\Rightarrow|f(x)-6|\lt0.2$$
Looking at the graphs, we can see that for values of $f(x)$ to be restricted between $5.8$ and $6.2$ (which is $|f(x)-6|\lt0.2$), $x$ must be placed between $4.9$ and $5.1$.
And since $5.1-5=0.1$, that means $0\lt (x-5)\lt0.1$.
Therefore, $\delta=0.1$ (or any smaller positives number is also fine).
