Answer
We can let $~~\delta = 0.3$
Work Step by Step
Let $f(x) = \frac{2x}{x^2+4}$
On the graph, we can see that when $\vert x-1 \vert \lt 0.3$, then $\vert \frac{2x}{x^2+4}-0.4\vert \lt 0.1$
Therefore, we can let $\delta = 0.3$
We can verify this as follows:
$f(0.7) = \frac{2(0.7)}{(0.7)^2+4} = 0.31$
Note that $\vert 0.31 -0.4 \vert \lt 0.1$
$f(1.3) = \frac{2(1.3)}{(1,3)^2+4} = 0.457$
Note that $\vert 0.457 -0.4 \vert \lt 0.1$
