I need help proving that $\frac{1}{x+2}$ is not uniformly continuous for $(-2,0]$, using an $ε-δ$ proof.
I understand that intuitively this is just the function $\frac{1}{x}$ which is not uniformly continuous on $(0,1)$ shifted 2 units to the left, but I am struggling as to how to write a technical proof.
Specifically, I am unsure what $f(x)$ and $δ$ I should use to prove that $|f(x)-f(y)|>ε$ when $|x-y|<δ$.