Hi, David! Thanks for leaving a comment. Sorry that I couldn’t answer sooner to your question.

Let \(f(x)=\exp(-x^{2})\). The function is monotone, decreasing and \(\lim_{x \to \infty}f(x)=0\).

Now let \(\exp(-\delta^{2})=x\). When \(\delta \to 0\) we have \(1 – \delta^{2} \approx x\). Thus \(\delta \approx \sqrt{1-x}\).