I am having some trouble showing $ \lim_{ x \rightarrow 4} \frac{1}{\sqrt{x}} = \frac{1}{2}. $
I chose $\delta$ to be the minimum of $(\frac{2}{1+2\epsilon})^2 - 4$ and $ 4 - (\frac{2}{1-2\epsilon})^2$. It works and was inspired by a picture, but I feel there is an easier trick.