The Limit Example from Class

$$ % Define colors used throughout LaTeX explanation \require{color} \definecolor{error}{RGB}{ 255, 0, 0 } \definecolor{taylor}{RGB}{ 0, 0, 255 } \definecolor{estimate}{RGB}{ 160, 80, 0 } \definecolor{normal}{RGB}{ 0, 0, 0 } % i.e. black \definecolor{builtin}{RGB}{ 0, 180, 0 } $$

In class, we proved that $ \displaystyle \lim_{x \rightarrow 2} \frac{1}{x} = \frac{1}{2} $ by finding the following function that could serve as the witness for the existential quantifier of $ \color{taylor} \delta \color{normal} $ in the definition of the limit:

function delta( epsilon ) {

}

You may edit the code in the above window. Once done, it and then adjust the $ \color{error} \varepsilon \in ( 0, 1 ) \color{normal} $ as needed:

If you get everything right, the blue portion of the graph (the one between the two blue vertical lines)^* must stay inside of the red (meaning the horizontal) strip.

^* If you don't see the blue vertical lines and the blue portion of the graph between them, you probably forgot to load the code in the window.