How do I find g? It's so confusing. I'm trying to learn this on my own, so bare with me. I'm going with an example I know the answer to, and maybe someone can work with me here. I'll ask questions through the solution. We will do x^3 since that is complicated enough, but I understand the steps, just not the logic to moving on to the next step. [tex]|x^3-a^3|<e[/tex] [tex]0<|x-a|<g[/tex] Find a value for g that satisfies the above. [tex]|x^3-a^3|=|x-a||x^2+ax+a^2|[/tex] [tex]|x^2+ax+a^2|<=|x|^2+|a||x|+|a|^2[/tex] Note: [tex]|x|-|a|<=|x-a|<1[/tex] If you don't understand why one is chosen maybe this isn't for you. In case you forgot, we take 1 because that guarantees that the difference won't be too big. [tex]|x|<1+|a|[/tex] Take the above and you get... [tex](1+|a|)^2+|a|(1+|a|)+|a|^2 WARNING: This is in the works. I will be back to complete it.