How do I find g?(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Precise Definition of a Limit

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