Demonstrating epsilon-delta definition with powers of 2

[likeke]

My textbook gives alot of quadratic functions to prove with epsilon-delta definition. Can you create a video that shows how to prove one of these problems?

like:



it shows something like this




For (1,3)


Where did 5 come from?

[mike]

Sure, I can make a video for that. I'll probably have time today. Once I make the video I'll respond in this forum with the link.

All the Best,
Mike

[mike]

Hey, I've been really busy and somethings came up last minute. I should be able to make the video this weekend though.

M.

[likeke]

Looking forward to it

[mike]

Here you go!

Links:
(4th video)

[likeke]

Great explanation. Thank you!

I found out that it helps to quickly review the rules of rewriting inequalities in order to understand the definition better.

Assume





OR

^^ not sure if that's right or not. Tried to be a little fancy.

[mike]

[likeke]

Let OR

I don't think needs to be restricted to because will be greater when or when

[mike]

I'm not exactly sure what you mean, but here are a couple of comments. When defining elements, like make sure that what you're defining is really an element. What you have is , but is a set and so it can not be an element of What I think you meant was, let or equivalently, let and

Also, when I stated the theorem, I forced just to save time. If you let be any real number than you should consider 2 cases, if then |x| < a is satisfied vacuously.

But all in all these are probably overly technical details. You've had the right ideas all along and that's the most important part.

If you want to see the proof of the theorem I stated in my first response let me know.

All the Best!
M.