Epsilon -Delta proof for cubic function limit

In this video, I showed how to do epsilon-delta proof of limit of cubic function.

[CASWELLCHAUKE-vx]

one of the most underrated teachers of all time

[Kwinnbujik]

I really appreciate the way factor the cubic function.

Your prodigy in making hard things become completely livable is really unmatched.

[nothingbutmathproofs]

Wait a minute. Your answer is not 100% correct. Since you restricted |x-1|< 5, then your answer should be that delta = d = min{1, epsilon/5}. That is, if epsilon is greater than 5, then you choose d =1. if epsilon <5, then you choose d= epsilon/5.

[josephparrish]

This was always such a hard topic for my students to understand. You did an excellent job.

[izzaimi]

FINALLYY SOMEONE MADE VIDEO ABOUT THE CUBIC AND THE EXPLANATION WAS SOO PERFECTT LURVE LURVE LURVE!!!😭❤️❤️❤️

[anirbanpandit]

Man this is incredible, I wish i had you back in my college days. Till now i found this as the most effective and literally understandable video on yt. keep bringing up this type of videos...thanks a ton!

[WritersDigest-bf]

2:59
1. Write general Definition of a limit
4:06
2. Apply the if and then condition to the actual problem at hand from the general definition

Thank u

4:20
3. Scratch work - look for delta as a function of epsilon

13:00
4. Check the delta chosen as a function of epsilon to prove the limit.

|F(x) -L|< epsilon
QED

In short
For scratch work
|F(x)-L|
leads to delta as a function of epsilon
For proving the limit
Delta leads to epsilon using
|F(x)-L|?

[ochukoobrikogho]

You're doing a great job Sir. The clarity in explanation is what I enjoy

[amlalashhab]

أستاذ شرحك رائع أشكرك على كل شيء تقدمه
ارجو المزيد من الفيديوهات في هدا الموضوع
أتابعك من ليبيا 🇱🇾

[kingbeauregard]

Finally, an epsilon-delta video I like! And you're even wearing my favorite hat!

I really like your observation that there's always an |x-a| hiding in the |f(x) - f(a)|, and you have to get good at factoring it. This is where your videos on the definition of derivatives have trained us well, because we need to use the same skills: the ability to cope with "f(x+h) - f(x)" is pretty much what you need to cope with "f(x) - f(a)".

In my experience, the main problem people have with epsilon-delta is conceptual: it's hard to see why we're doing this "f(x) - f(a)" business. So I think of it like this: imagine a rectangle centered at (a, L) that is tall enough, and narrow enough, that the function f(x) never touches the top or bottom edges of the rectangle. Now, can you also shrink that rectangle down to any size, all the way down to nothing, and f(x) still never touches the top or bottom edges? If you can work out the geometry of a rectangle that makes that possible, then it means that "x" reliably gets closer to "a" as f(x) gets closer to "L". And if you can say that, then the limit exists.

The height of those rectangles is 2*epsilon (i.e. it goes from L - epsilon to L + epsilon), and the width of those rectangles is 2*delta (i.e. it goes from a - delta to a + delta). So that is the game, counterintuitively enough: if you can work out dimensions for the shrinking rectangle, then the limit exists.

From there, it is as you described: you factor out an |x-a| and then deal with the rest. To clean up that mess, there are two tricks you can use: you can limit your delta to a narrow region around "a" (in this case you used a value of "1"), and then you replace the entire mess with a value that you are confident will be larger than the mess in the narrow region. At that point, you're actually shifting to doing epsilon-delta on a different and simpler function, and then counting on squeeze proof logic: if your simpler function satisfies epsilon-delta, so must the original function.

We probably need to say that delta = min {1, epsilon / 5} so that we don't forget that we've restricted our deltas to that narrow region.

[WritersDigest-bf]

Could u do more epsilon delta proofs for functions with polynomial in numerator and denominator, many more slightly harder proof for square root, reciprocal functions, trigonometric functions.

Thank you so much, u educated with so much patience, love and a happy face, and explain every step.

[EE-Spectrum]

I love this. I just love it. Thanks for such a lucid explanation of the Epsilon-Delta limit.

[munashe]

this is very good. You are an excellent teacher

[MBVH]

Grazie per la spiegazzione così chiara e semplice, sei molto didattico per spiegare questi concetti astratti,

[AGTfan-seql]

Awesome video. Epsilon delta proofs were my favorite topic in advanced calculus

[marcbennet]

Je trouve votre style d'enseignement très sympathique et bien sûr efficace
(I find your teaching style very nice and of course effective).

[eastonpeter]

Regarding August 28, 2023 "Epsilon-Delta" proof of cubic function.
At 9:20 you presented an analogy/metaphor with "income and bills." Wonderful! Would it be possible with your busy schedule to continue the metaphor to the conclusion?

[silvo]

you are a amzaing teacher wow!. Keep posting!

[nurathirah]

OMG I LOVE THIS ONE !! REALLY II HELPFUL THANKYOU SO MUCH ❤❤❤❤

[WritersDigest-bf]

6:56
We can also divide (x to the power 3 - 2x +1) by x-1 and get
Thanks x to the power 2 +x-1 or

Or by equating the coefficients of same powers of x.
Thanks