Epsilon - Delta Proof (precise definition of the limit)

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Prime Newtons

5 ай бұрын

In this video, I showed how to use the precise definition of a limit to prove it using epsilon -delta

Пікірлер: 99

@JourneyThroughMath 5 ай бұрын

I think my biggest confusion has always been, it doesnt seem like weve proven anything but rather generalized the relationship between epsilon and delta. Would it be possible to get a video where this definition fails. Say the limit of 1/x as x approaches 0 is undefined?

@AutoDisheep 4 ай бұрын

That is a great point! This is why it was so frustrating to work with real analysis.

@kingbeauregard 4 ай бұрын

sin(1/x) as x approaches 0. I look at it like this. A function is continuous at a given point if you can draw a rectangle around that point such that the function doesn't hit the top or bottom edge, AND you can shrink that rectangle down to nothing without the function hitting the top or bottom edge. If you can do that, then the function is continuous. Epsilon-delta is a matter of stating with confidence, "if the dimensions of the rectangle are two-epsilon high by two-delta wide, the function won't touch the top or bottom edge no matter how small you shrink it". Note that it's okay to change the shape of the rectangle as it shrinks, just so long as the width and height hit zero at the same time.

@repsaknivek 2 ай бұрын

Fantastic. You’re the only person on the internet that does all three parts: 1.) outline the formal definition. 2.) explain WHY you MUST choose certain things and why you MUST set up equations a certain way, because of what exactly you’re shooting for. 3.) work through an example while explaining “2.)”. Everyone else has a video explaining “1.)” or else does a video showing “3.).” But nobody except you does “2.)”, so we all end up like mindless robots simply imitating by doing the steps in “3.)” without really understanding why we are doing it that way (which means “1.)” was pointless - because we don’t get the connection between the formal definition and the problem solving). You’re the only person that provides the mental bridge between the theory and the practical, so we can be mentally equipped with theory only (as it should be) and use it as a proper weapon to defeat the problems given to us in our classwork. So thank you very much. Nobody else explains what we have to shoot for and why we have to shoot for it (how the theory/definition works.) Bravo.

@brendanward2991 5 ай бұрын

Epsilon is on the y-axis, delta on the x-axis. I never really got that ... until today. Thanks.

@the_informative_edge 4 күн бұрын

Epsilon and delta are both radius of open intervals on x-axis and y-axis. How they are on x and y axis?

@tembomathematician3814 5 ай бұрын

My whole lectures I could just hear two words EPSILON and DELTA the rest is history. But thanks to you man you have made it simple. Thanks

@jensberling2341 5 ай бұрын

Wonderfully explained. It reminded me that using a definition in a proof requires an if and only if proof. And that is what you just did. It is so easy and elegant explained. Thank you

@zeyohabesha4628 5 күн бұрын

You are such an amazing teacher that i have ever know Keep going Prime ! One of your student from Ethiopia.

@blackovich 5 ай бұрын

Thank you again. You always deliver the best explanation.

@Anandulasida 7 сағат бұрын

Appreciate your enthusiasm ❤

@user-bt1bj1mq2m 3 ай бұрын

Thank you prime network as you said never stop learning and I tell you never stop giving the good explanations✍️✍️✍️

@jensberling2341 2 ай бұрын

Thank you. The way you explain that to choose the shorter distance for delta to be within the range of epsilon is essential to understand the epsilon-delta proof is mind opening. Thank you again. I rejoice in understanding this kind of proofs.

@migfed 3 ай бұрын

This man deserves at the very least a plaque on the moon 🎉

@herbertsusmann986 2 ай бұрын

This is probably the best math channel I have found on KZfaq!

@tsitso24 4 ай бұрын

Kea leboha Monghali. All the way from Lesotho🇱🇸

@mahmoodhussam5866 3 ай бұрын

مبدع و متألق استاذ ابو العبد، عندي امتحان رياضيات اليوم وفعلا انقذتني. ربي يوفقك ويحفظك بحق محمد وال محمد

@sohaalavi8743 2 ай бұрын

Thankyou so much man ! ❤ great way to deliver lecture ❤

@Yoavlevavi Ай бұрын

Defiantly deserves a subscription.

@musicphysics-mathematicsfu1840 3 ай бұрын

This guy is a WIZARD! He uses his wizardry to " heal" Mathematics patients! Kudos,Newton a.ka. NEW-THING ( in your maths tutoring!) I hope we meet in person someday...I need to give you a handshake! Orekoya olusegun,University of Ibadan,Nigeria,W/A

@PrimeNewtons 3 ай бұрын

You rock!

@WaneesaGrant 5 ай бұрын

Such a cute aesthetic perf ✨

@vincentmudimeli4430 2 ай бұрын

great explanation and you always make maths enjoyable

@victoravwerosuogheneokoro8179 3 ай бұрын

God bless you for me, u literally made my day ❤🙏

@poucatelha1983 11 күн бұрын

This was so very helpful. Thank you!

@solardale7908 Ай бұрын

for the best understanding of this concept, you also need to show an example where the limit fails. Nice channel

@lkern6238 5 ай бұрын

Nicely explained.❤

@blakeklemenhagen7920 3 ай бұрын

Super helpful! Thank you so much!

@cerysmiller6716 5 ай бұрын

I think people would love this 💕

@goymath 5 ай бұрын

Well presented Sir👍

@trelosyiaellinika 5 ай бұрын

I think it's the ε & δ that bring the confusion into play when you fail to see their association to the y & x on their respective axes... It's the same as saying for every dy>0 there is a dx>0 such that 0

@aravindhvijayanandan3010 4 ай бұрын

i don't think its dx and dy, it is delta(x) and delta(y)

@sana_136 22 күн бұрын

Thank you sir really helpful, God bless you ♥️

@emilybird9761 5 ай бұрын

Fine & sweet,This is delightful

@user-ds7po7kc7j 5 ай бұрын

very very thanks to for this video. really so so helpful for me ,and finally this definition made clear sense for me. i get finally understand very well what this defniton is states after 3 weeks:Dddd thansk so you for this video

@punditgi 4 ай бұрын

Prime Newtons always shows the way! 🎉😊

@SizakeleMaphumulo 2 ай бұрын

YOU ARE THE BEST THANKYOU SO MUCH

@user-ml8we4cl8g 5 ай бұрын

Hello there sir, I have been watching you for a long time, and i am quite glad to see your channel to make such a good progress. I want to ask you some questions regarding mathematics but i dont know where to write to you about it, can u help me with this, sir?

@PrimeNewtons 5 ай бұрын

Please send me an email. Primenewtons@gmail.com

@sunilbiswas2301 Ай бұрын

It's Amazing.

@DustinaWatkins 5 ай бұрын

Yes 👏🏻👏🏻👏🏻👏🏻👏🏻 love it 😍

@vaibhavpandey7798 4 ай бұрын

Love from India ❤

@VytalParks 5 ай бұрын

Magnificent

@fitover-hw4mw 3 ай бұрын

Thank you ❤

@y_auc60seb20 4 ай бұрын

Fantastic explanation of the definition of a Limit

@PrimeNewtons 4 ай бұрын

Glad it was helpful!

@michaelnaholo Ай бұрын

Thanks a lot 🙏

@brendawilliams8062 20 күн бұрын

That’s a good show and explanation. It’s a strange way to do it

@AntonneNash 5 ай бұрын

you're my idol💕 LOVE YOU TO THE MILKY WAY AND BACK #love #Videosoftheday

@user-kq7jb6rh5f 4 ай бұрын

thank you

@MenbereMena-pr3ek 14 күн бұрын

Thanks mister ❤

@evaatkinson7932 5 ай бұрын

Most Important for me 🙏😙😙💘

@DonnaQuinn-ic6fr 5 ай бұрын

ohhhhhh lord Sooooooo spectacular

@ArioGraham 5 ай бұрын

Very nice😋👏

@sibor5576 5 ай бұрын

Thank you

@nanamacapagal8342 5 ай бұрын

I wonder how square roots and cube roots would work with the definition of limit? I can figure out lim_x->64(sqrt(x)) = 8 but not lim_x->64(cbrt(x) + sqrt(x)) = 12

@mikefochtman7164 5 ай бұрын

Maybe those last two lines could be changed. Once you have the RHS as < 4*delta, then the next line would be

@PrimeNewtons 5 ай бұрын

I used to think so too, but using < will have a different meaning. An alternative is to write them on the same line.

@YordanosYohans-jb9jp Ай бұрын

i like it was help full🙏

@ShaleighFerguson 5 ай бұрын

✌✌Amazing 😍

@user-so5ir7ul9v 5 ай бұрын

Think you bro

@YiannisHeard 5 ай бұрын

Ideal💣

@dydx_mathematics2 5 ай бұрын

❤❤

@klaraprice2355 5 ай бұрын

So very Fabulous😍💘

@ShaquiraMack 5 ай бұрын

I Like your video

@user-sw7rw3px6n 5 ай бұрын

wass very helpful

@sadeqirfan5582 3 ай бұрын

Nice, but still a little short. It would be even better if you had explained the meaning of “there exists” and “for all”. Epsilon is arbitrary. For any epsilon greater than 0 we pick there should be a delta with that condition. People need to understand this to really understand the concept of limit. I enjoy your videos. Thanks.

@omargaber3122 5 ай бұрын

I never thought I'd ever understand that one day. It's been ten years since I watched that ridiculous nightmare (Epsilon and Delta) at university😅

@ParasJee-jc3zm 3 ай бұрын

Genius mind.

@h1a8 4 ай бұрын

When doing proofs always define the variables and constants. Let e>0 Here’s my proof: Let e>0 and x =/= 3 Let d=e/4 So |x-3|

@DonjaeHarmon 5 ай бұрын

Fab Videos

@ti84satact12 5 ай бұрын

It seems like we’re playing a shell game!

@emilyhumphreys6110 5 ай бұрын

CHEERS!!✨

@MusaJamel 28 күн бұрын

❤❤❤

@DeveronMorrison 5 ай бұрын

You 👍 should be proud of yourself

@tebohomokejane6414 3 ай бұрын

The whole tutorial made sense to me, but I am a little bit confused on that part where you changed 4 times an absolute of x-3 to 4 times delta. What actually happened there, sir?

@WaneesaHoward 5 ай бұрын

Qué hermosa😍❣️💗💜

@JamettaWillis 5 ай бұрын

💚

@WaneesaGrant 5 ай бұрын

OMG💜

@AlimaPrice 5 ай бұрын

Bravo 🎅 👧 👷

@ZulqarnaynAkologoSalam 3 ай бұрын

How can we prove that this same limit I not equal to say 12 or anything apart from 11....

@KeantayRoberson 5 ай бұрын

Aww🙏 💕💓 so Cute

@mikefochtman7164 5 ай бұрын

Soooo.... if I have a really simple function like f(x) = 3 (a horizontal line), then the limit as x->10 f(x) does not exist? I mean, f(x) is always 3, but the limit doesn't exist because no value of delta can give me an epsilon greater than zero?!?! I know this is somewhat contrived, but if epsilon has to be greater than zero, it can't work in this function??

@PrimeNewtons 5 ай бұрын

You are mixing them up. Since there is no epsilon greater than zero, we don't have to worry about delta. Any delta will work. So there are infinitely many deltas.

@ti84satact12 5 ай бұрын

I think an example of where the limit DOES NOT exist would be useful!

@user-bd3vc6ih1z 27 күн бұрын

Do you know many Ethiopians admire you?

@PrimeNewtons 27 күн бұрын

That's a great honor. I play soccer weekly with many Ethiopian friends. Amazing people.

@SenaDebisa 15 күн бұрын

Yea I swear to God I never see teacher like u thanku we love u do much am also from Ethiopia

@angelgray8899 2 ай бұрын

ASM vibes

@Perfect_cut44 Ай бұрын

im watching this video at 3am😂😂felt like someone will wake up and say it was just a nightmare

@PrimeNewtons Ай бұрын

Sleep well

@Perfect_cut44 Ай бұрын

@@PrimeNewtons you explained well brother,😌

@mircoceccarelli6689 Ай бұрын

👍👍👍😁🤪👋

@comdo777 5 ай бұрын

answer=1 xd

@chiensyang 23 күн бұрын

You look more like a golfer rather than a mathemaician.

@sazan-ga-9 5 ай бұрын

I’m sorry, but are you so kind to help me to solve this problem？ If you don't mind, I would like you to explain it in a video. ￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣ f(x)=x³+ax²+bx+c (a,b,c∈R) (∀α):f(α)=0⇒f(α³)=0 (α∈C) (a,b,c)=？ (from Kyoto Uni.)