Epsilon - Delta Proof (precise definition of the limit)

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

[@JourneyThroughMath]

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]

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

[@kingbeauregard]

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.

[@tjalferes]

See: John Gabriel New Calculus

[@rollandzumba1264]

Good work! Feel appreciated sir

[@repsaknivek]

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.

[@PrimeNewtons]

Thank you

[@tembomathematician3814]

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

[@Lea-u4h]

thought i was alone broo...

[@GivenShokobishi-zt9lp]

Me too

[@brendanward2991]

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

[@the_informative_edge]

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

[@jensberling2341]

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

[@mahmoodhussam5866]

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

[@musicphysics-mathematicsfu1840]

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]

You rock!

[@Tee0313]

Struggled on this for 2 weeks Had consultation after consultation with my professor spanning over 2h ,there was a point where i even thought im dumb and math is not for me ,but this video explained this topic so clearly Thank you very much prime newtons 🎉

[@BasilElsydabi]

You are the best!!! It all finally clicked the confusion around this topic is completely gone. Thank you truly from the core of my heart I really appreciate you and the work you do.

[@LifeIsBeautiful_20]

I'm from India I've been struggling with this topic. Thanks for clearing my doubt. Tq sir..

[@diablo8776]

"Wow, this video is incredibly well-explained! You made a complex topic so much easier to understand. Thank you for breaking it down in such a clear and engaging way-I'm sure it's going to help a lot of people on their learning journey! Keep up the great work!"

[@cary_domiii]

By 15:05, I was totally mind-blown as to why the proof makes so much sense now....I can now confidently teach this to my students next week....

[@joncavalliemester]

Same, it was really an aha moment. Amazing lecture

[@jensberling2341]

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.

[@blackovich]

Thank you again. You always deliver the best explanation.

[@CoreanDramas-c5q]

I am thankful to you because you resolve my biggest confussion

[@78477]

what a great tutorial of delta epsion criteria. nobody has explained it better. thank you so much. i finally understand it now and can use it in a math problem. keep making videos like this. much love!!

[@GladnessGeorge-g5r]

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

[@InsightfulMinds3]

give this guy a nobel prize please ... We as students would like to thank you and we appreciate your service!👌👌

[@BrianMayanja-s3h]

Hey prof Newton. Thanks so much for the good work you do for us . Calculus had become a tag of war but now a piece of cake.

[@christianking4272]

Bro i have been strugling with this topic for a while now but you have explained it so well and it now makes so much sense and its very easy concept to grasp. Brother your teaching is amazing congrats you have a new subscriber.

[@herbertsusmann986]

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

[@everything5831]

you are the best math teacher i have ever seen in my entire life❤❤❤

[@talkholevietsky7721]

YOU ARE THE BEST! Thank you so much for this video! I watched many videos and went over my uni teacher's explanation, but THIS video helped me really to start getting it down! Man you are the absolute best♥️♥️🫡

[@praneelbhatnagar2333]

bro thank you honestly such a good explanation in 20 minutes

[@kasakchoradia1635]

I don't usually comment but I was finding it very difficult to understand but this is the best video so far.

[@SuditiKedambadi]

Thank you very much for your videos! This one was especially helpful for my upcoming math test. I appreciate all your hard work and dedication.

[@adkhambekyashnarbekov5758]

Thanks teacher! I guess I shouldn't be afraid of this topic anymore and beat my final exam!

[@EducationUpdatesMalawi]

This is nice sir. you have helped us here in Malawi

[@shahdElkenani12]

It's the best way to explain I've ever seen❤.

[@zeyohabesha4628]

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

[@kdagi34]

you are amazing person. you're funny, passionated and intelligent person. I love your passion.. thankyou man bless you in the name of jesus..

[@migfed]

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

[@trelosyiaellinika]

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]

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

[@anirudhmannattil9745]

Thank you so much for explaining this difficult topic! Have learnt much and will continue to watch more videos!

[@astro20400]

The last minute impressive words! never stop learning!

[@solardale7908]

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

[@JuanFernandez-kr4wh]

Theres some times when you study a subject for hours or days and you still cant uderstand what you´re missing in the subject, and then, sombody just say the simplest frase that makes your brain conect all the info, some little words that you where missing, thanks a lot for being that person

[@trader9442]

I have watched a lot of videos, but this one is best !!

[@SpheleleSibisi-nm2id]

what a best intro i understood the content before i get deep to the video💯

[@dioniziomorais8138]

I would like this video 100 times if possible!

[@punditgi]

Prime Newtons always shows the way! 🎉😊

[@grinishkin]

Thanks a lot! The only point to mention: I'd put (4x - 1) in the parenthesis under the lim as well for more clarity

[@supe-ns3gl]

You're good bro 🙌 Much love from Nigeria

[@PrimeNewtons]

Naija for life!

[@goymath]

Well presented Sir👍

[@vincentmudimeli4430]

great explanation and you always make maths enjoyable

[@Anandulasida]

Appreciate your enthusiasm ❤

[@victoravwerosuogheneokoro8179]

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

[@cadeaulazare1427]

Wow😲😲 you're the best, i never nee i would understand these things again but you just did it, i get it now You didn't only got a view from me, i have also subscribed Gos bless you sit ❤❤❤

[@kondofu]

i'm not understanding @18:56 how the abs value of x-3 < delta changes all that to just a delta???

[@lewessays]

We claimed that |x-3| < delta so x-3 will be represented/replaced by delta

[@FedhaHailu]

❤thanks from Ethiopia 🇪🇹

[@靳寧爾]

Your video certainly helps me a lot! I appreciate your sharing~

[@sohaalavi8743]

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

[@bostakılan1]

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

[@fire_phoenix2335]

I dont understand how at 14:48 just because that |x-3| < epsilon/4 and |x-3| < delta, how you can assume epsilon/4 = delta. If a

[@y_auc60seb20]

Fantastic explanation of the definition of a Limit

[@PrimeNewtons]

Glad it was helpful!

[@WaneesaGrant]

Such a cute aesthetic perf ✨

[@matejvanek1059]

Really excellent explanation, many thanks

[@lkern6238]

Nicely explained.❤

[@Divine-Education-1980]

Excellent sir (from India)

[@Yoavlevavi]

Defiantly deserves a subscription.

[@sana_136]

Thank you sir really helpful, God bless you ♥️

[@Aztekingas]

I will never be able to thank you enough!

[@ISRoptional]

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]

Please send me an email. [e-mail]

[@gamingmaster3522]

nah you a real one for this, shoutout prime newtons

[@fellingpro7574]

I understand sir 🥰🥰🥰🥰🥰 Thank you so much ,,

[@poucatelha1983]

This was so very helpful. Thank you!

[@Enzo-mi8dq]

how cool ur explanations are...omg..

[@LithakaziNokubeka]

You explained it so well, than you!!!😃

[@beebeewijaya1374]

i'm very grateful sir, thanks

[@erickkaaya8879]

blessed for good explanation

[@manokoluyega789]

Omg! This was helpful thank you bro

[@AntonneNash]

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

[@blakeklemenhagen7920]

Super helpful! Thank you so much!

[@vaibhavpandey7798]

Love from India ❤

[@omargaber3122]

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😅

[@InnocentgweduKgosiemang]

f of x - L should be less than [3 * delta which's = epsilone] not equals to it thanks sir learned a lot

[@Kiros-r1q]

Do you know many Ethiopians admire you?

[@PrimeNewtons]

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

[@SenaDebisa]

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

[@JoshMedill]

Yea we do love you

[@mikefochtman7164]

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

[@PrimeNewtons]

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

[@PrashantKumar-de2yx]

Thanks man it was really helpful..

[@cerysmiller6716]

I think people would love this 💕

[@brendawilliams8062]

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

[@fortyacres]

And for those who are wondering, yes for f(x)=ax+b, |a| will show up in your choice of delta.

[@SANKETNANDA]

❤ from India thanks

[@IsiahHopkins-wr2ph]

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

[@emilybird9761]

Fine & sweet,This is delightful

[@7George7_]

amazing explanation

[@unknown_ak-47]

Thankyou sir it really help me

[@RODNEYSaka]

Really helpful. Appreciated

[@guevaramariano]

Nice explanation

[@nanamacapagal8342]

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

[@avnitutuncu9297]

This was helpful thanks

[@Abhishek-ti5er]

Beautifully explained sir.

[@captainjacksparrow698]

Lol bro no way you made the video again for the second time and still screwed the ending ( "= 4 . epsilon/4" should be "< 4. epsilon/4" and so the last line should be "< epsilon" ).But jokes aside, great video bro thanks, it felt like tupac is explaining calculus. Somehow helped a lot

[@wannabeactuary01]

That was brilliant and clarifies plenty. I would have preferred this though for the last bit. 0 < |x - 3| < δ ⇒ 0 < < 4|x - 3| < 4δ ⇒ 0 < |4x - 12| = |4x - 1 - 11| = |f(x) - 11| < 4δ = ϵ and L = 11

[@sadeqirfan5582]

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.

[@lucasmigliori6764]

you should start by defining what is "a" and "x" and what does de subtraction of the two quantities relates to the second part after the arrow.

[@samsayman-i6x]

i loved that thank you very much bro

[@SizakeleMaphumulo]

YOU ARE THE BEST THANKYOU SO MUCH

[@DustinaWatkins]

Yes 👏🏻👏🏻👏🏻👏🏻👏🏻 love it 😍

[@princbouyah]

you are the best 👏