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?
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.
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
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.
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
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
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?
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 ❤❤❤
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.
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?
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 🎉
actually you told WRONG thing around 9:40 that delta must be the smaller one . Actually delta must be the bigger one as definition states that for a given epsilon>0 there exist a delta>0 , not as you have said that for bigger value of delta we don't have any epsilon value . Therefore please correct it . EVERYBODY JUST HAVE A LOOK
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
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.
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.)
I don't understand what we actually prove here. Can you please do a video proving that the limt of (4x-1) does not equal 12 as x approaches 3 using this method.
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.
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
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
