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.
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.
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 🎉
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
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?
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 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
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
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.
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 ❤❤❤
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.
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.
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
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?
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
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??
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.
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?
That is a great point! This is why it was so frustrating to work with real analysis.
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.
See: John Gabriel New Calculus
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.
Thank you
Epsilon is on the y-axis, delta on the x-axis. I never really got that ... until today. Thanks.
Epsilon and delta are both radius of open intervals on x-axis and y-axis. How they are on x and y axis?
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
Do you know many Ethiopians admire you?
That's a great honor. I play soccer weekly with many Ethiopian friends. Amazing people.
Yea I swear to God I never see teacher like u thanku we love u do much am also from Ethiopia
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 🎉
Really excellent explanation, many thanks
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
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?
Please send me an email. Primenewtons@gmail.com
❤❤
i'm not understanding @18:56 how the abs value of x-3 < delta changes all that to just a delta???
Thank you again. You always deliver the best explanation.
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
You rock!
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
Thank you prime network as you said never stop learning and I tell you never stop giving the good explanations✍️✍️✍️
Prime Newtons always shows the way! 🎉😊
for the best understanding of this concept, you also need to show an example where the limit fails. Nice channel
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
i don't think its dx and dy, it is delta(x) and delta(y)
This man deserves at the very least a plaque on the moon 🎉
مبدع و متألق استاذ ابو العبد، عندي امتحان رياضيات اليوم وفعلا انقذتني. ربي يوفقك ويحفظك بحق محمد وال محمد
i'm very grateful sir, thanks
Maybe those last two lines could be changed. Once you have the RHS as < 4*delta, then the next line would be
I used to think so too, but using < will have a different meaning. An alternative is to write them on the same line.
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....
Same, it was really an aha moment. Amazing lecture
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.
This is probably the best math channel I have found on TH-cam!
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.)
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|
Well presented Sir👍
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.
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 ❤❤❤
Appreciate your enthusiasm ❤
And for those who are wondering, yes for f(x)=ax+b, |a| will show up in your choice of delta.
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.
helpful video
How can we prove that this same limit I not equal to say 12 or anything apart from 11....
f of x - L should be less than [3 * delta which's = epsilone] not equals to it thanks sir learned a lot
Kea leboha Monghali.
All the way from Lesotho🇱🇸
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.
Your video certainly helps me a lot! I appreciate your sharing~
Very nice😋👏
Nicely explained.❤
thank you
The last minute impressive words! never stop learning!
Excellent sir (from India)
Arent we supposed to prove epsilon/4 against the delta statement?
what a best intro i understood the content before i get deep to the video💯
That’s a good show and explanation. It’s a strange way to do it
I would like this video 100 times if possible!
Fine & sweet,This is delightful
You explained it so well, than you!!!😃
Love from India ❤
I have watched a lot of videos, but this one is best !!
Super helpful! Thank you so much!
You look more like a golfer rather than a mathemaician.
Thank you ❤
You are such an amazing teacher that i have ever know Keep going Prime !
One of your student from Ethiopia.
Thanks man it was really helpful..
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.
Yes 👏🏻👏🏻👏🏻👏🏻👏🏻 love it 😍
I will never be able to thank you enough!
I understand sir 🥰🥰🥰🥰🥰
Thank you so much ,,
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
Thank you so much for explaining this difficult topic! Have learnt much and will continue to watch more videos!
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?
Thanks a lot! The only point to mention: I'd put (4x - 1) in the parenthesis under the lim as well for more clarity
Magnificent
you're my idol💞 LOVE YOU TO THE MILKY WAY AND BACK #love #Videosoftheday
Think you bro
Really helpful. Appreciated
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😅
Beautifully explained sir.
Thankyou sir it really help me
you're my idol💕 LOVE YOU TO THE MILKY WAY AND BACK #love #Videosoftheday
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
Tchyalesh man, ymechsh
Thank you sir really helpful, God bless you ♥️
i like it was help full🙏
Thankyou so much man ! ❤ great way to deliver lecture ❤
You're good bro 🙌
Much love from Nigeria
Naija for life!
Thanks mister ❤
im watching this video at 3am😂😂felt like someone will wake up and say it was just a nightmare
Sleep well
@@PrimeNewtons you explained well brother,😌
i need it every day
thank you sir
ASM vibes
This was so very helpful. Thank you!
Not your best explanation, but okay.
great explanation and you always make maths enjoyable
It seems like we’re playing a shell game!
Nice and cold
Thanks a lot 🙏
Aww🙏 💕💓 so Cute
Fantastic explanation of the definition of a Limit
Glad it was helpful!
Defiantly deserves a subscription.
Genius mind.
Fab Videos
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??
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.
I think an example of where the limit DOES NOT exist would be useful!
answer=1 xd
YOU ARE THE BEST THANKYOU SO MUCH
God bless you for me, u literally made my day ❤🙏
You 👍 should be proud of yourself