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.
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.
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
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.
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
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 ❤❤❤
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
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
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?
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
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.
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.
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?
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
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
thought i was alone broo...
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?
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.
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
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.
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.
The last minute impressive words! never stop learning!
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!
مبدع و متألق استاذ ابو العبد، عندي امتحان رياضيات اليوم وفعلا انقذتني. ربي يوفقك ويحفظك بحق محمد وال محمد
Thank you prime network as you said never stop learning and I tell you never stop giving the good explanations✍️✍️✍️
This is probably the best math channel I have found on UA-cam!
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
what a best intro i understood the content before i get deep to the video💯
I have watched a lot of videos, but this one is best !!
I would like this video 100 times if possible!
Beautifully explained sir.
Thank you so much for explaining this difficult topic! Have learnt much and will continue to watch more videos!
Your video certainly helps me a lot! I appreciate your sharing~
Really excellent explanation, many thanks
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Appreciate your enthusiasm ❤
You're good bro 🙌
Much love from Nigeria
Naija for life!
I will never be able to thank you enough!
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One of your student from Ethiopia.
for the best understanding of this concept, you also need to show an example where the limit fails. Nice channel
Fantastic explanation of the definition of a Limit
Glad it was helpful!
i'm very grateful sir, thanks
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 ❤❤❤
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)
Prime Newtons always shows the way! 🎉😊
Well presented 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
Defiantly deserves a subscription.
Nicely explained.❤
Really helpful. Appreciated
great explanation and you always make maths enjoyable
Thankyou so much man ! ❤ great way to deliver lecture ❤
Excellent sir (from India)
This was so very helpful. Thank you!
Super helpful! 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
God bless you for me, u literally made my day ❤🙏
Thanks man it was really helpful..
Thank you sir really helpful, God bless you ♥️
Fine & sweet,This is delightful
Thankyou sir it really help me
You explained it so well, than you!!!😃
i need it every day
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
I understand sir 🥰🥰🥰🥰🥰
Thank you so much ,,
Love from India ❤
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That's a great honor. I play soccer weekly with many Ethiopian friends. Amazing people.
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Thank you ❤
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f of x - L should be less than [3 * delta which's = epsilone] not equals to it thanks sir learned a lot
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
And for those who are wondering, yes for f(x)=ax+b, |a| will show up in your choice of delta.
Magnificent
I think people would love this 💕
That’s a good show and explanation. It’s a strange way to do it
thank you
❤❤
Very nice😋👏
YOU ARE THE BEST THANKYOU SO MUCH
Thanks mister ❤
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😅
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.
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.
you're my idol💕 LOVE YOU TO THE MILKY WAY AND BACK #love #Videosoftheday
helpful video
Thanks a lot 🙏
thank you sir
Think you bro
you're my idol💞 LOVE YOU TO THE MILKY WAY AND BACK #love #Videosoftheday
i'm not understanding @18:56 how the abs value of x-3 < delta changes all that to just a delta???
Nice and cold
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
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|
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.
Most Important for me 🙏😙😙💘
i like it was help full🙏
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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.
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,😌
Arent we supposed to prove epsilon/4 against the delta statement?
Genius mind.
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So very Fabulous😍💘
Tchyalesh man, ymechsh
Fab Videos
Kea leboha Monghali.
All the way from Lesotho🇱🇸
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?
I Like your video
How can we prove that this same limit I not equal to say 12 or anything apart from 11....
Ideal💣
wass very helpful