how to easily write the epsilon-delta proofs for limits
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- Опубликовано: 23 июл 2024
- This calculus tutorial shows 2 examples of using the epsilon-delta definition to prove limits! Writing the epsilon-delta proof for a limit is usually considered to be the hardest topic when you first start learning calculus, especially at a college or university level. Hope this video gives you a better insight and my 4-step blueprint gives you a better guide to writing a beautiful math proof. Understand the epsilon-delta definition: 👉 • epsilon-delta definiti...
more examples
linear, square root, and quadratic 👉 • limits with epsilon-de...
1/x and x^3 👉 • limits with epsilon-de...
Start the epsilon-delta proof by writing
1. given
2. choose
3. suppose
4. check
0:00 this could be your GPA saver
0:10 ex1, linear function limit
3:09 ex2, sqrt function limit
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The ultimate introduction to the εδ definition ruclips.net/video/DdtEQk_DHQs/видео.html
This taught me delta epsilon proofs better in 15 minutes than anyone else ever could in 10 hours of lectures
Same here. Although I get the aversion to "easy step by step formulas" of some teachers I think some things are better taught with some sort of "fixed procedure" until you start getting the handle of it... great lesson.
Tell me about it. I've been struggling for so long😅😅
You mean 8 minutes and 27 seconds.
@@Redeemed_Daughter yeah,I learnt the thing in just an 8 minutes video just imagine after wasting hours streaming useless videos that won't even explain what they are doing and why they are doing it
I'm a simple man. If π≈3 and e≈3 then π≈e. Done ✅
Hey look, it's an engineer!!
Ha ha ha true but it'works, that's why you got an iphone in your hands.
By pseudo-transitivity.
If it's close enough, it's good enough
does anyone know why in the beginning we have to say "Given epsilon > 0" but not "delta > 0".
Why cant we just "0 < |f(x)-L| < epsilon" just like delta?
*In the one hour exam*
"Oh I'm not sure about this limit, let me prove it"
finding the limit is easier than proving it
LOL
I have followed you through my high school and now I am still relying on your videos in my first year of engineering you have amazing content keep up the good work.Thanks a lot Sir.
"GPA saver"...
More like career saver. It's necessary.
Definitely!
I thought you were me for a second and I was going loopy watching videos I'd already seen. Never seen anyone else with a map of CMB radiation as a profile pic. :)
I really had a hard time with epsilon-delta in my first semester in engineering but it turns out it's just matter of practice(for linear and 2nd degree polynomials 😅). It would be great if BPRP could show us geometrically the epsilon Delta
Wow, this really is the single greatest video about Epsilon-Delta proofs.
I have never seen some one explain this as detailed and well as this guy.
I agree. This is the only video that enlightened me with this shit.
Extremely concise, thoughtful, and thorough explanation of how to use the epsilon-delta definition effectively and smoothly. This was so much more help than the book I'm reading through for Calculus. Thank you so much! This is a life-saver for college-level Calculus.
For the second last line in the last problem you should not write
= 8 * epsilon/8
but instead
Yes, I think you are correct.
Thanks. Let me pin this comment so that others can see it. Thank you.
thank you filthy frank
Yes
But you might also set ε < 8 so you are sure that what BPRP wrote is clear.
( ͡° ͜ʖ ͡°)
Also this is a joke, but still this would be without loss of generality (the statement for limits works ∀ε>0 if and only if it works ∀ε/ 0
@@Cannongabang yeah its a very tiny tweak. The full power of the epsilon delta definition is when epsilon is small anyway.
more examples:
linear, square root, and quadratic 👉 ruclips.net/video/yC8Y50H6kw8/видео.html
1/x and x^3 👉 ruclips.net/video/7VSG9G6EXrU/видео.html
where did you get your shirt from????
Shouldn't delta be smaller than epsilon? Such as Delta = e/3 ?
exactly what I needed to help me in calc. love the way you can explain this dreaded topic so simply and have it be so effective!
This brings back so many memories!
i was reading a calculus book and i didn't understand a thing about this part but you made everything clear in 8 minutes! thank you so much!!!
this might be the most useful video i've ever seen. somehow managed to gaslight me into thinking it was easy and simple and then it really became easy and simple thank you you are a magician
This man just explained the hardest topic in limits in just 15 Mins. Hats Off!!
Best professor of all time♥️🔝
was waiting for this video thanks man ❤️
I've never seen a simpler walkthrough for this! Thank you so much! Calc AB final is coming up in a couple of days
Hopefully you failed 🤣🙋🙏
Wouldnt have been ever able to grasp this concept otherwise without this video. Thanks.
I've never been thought this method. I'll try to practice with it!
I’m not taking calc(not old enough yet to take it lol) but it was always difficult for me to wrap my head around quadratic epsilon delta proofs, it feels like this opened my 3rd eye
I wish I had found this video during my first college year. It is so well explained!
I almost wish my university would've had more time to focus on the delta-epsilon proof. We never went over the notation used for the limit of the quadratic so thankfully I learned about it before moving on from being an undergrad.
Learned something new. This was a bit different from other vids as I could try the problems along with you. Really a great experience.
Please do keep having more such alongside trial videos.
BPRP Yay!
I wish I had these videos back in times i was taking calculus I class. However I succeed my Calculus I part 2 exam (mostly based on series and series of functions) thanks to your videos
Thanks so much, you helped me to understand easily and fully about limits with epsilon, delta, thanks so much for your videos
DAMN! you explained it to me in just 15 minutes and I was struggling with it for last 2 hours . ......Thanks , man.
Excellent explanation! You're a life saver, man!
You're a lifesaver. Thank you!
Every Math professor should be simple, clear and paced as you are. Thanks a ton !
Thank you so much for this... I am trying to get a headstart on calc out of Stewarts Calculus and they really don't do a very good job of explaining in the text so you just got me dug out of a ditch trying to understand what to do with exponents.
excellent video! It was the one that finally made it make sense!!!!!!!
This is an amazing video, thank you so much!!
great explanation, made a complicated topic seem easy and simple!
this dude's actually the best i can't even put it into words how grateful i am for him and his wonderful content!!
Thanks. I'm not in university yet, but I do like calculus and I think this is important.
Better explanation than the lecturers at uni, tysm!
This was so helpful thank you 😁😁🙏🙏
You're awesome mate!
Thank you so much, i should have known this channel before
thank you this is exactly what i needed
You are the best man🥺🥺 thankyou
I've just started calculus. It's nice
Thank you so much for your help sir.
Thanks, you explained it much better than my professor. It clicked!!
thank you bro you explained better than my lecture did in 2hrs
that was so clear thanks
Thank you very much you explaination is very efficient
very nice presentation. Thanks man!
This is the best explanation I've ever seen. Every other Real Analysis lecture makes this way too difficult and confusing.
Hey man, love your videos. If you have time, could you please make a video series on the basics of linear algebra and calculus for beginners like me? Would be appreciated, as it's hard to come across quality content for beginners to grasp.
Nice explanation, very clear
Please make same type of video on two variable limits also . I am going through limits of two variables in my college but mostly sticking on proving the limit through epsilon delta definition
what a great video thanks for what you do on your channel
Bro you are nothing less than a life saver man thanks a lot bruh this video is amazing. .
Thanks teacher
You save my life
I swear I heard him say "Idiot" at 2:28 (I know he says "in the end" but it confused me for a minute)
It sounds like "in D yet" :)
live lol
I felt like he was speaking directly to me.
@@navaerick86 To me as well, and he's right
this is kind of on me for not attending class after convo, but this man probably just saved me
thanks for clear explanation
Thank you is wonderful.
Excellent … thank you so much sir…
Amazing . Thanks !
Where was this kind of content when I was in calc 1? Amazing video man!
This isn’t in calc 1 b/c u don’t focus on proofs in that course. This content comes up in advanced courses
@@aliaziz1145 we definitely had a couple sections in my calc 1 class that were dedicated to delta epsilon proofs. Technically optional but not as far as my teacher was concerned haha
@@Bayesic this definition of a limit is so much more satisfying than the lower level sanitized definition from freshman year college 😂
Owww thanks it helped a lot
Thanks, I understand this well
This video comes to me 1 year later 😭 still awesome for the new people :)
Tnxs you are a savior it was fun 👍👍
Very Nice, thanks a lot!
Awesome video, u know real numbers so good 👌👌
many thanks! 💌
Even tho, I don't need this at school now, cool video.
THANK YOU!
Hello, thank you for this video, it is really helpful.
I have a question in mind: In a new video, can you use the same method for the trigonometric and exponantial functions as well as a polynomial function which we cannot write as product of two or more polynomials? For instance as lim x->10 (x^2 -x+89). Because in the example showed in video, we reached x-2 easily so our assumption about delta was helpful. How are we going to do when it won't be like this?
Thank you in advance and thank you for this amazing channel! Videos are not only helpful but also inspirational!
@blackpenredpen could i just square the limit in the second one to get rid of the square root? i got delta = epsilon/2 thanks!
it was really helpful, thanks a lot
Glad to help 😃
The last sentence of "We Are Done." is too satisfying!!!
thank you from Zambia
Thank you so much sir
That's a nice way😀 thanks
can you please love this for no reason
This guy is evolving to Master Xehanort
How do you formally prove this using the delta epsilon definition? Also, in the second problem, I got E^2/2-4E
Thank you man
Dude I was so fucked up by delta and Epsilon... You just solved it under 15 min.. Cool man.. You are a really good teacher.. Good Luck ❤️❤️❤️
That Pokeball looks awesome 😁
Thank you!
Thank you lifesaver
Enjoyed it, explained with clarity, thank u, I will look for similar examples on YT from you to be able to solve all problem of this nature.
Glad it was helpful! This is the video
24 rigorous limit proofs (ultimate calculus tutorial)
ruclips.net/video/AfrnYS5S8VE/видео.html
Nice - I wish I had you for my calc 1 professor. :-)
Thank you so much
Thx thx really thx it took me several years to understand that damnned e-d stuff until I see your video.
Verry helpful.
Thanks alot🙇
This is so much more understandable than how my professor explained it to me
What about for the cases when X approaches to infinity?🙏🏽
Thnx for this vid❤️
great explamation!!! do you have some examples with x going to infinity ?
Thank you! Do you have explanations of delta epsilon proofs in other contexts than just a limit (such as limit of a sequence, uniform continuity, etc)?
ruclips.net/video/2xmKUBgWk78/видео.html
This dude is a legend