how to easily write the epsilon-delta proofs for limits

Рет қаралды 299,637

Күн бұрын

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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Пікірлер: 464

@blackpenredpen Жыл бұрын

The ultimate introduction to the εδ definition kzfaq.info/get/bejne/esqkeLScxKqsgac.html

@serenitymayfair623 2 жыл бұрын

This taught me delta epsilon proofs better in 15 minutes than anyone else ever could in 10 hours of lectures

@richerram1 2 жыл бұрын

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.

@Redeemed_Daughter 2 жыл бұрын

Tell me about it. I've been struggling for so long😅😅

@shivrajpatil1770 Жыл бұрын

You mean 8 minutes and 27 seconds.

@kayceestudios6234 Жыл бұрын

@@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

@Denis-vj2hz 3 жыл бұрын

I'm a simple man. If π≈3 and e≈3 then π≈e. Done ✅

@pyyrr 3 жыл бұрын

Hey look, it's an engineer!!

@El_Dr_Tacco 3 жыл бұрын

Ha ha ha true but it'works, that's why you got an iphone in your hands.

@BiscuitZombies 3 жыл бұрын

By pseudo-transitivity.

@akshatvats7992 3 жыл бұрын

If it's close enough, it's good enough

@chill4r585 Ай бұрын

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?

@martinpena7949 3 жыл бұрын

*In the one hour exam* "Oh I'm not sure about this limit, let me prove it"

@va-y-dit7843 3 жыл бұрын

finding the limit is easier than proving it

@valsnemakonde6936 3 жыл бұрын

LOL

@einsteingonzalez4336 3 жыл бұрын

"GPA saver"... More like career saver. It's necessary.

@blackpenredpen 3 жыл бұрын

Definitely!

@benextinction__144 3 жыл бұрын

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. :)

@divishthamalik309 3 жыл бұрын

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.

@osuh4947 2 жыл бұрын

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.

@schezum 2 жыл бұрын

I agree. This is the only video that enlightened me with this shit.

@tzonic8655 3 жыл бұрын

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

@kennethgibson288 3 жыл бұрын

This brings back so many memories!

@SergeantTeabag 2 жыл бұрын

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.

@mohamedibrahim1023 3 жыл бұрын

Best professor of all time♥️🔝

@Rachel-tu8pq Жыл бұрын

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!

@blackpenredpen 2 жыл бұрын

more examples: linear, square root, and quadratic 👉 kzfaq.info/get/bejne/r6lojJhhrZzPp2w.html 1/x and x^3 👉 kzfaq.info/get/bejne/bbyDepx4m6u8ook.html

@dunemeister5718 2 жыл бұрын

where did you get your shirt from????

@mikevaldez7684 Жыл бұрын

Shouldn't delta be smaller than epsilon? Such as Delta = e/3 ?

@hybmnzz2658 3 жыл бұрын

For the second last line in the last problem you should not write = 8 * epsilon/8 but instead

@blackpenredpen 3 жыл бұрын

Yes, I think you are correct. Thanks. Let me pin this comment so that others can see it. Thank you.

@daray21 3 жыл бұрын

thank you filthy frank

@patriciaelenabarrosoberroc8032 3 жыл бұрын

Yes

@Cannongabang 3 жыл бұрын

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

@hybmnzz2658 3 жыл бұрын

@@Cannongabang yeah its a very tiny tweak. The full power of the epsilon delta definition is when epsilon is small anyway.

@harisl5994 2 жыл бұрын

This man just explained the hardest topic in limits in just 15 Mins. Hats Off!!

@ikersanchez8222 3 жыл бұрын

I wish I had found this video during my first college year. It is so well explained!

@user-lt5wt9sv4j 5 ай бұрын

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

@caghey Жыл бұрын

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!!!

@flyingcola7616 3 жыл бұрын

I've never seen a simpler walkthrough for this! Thank you so much! Calc AB final is coming up in a couple of days

@mikevaldez7684 Жыл бұрын

Hopefully you failed 🤣🙋🙏

@iwonthide 3 жыл бұрын

was waiting for this video thanks man ❤️

@smackdashitoutchu7755 2 жыл бұрын

Wouldnt have been ever able to grasp this concept otherwise without this video. Thanks.

@frostinfy169 3 жыл бұрын

I've never been thought this method. I'll try to practice with it!

@AJ69238 2 жыл бұрын

Excellent explanation! You're a life saver, man!

@adityakulkarni9230 3 жыл бұрын

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!

@shawnpcyril4200 2 жыл бұрын

Every Math professor should be simple, clear and paced as you are. Thanks a ton !

@kr4301 3 жыл бұрын

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

@hb1318 Жыл бұрын

You're a lifesaver. Thank you!

@jaloliddinzukhriddinov5820 2 жыл бұрын

Thanks so much, you helped me to understand easily and fully about limits with epsilon, delta, thanks so much for your videos

@_AmitabhShukla 2 жыл бұрын

DAMN! you explained it to me in just 15 minutes and I was struggling with it for last 2 hours . ......Thanks , man.

@foudilbenouci482 Жыл бұрын

Thank you very much you explaination is very efficient

@UnevenerGgc2 3 жыл бұрын

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

@dansantner 6 ай бұрын

This is the best explanation I've ever seen. Every other Real Analysis lecture makes this way too difficult and confusing.

@thiwankapathirana9532 Жыл бұрын

Thank you so much for your help sir.

@ahadkhan7290 3 жыл бұрын

great explanation, made a complicated topic seem easy and simple!

@chrisxd146 3 жыл бұрын

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.

@rishikagudlavalleti5241 3 жыл бұрын

This was so helpful thank you 😁😁🙏🙏

@BiscuitZombies 3 жыл бұрын

Thanks. I'm not in university yet, but I do like calculus and I think this is important.

@ludwigfredriksson3786 3 жыл бұрын

Thanks, you explained it much better than my professor. It clicked!!

@cellothere5723 Жыл бұрын

This is an amazing video, thank you so much!!

@ShermukhammadKarimov Ай бұрын

thanks for clear explanation

@user-pj9ez4xp4r 8 ай бұрын

this dude's actually the best i can't even put it into words how grateful i am for him and his wonderful content!!

@MichaelDuder 2 жыл бұрын

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.

@2manynathans Жыл бұрын

excellent video! It was the one that finally made it make sense!!!!!!!

@amyholmes8373 2 жыл бұрын

Better explanation than the lecturers at uni, tysm!

@raghadsan603 2 жыл бұрын

that was so clear thanks

@isaklyon7660 2 жыл бұрын

thank you bro you explained better than my lecture did in 2hrs

@Nikolaij02 2 жыл бұрын

thank you this is exactly what i needed

@mr.jennycano1701 3 жыл бұрын

very nice presentation. Thanks man!

@jeremypolancolara2154 2 жыл бұрын

Nice explanation, very clear

@valsnemakonde6936 3 жыл бұрын

Thank you so much, i should have known this channel before

@Redeemed_Daughter 2 жыл бұрын

You are the best man🥺🥺 thankyou

@dognip 3 жыл бұрын

I've just started calculus. It's nice

@Ommbye 3 жыл бұрын

Thank you is wonderful.

@Bayesic 3 жыл бұрын

Where was this kind of content when I was in calc 1? Amazing video man!

@aliaziz1145 3 жыл бұрын

This isn’t in calc 1 b/c u don’t focus on proofs in that course. This content comes up in advanced courses

@Bayesic 3 жыл бұрын

@@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

@aliaziz1145 3 жыл бұрын

@@Bayesic this definition of a limit is so much more satisfying than the lower level sanitized definition from freshman year college 😂

@Engineering_conceptsUOM 2 жыл бұрын

Excellent … thank you so much sir…

@LaBonneVentree 2 жыл бұрын

what a great video thanks for what you do on your channel

@MrDZ-xc9ip 2 жыл бұрын

Thanks teacher You save my life

@danieltreuherz8752 3 жыл бұрын

@blackpenredpen could i just square the limit in the second one to get rid of the square root? i got delta = epsilon/2 thanks!

@younesyounes3503 2 жыл бұрын

Thanks, I understand this well

@AnmolWanderer 2 жыл бұрын

Amazing . Thanks !

@darkwing73 3 жыл бұрын

How do you formally prove this using the delta epsilon definition? Also, in the second problem, I got E^2/2-4E

@ayberkkarakas6898 2 жыл бұрын

You're awesome mate!

@Mrsidd328 3 жыл бұрын

I swear I heard him say "Idiot" at 2:28 (I know he says "in the end" but it confused me for a minute)

@przemezio 3 жыл бұрын

It sounds like "in D yet" :)

@valsnemakonde6936 3 жыл бұрын

live lol

@navaerick86 3 жыл бұрын

I felt like he was speaking directly to me.

@j.6230 2 жыл бұрын

@@navaerick86 To me as well, and he's right

@muhammadmuaaz3704 2 жыл бұрын

Bro you are nothing less than a life saver man thanks a lot bruh this video is amazing. .

@SuperYoonHo Жыл бұрын

THANK YOU!

@shivrajpatil1770 Жыл бұрын

The last sentence of "We Are Done." is too satisfying!!!

@natnaelh.baraki2869 3 жыл бұрын

What about for the cases when X approaches to infinity?🙏🏽

@medhanitgetachew1706 3 жыл бұрын

Tnxs you are a savior it was fun 👍👍

@insectus4759 3 жыл бұрын

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!

@ElemenTalParkour 2 жыл бұрын

great explamation!!! do you have some examples with x going to infinity ?

@Jearbearjenkins Жыл бұрын

Jesus this is the best explanation of how to do this I have ever seen. Blackpenredpen is the calculus youtube GOAT

@147TINO147 3 жыл бұрын

Very Nice, thanks a lot!

@w7lves 2 жыл бұрын

this is kind of on me for not attending class after convo, but this man probably just saved me

@nadhirelhaouari5659 2 жыл бұрын

Thank you so much sir

@technicalbrains7675 3 жыл бұрын

That Pokeball looks awesome 😁

@arunasadeepa2795 3 жыл бұрын

That's a nice way😀 thanks

@selamkibrom5618 8 ай бұрын

Owww thanks it helped a lot

@mikoajmackowiak6993 3 жыл бұрын

Even tho, I don't need this at school now, cool video.

@advaitlath7221 3 жыл бұрын

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.

@MaadEngineer 11 ай бұрын

many thanks! 💌

@chileshesikazwe8500 3 жыл бұрын

thank you from Zambia

@dakshthawani6704 2 жыл бұрын

it was really helpful, thanks a lot

@blackpenredpen 2 жыл бұрын

Glad to help 😃

@charlesrothauser1328 3 жыл бұрын

Nice - I wish I had you for my calc 1 professor. :-)

@shadrach05 9 ай бұрын

Thank you so much

@paulnelson112 3 жыл бұрын

Awesome video, u know real numbers so good 👌👌

@tharinduprabhath3377 2 жыл бұрын

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 ❤️❤️❤️

@anikbhowmick1044 3 жыл бұрын

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

@joeyrunnion8042 2 жыл бұрын

Thank you!

@fernandogaray1681 3 жыл бұрын

This video comes to me 1 year later 😭 still awesome for the new people :)

@user-qj3rv2mo1b 8 ай бұрын

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.

@blackpenredpen 8 ай бұрын

Glad it was helpful! This is the video 24 rigorous limit proofs (ultimate calculus tutorial) kzfaq.info/get/bejne/d8yiobyEmrmchnk.html

@hilaalimrit640 3 жыл бұрын

Me skipping every else delta-epsilon explication and watching his, just because he is holding a pokeball 👌

@ibrahim203 2 жыл бұрын

Thank you so much. Example 2 is a bit confusing. Can you upload more examples of it on any of your social platforms? And secondly, is there any other method to solve epsilon delta relations?

@aidenhastings6341 2 жыл бұрын

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)?

@blackpenredpen 2 жыл бұрын

kzfaq.info/get/bejne/aN6dfrhzzL3PZ2w.html