how to easily write the epsilon-delta proofs for limits

[@blackpenredpen]

The ultimate introduction to the εδ definition kzbin.info/www/bejne/epXXdoShlKl7h9U

[@serenitymayfair623]

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

[@richerram1]

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]

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

[@shivrajpatil1770]

You mean 8 minutes and 27 seconds.

[@kayceestudios6234]

@@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]

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

[@pyyrr]

Hey look, it's an engineer!!

[@El_Dr_Tacco]

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

[@BiscuitZombies]

By pseudo-transitivity.

[@akshatvats7992]

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

[@chill4r585]

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]

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

[@va-y-dit7843]

finding the limit is easier than proving it

[@valsnemakonde6936]

LOL

[@osuh4947]

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]

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

[@divishthamalik309]

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.

[@SergeantTeabag]

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.

[@tzonic8655]

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

[@AdelaCervantes-r4c]

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

[@kennethgibson288]

This brings back so many memories!

[@harisl5994]

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

[@mohamedibrahim1023]

Best professor of all time♥️🔝

[@Rachel-tu8pq]

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!

[@dansantner]

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

[@flyingcola7616]

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]

Hopefully you failed 🤣🙋🙏

[@Ibrahim-tt3fx]

yeah they arent on there lol

[@einsteingonzalez4336]

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

[@blackpenredpen]

Definitely!

[@benextinction__144]

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. :)

[@imsonecka]

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!!!

[@ellielinyan1521]

watching this 2 days before my calculus paper and suddenly it all makes sense...LMAOOOO

[@eduardocastelvi3009]

Dude, you are the king of explaining this. I am laughing at how simple you just made this

[@blackpenredpen]

Thanks!

[@Bayesic]

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

[@aliaziz1145]

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]

@@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]

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

[@ikersanchez8222]

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

[@BhaveeRathod]

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

[@smackdashitoutchu7755]

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

[@UnevenerGgc2]

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

[@chrisxd146]

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.

[@mathosophy3655]

For the last problem, we could instead choose δ to be (sqrt(49 + 4ε)-7)/2, and it would be a less strict condition as min{1,ε/8} ≤ (sqrt(49 + 4ε)-7)/2 for all ε. If, say hypothetically, we had to pay according to how small we chose δ to be, then we wouldn't want to choose it any smaller than we actually need to. In that case, the more complicated expression would cost the least. In any case, it was a great video, as always!

[@adityakulkarni9230]

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!

[@_AmitabhShukla]

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

[@w7lves]

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

[@MichaelDuder]

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.

[@shawnpcyril4200]

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

[@iwonthide]

was waiting for this video thanks man ❤️

[@shivrajpatil1770]

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

[@amyholmes8373]

Better explanation than the lecturers at uni, tysm!

[@frostinfy169]

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

[@tharinduprabhath3377]

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 ❤️❤️❤️

[@BiscuitZombies]

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

[@spider-uh5ws]

bro I am 14 and this is so nice and understandable, honestly you are the best teacher ever.

[@isaklyon7660]

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

[@ludwigfredriksson3786]

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

[@blackpenredpen]

more examples: linear, square root, and quadratic 👉 kzbin.info/www/bejne/r3SbimhmfZuerZo 1/x and x^3 👉 kzbin.info/www/bejne/bYe2eGx9a6qLqLc

[@dunemeister5718]

where did you get your shirt from????

[@mikevaldez7684]

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

[@m.ehsaan.]

@@mikevaldez7684 yeah it is smaller than epsilon in this case, but that really doesn't make any difference and is unrelated to the proof.

[@TheKiller-me3uy]

كبيييير واصلي دوووود

[@2manynathans]

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

[@jaloliddinzukhriddinov5820]

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

[@phyokhant6472]

thanks god I found you before my next week exam.

[@Chris-ng9zi]

For the second example where you said (@(8:27) root (2x+6) is always positive and thus {(2|x-5|) / (root(2x+6) + 4)} < (2|x-5|) / 4. Instead, could you have said the entire denominator (root(2x+6) + 4) is also positive and thus { (2|x-5|) / (root(2x+6) + 4) } < (2|x-5|). The result is that delta is equal to Epsilon/2 vs 2.epsilon. Is "Epsilon/2" an acceptable answer?

[@ignacioezequielforte1816]

i have the same doubt

[@TheTesteurr3808]

@@ignacioezequielforte1816 Same

[@ayberkkarakas6898]

You're awesome mate!

[@laizquierdomx]

thank you sir you saved my exam !!

[@tangpiseth8416]

6:04 me having a flashback to my 7th grade trying to simplify a radical expression...

[@Mrsidd328]

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]

It sounds like "in D yet" :)

[@valsnemakonde6936]

live lol

[@navaerick86]

I felt like he was speaking directly to me.

[@j.6230]

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

[@jimmorrison6177]

In the second problem you need d=min{8,2e} because in the current state, for e=5 we get d=10 but then x can be -4 (0

[@angelmendez-rivera351]

No, because x = -4 is not in the domain of the function in question anyway.

[@AJ69238]

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

[@muhammadmuaaz3704]

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

[@WritersDigest-b8f]

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]

Glad it was helpful! This is the video 24 rigorous limit proofs (ultimate calculus tutorial) kzbin.info/www/bejne/d5fVn4yJarhrjKc

[@epsa9324]

taught better than our college professor..... do uploa more videos.....

[@kr4301]

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

[@foudilbenouci482]

Thank you very much you explaination is very efficient

[@strixytom]

That was a really nice video. Thanks!

[@MrDZ-xc9ip]

Thanks teacher You save my life

[@taurus7868]

It always amazes me how smooth and fast you can shift your pen colors..

[@anikbhowmick1044]

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

[@alexandremargar123]

Thx thx really thx it took me several years to understand that damnned e-d stuff until I see your video.

[@hb1318]

You're a lifesaver. Thank you!

[@firenzetanke2272]

This is so much more understandable than how my professor explained it to me

[@dognip]

I've just started calculus. It's nice

[@technicalbrains7675]

That Pokeball looks awesome 😁

[@cezarkaja2405]

Man he explains it better than my teacher . And also holds a pokeball all along

[@cellothere5723]

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

[@approachinglimits]

Thank you for this video! I could not figure out how to do the quadratics of these for the life of me. The answer key in the back of the book has the answer but no sufficient explanation. And the only other example I could find on KZbin was of a quadratic the factored to a perfect square which comes out much nicer in these circumstances.

[@thiwankapathirana9532]

Thank you so much for your help sir.

[@AyushsinghDhanola]

Very great explanation

[@linkoffate]

This guy is evolving to Master Xehanort

[@valsnemakonde6936]

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

[@Redeemed_Daughter]

You are the best man🥺🥺 thankyou

[@RUTHLESSS19]

Damn, this makes so much more sense! I really appreciate your work!

[@blackpenredpen]

Glad to hear!

[@rishikagudlavalleti5241]

This was so helpful thank you 😁😁🙏🙏

[@mikoajmackowiak6993]

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

[@aidenhastings6341]

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]

kzbin.info/www/bejne/aKnQfIh4nLyebZo

[@joseph-ianex]

Great video! I'm a bit confused when I was supposed to learn this though because I'm taking Calc 2 now and was never taught this in Calc 1 or 2 so I guess the teachers assumed it wasn't important or just didn't have time

[@natnaelh.baraki2869]

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

[@qin2500]

AY YO! Bro, my midterm is tomorrow, you just saved my ass.

[@ahadkhan7290]

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

[@jianzhao4208]

|x+5|=|x-2+7|

[@blackpenredpen]

Yes This is a way better (and more mathematical) explain. 😃

[@leif1075]

@@blackpenredpen Why do you have epislon and delta??..why not just one variable...seems needlessly complicated.and confusing

[@angelmendez-rivera351]

@@leif1075 That is just the definition of a limit.

[@leif1075]

@@angelmendez-rivera351 oh it's been a while..so one corresponds to x and the other to f(x) I take it? Epsilon for x and delta for f(x) or vice versa..

[@angelmendez-rivera351]

@@leif1075 ε corresponds to f(x), and δ to x.

[@frozenmoon998]

Hardest Calc 1 problems made easy by bprp himself.

[@blackpenredpen]

😆 thanks.

[@Nikolaij02]

thank you this is exactly what i needed

[@lastdivantruther]

My plants are watered my face is cleaned and my grade is saved. Thank you!

[@hilaalimrit640]

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

[@ShermukhammadKarimov]

thanks for clear explanation

[@jeremypolancolara2154]

Nice explanation, very clear

[@Emilio-rf1ww]

I was doing an exercise: lim x->3 x^2 =9 and I really don’t know if I’m correct, my answer was Delta = epsilon/7

[@Emilio-rf1ww]

And if someone is reading this I have another question, is it possible that the value of Delta has an X in it?

[@sanghwa0_4]

@@Emilio-rf1ww Delta = min{epsilon/7, 1}

[@sanghwa0_4]

@@Emilio-rf1ww if epsilon is bigger than 7, there is a contradiction. It must be coupled with 1.

[@sanghwa0_4]

@@Emilio-rf1ww Also, there must not be x in it. Thats why we use the minimum function😀

[@Emilio-rf1ww]

Thank you! I really appreciate it

[@ninjapirate123]

This dude is a legend

[@sajinilakshika5000]

I got an A for real analysis (continuous/discontinuous functions ) just bcz of this 8 minutes video.. tnx blackpenredpen ❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤

[@sajinilakshika5000]

From Srilanka

[@Engineering_conceptsUOM]

Excellent … thank you so much sir…

[@zayk9532]

I actually understood it. My teacher is great but I just need a little more time to learn the concept.

[@insectus4759]

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!

[@hqs9585]

I do like your lectures but I have a few comments in this delta epsilon subject. Suppose(?) that is a big step to come out with possible delta. One should first work with the f(x) and find factors, then from there you start your delta value. The value of epsilon you get by just dividing by a factor to make it ! is also arbitrary. Just compare the |f(x) - limit value| and from there you automatically get that fraction relating delta and epsilon. Thanks

[@ElemenTalParkour]

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

[@alifetimeoflearning]

It is so important to keep sharp with these proofs. In today’s world of “dumbing down” we are graduating students who, more or less are not able to think outside of the box. #alifetimeoflearning.

[@umat4892]

Could you please solve this? Let lim n approaches to Infinity n(cube root of(n^3+6n^2+3n+2)+ square rootof (n^2-4n+2)-2n) = p/q where p and q are coprimes then the value of p+q is equal to ? Please make a video on this!

[@raghadsan603]

that was so clear thanks