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.

[@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

[@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.

[@kennethgibson288]

This brings back so many memories!

[@hybmnzz2658]

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

[@blackpenredpen]

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

[@daray21]

thank you filthy frank

[@patriciaelenabarrosoberroc8032]

Yes

[@Cannongabang]

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]

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

[@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. :)

[@mohamedibrahim1023]

Best professor of all time♥️🔝

[@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 ?

[@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 🤣🙋🙏

[@user-lt5wt9sv4j]

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

[@harisl5994]

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

[@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!

[@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 😂

[@shawnpcyril4200]

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

[@user-pj9ez4xp4r]

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

[@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

[@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.

[@dansantner]

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

[@caghey]

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!!!

[@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!

[@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

[@smackdashitoutchu7755]

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

[@ikersanchez8222]

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

[@w7lves]

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

[@iwonthide]

was waiting for this video thanks man ❤️

[@shivrajpatil1770]

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

[@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!

[@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.

[@_AmitabhShukla]

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

[@frostinfy169]

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

[@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

[@tangpiseth8416]

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

[@BiscuitZombies]

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

[@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 ❤️❤️❤️

[@hilaalimrit640]

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

[@ludwigfredriksson3786]

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

[@user-qj3rv2mo1b]

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

[@amyholmes8373]

Better explanation than the lecturers at uni, tysm!

[@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.

[@jaloliddinzukhriddinov5820]

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

[@dakshthawani6704]

it was really helpful, thanks a lot

[@blackpenredpen]

Glad to help 😃

[@2manynathans]

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

[@foudilbenouci482]

Thank you very much you explaination is very efficient

[@technicalbrains7675]

That Pokeball looks awesome 😁

[@RUTHLESSS19]

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

[@blackpenredpen]

Glad to hear!

[@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

[@spider-uh5ws]

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

[@epsa9324]

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

[@isaklyon7660]

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

[@cezarkaja2405]

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

[@linkoffate]

This guy is evolving to Master Xehanort

[@AJ69238]

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

[@hb1318]

You're a lifesaver. Thank you!

[@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.

[@thiwankapathirana9532]

Thank you so much for your help sir.

[@MrDZ-xc9ip]

Thanks teacher You save my life

[@cellothere5723]

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

[@muhammadmuaaz3704]

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

[@taurus7868]

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

[@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

[@thedoublehelix5661]

proof: trivial. proof (assuming we're allowed to use the algebraic limit theorem): Note that lim (ax + b) = a lim x + b.

[@valsnemakonde6936]

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

[@ellielinyan1521]

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

[@alexandreclemson9445]

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

[@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.

[@frozenmoon998]

Hardest Calc 1 problems made easy by bprp himself.

[@blackpenredpen]

😆 thanks.

[@Cris-qn2ii]

Actually this is stuff we're just about to study. Sa damn thanks

[@blackpenredpen]

Just wondering, r u in AP calc or calc 1 in a uni?

[@Cris-qn2ii]

@@blackpenredpen I'm not sure how the system works in other countries. But mine is the french system. After high school, to get to engineering schools you gotta pass from prepatrory classes in 2 years. They're called prepatory classes to the big schools. Not sure its equivalent in other countries tho.

[@firenzetanke2272]

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

[@ayberkkarakas6898]

You're awesome mate!

[@dognip]

I've just started calculus. It's nice

[@mikoajmackowiak6993]

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

[@ahadkhan7290]

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

[@rishikagudlavalleti5241]

This was so helpful thank you 😁😁🙏🙏

[@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!

[@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.

[@ShermukhammadKarimov]

thanks for clear explanation

[@sajinilakshika5000]

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

[@sajinilakshika5000]

From Srilanka

[@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

[@darkwing73]

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

[@HDitzzDH]

How could we just remove the sqrt(2x+6) part for the second example? And what are we really doing to justify that? Are we looking for the minimum value that specific term can take (which is 0)? Aka min{ sqrt(2x+6) } = 0?

[@Supervergil1]

By removing a NON NEGATIVE value from a POSITIVE SUM in the denominator, you're GUARANTEEING that you're making the denominator SMALLER, but you're also keeping it POSITIVE. That in turn guarantees that the whole value becomes bigger (try it on simple numbers like he did - 1/4 vs 1/(4+1)) Do notice that if the denominator was the product of two positive things and not sum, he couldn't have done that move so easily (if at all), Because he can't know if he'll be removing a number between 0 and 1, or a number larger than 1, so won't be able to guarantee that the denominator will actually become bigger, probably unless he plays with the delta requirement or something that I'm too lazy to think about. When adding / removing things in the inequality trip, you'll mainly want to pay attention to positive /negative values, values that you don't know if they're always positive or not, checking if values are a fraction or bigger than 1 ( matters when a product is included in the game).

[@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!

[@Redeemed_Daughter]

You are the best man🥺🥺 thankyou

[@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.

[@Nikolaij02]

thank you this is exactly what i needed

[@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

[@zayk9532]

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

[@ElemenTalParkour]

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

[@mohamedfarouk9654]

I don't know if it's valid but |x-2| < delta |x+5| < delta+7 So |x+5|•|x-2| < (delta + 7)delta = delta² + 7•delta We want delta²+7•delta = epsilon delta² + 7•delta + 49/4 = epsilon+49/4 (delta + 7/2)² = epsilon + 49/4 delta + 7/2 = √(epsilon + 49/4) delta = √(epsilon + 49/4) - 7/2

[@angelmendez-rivera351]

Yes, this is valid.

[@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

[@Engineering_conceptsUOM]

Excellent … thank you so much sir…

[@jeremypolancolara2154]

Nice explanation, very clear

[@ninjapirate123]

This dude is a legend

[@ququ5463]

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

[@MrCrazydooker]

7:30 Since we can remove the square root part of the denominator which makes the resulting fraction is bigger, couldn't we just remove the positive denominator all together? That would result in 2abs(x - 5) < ε which gives us δ = ε/2. You ended up with δ = 2ε. Are both okay or am I missing something here?

[@adirbarak5256]

I think that's true but in the context of a "step by step tutorial" it might be for the best that he doesn't go the most direct efficient path. Anyway thank you for your comment, I hadn't notice it.

[@McBlueskai]

Hey im also interested in that, why not remove the whole denominator?

[@thisis_shashwat]

Both okay, to check you can give some values to epsilon or delta, Eg you can take delta as 1 & epsilon as 2. You'll see that they satisfy both inequalities