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 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
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?
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.
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.
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
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
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. :)
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!
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.
@@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
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!
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?
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
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.
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
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?
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.
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
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.
At 6:33, why do you keep the integer in the denominator? In a previous video titled "limits with epsilon-delta definition! (linear, square root, and quadratic examples)" you ignored the denominator entirely and got rid of both the square root part and integer part (this happened at 7:22 in the other video). Why do you use two different methods in these two very similar cases???
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 UA-cam was of a quadratic the factored to a perfect square which comes out much nicer in these circumstances.
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)?
@@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..
@@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.
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
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
The ultimate introduction to the εδ definition ua-cam.com/video/DdtEQk_DHQs/v-deo.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
*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'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?
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.
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.
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.
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
This brings back so many memories!
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!!
more examples:
linear, square root, and quadratic 👉 ua-cam.com/video/yC8Y50H6kw8/v-deo.html
1/x and x^3 👉 ua-cam.com/video/7VSG9G6EXrU/v-deo.html
where did you get your shirt from????
Shouldn't delta be smaller than epsilon? Such as Delta = e/3 ?
Best professor of all time♥️🔝
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!
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 🤣🙋🙏
yeah they arent on there lol
"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. :)
this dude's actually the best i can't even put it into words how grateful i am for him and his wonderful content!!
This is the best explanation I've ever seen. Every other Real Analysis lecture makes this way too difficult and confusing.
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!!!
Every Math professor should be simple, clear and paced as you are. Thanks a ton !
watching this 2 days before my calculus paper and suddenly it all makes sense...LMAOOOO
I wish I had found this video during my first college year. It is so well explained!
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!
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.
DAMN! you explained it to me in just 15 minutes and I was struggling with it for last 2 hours . ......Thanks , man.
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 😂
Wouldnt have been ever able to grasp this concept otherwise without this video. Thanks.
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!
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?
i have the same doubt
@@ignacioezequielforte1816 Same
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
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.
The last sentence of "We Are Done." is too satisfying!!!
this is kind of on me for not attending class after convo, but this man probably just saved me
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 ❤️❤️❤️
6:04 me having a flashback to my 7th grade trying to simplify a radical expression...
Better explanation than the lecturers at uni, tysm!
thank you sir you saved my exam !!
was waiting for this video thanks man ❤️
I've never been thought this method. I'll try to practice with it!
bro I am 14 and this is so nice and understandable, honestly you are the best teacher ever.
thank you bro you explained better than my lecture did in 2hrs
Thanks. I'm not in university yet, but I do like calculus and I think this is important.
Thanks so much, you helped me to understand easily and fully about limits with epsilon, delta, thanks so much for your videos
Thanks, you explained it much better than my professor. It clicked!!
taught better than our college professor..... do uploa more videos.....
thanks god I found you before my next week exam.
Bro you are nothing less than a life saver man thanks a lot bruh this video is amazing. .
excellent video! It was the one that finally made it make sense!!!!!!!
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 teacher
You save my life
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)
ua-cam.com/video/AfrnYS5S8VE/v-deo.html
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
At 6:26, why we can't say that it's less than 2*|x-5| (in stead of 2*|x-5| over 4)? so delta = epsilon/2...
I've just started calculus. It's nice
Excellent explanation! You're a life saver, man!
You're a lifesaver. Thank you!
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?
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.
Hey im also interested in that, why not remove the whole denominator?
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
Thank you very much you explaination is very efficient
That was a really nice video. Thanks!
You're awesome mate!
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
No, because x = -4 is not in the domain of the function in question anyway.
This guy is evolving to Master Xehanort
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.
Thank you so much, i should have known this channel before
This is an amazing video, thank you so much!!
This dude is a legend
That Pokeball looks awesome 😁
Me skipping every else delta-epsilon explication and watching his, just because he is holding a pokeball 👌
Thx thx really thx it took me several years to understand that damnned e-d stuff until I see your video.
I got an A for real analysis (continuous/discontinuous functions ) just bcz of this 8 minutes video.. tnx blackpenredpen ❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤
From Srilanka
It always amazes me how smooth and fast you can shift your pen colors..
AY YO! Bro, my midterm is tomorrow, you just saved my ass.
What about for the cases when X approaches to infinity?🙏🏽
Thank you so much for your help sir.
Damn, this makes so much more sense! I really appreciate your work!
Glad to hear!
This is so much more understandable than how my professor explained it to me
I actually understood it. My teacher is great but I just need a little more time to learn the concept.
You are the best man🥺🥺 thankyou
proof: trivial.
proof (assuming we're allowed to use the algebraic limit theorem): Note that lim (ax + b) = a lim x + b.
Man he explains it better than my teacher . And also holds a pokeball all along
great explanation, made a complicated topic seem easy and simple!
My plants are watered my face is cleaned and my grade is saved. Thank you!
thank you this is exactly what i needed
At 6:33, why do you keep the integer in the denominator? In a previous video titled "limits with epsilon-delta definition! (linear, square root, and quadratic examples)" you ignored the denominator entirely and got rid of both the square root part and integer part (this happened at 7:22 in the other video).
Why do you use two different methods in these two very similar cases???
can you please love this for no reason
Even tho, I don't need this at school now, cool video.
How can I like this video twice 😍
thank you from Zambia
Nice explanation, very clear
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 UA-cam was of a quadratic the factored to a perfect square which comes out much nicer in these circumstances.
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)?
ua-cam.com/video/2xmKUBgWk78/v-deo.html
This is a true homie right here
كبيييير واصلي دوووود
Hardest Calc 1 problems made easy by bprp himself.
😆 thanks.
Wow bro, u are so brilliant, I like u bro, u help me so much to understand
|x+5|=|x-2+7|
Yes
This is a way better (and more mathematical) explain. 😃
@@blackpenredpen Why do you have epislon and delta??..why not just one variable...seems needlessly complicated.and confusing
@@leif1075 That is just the definition of a limit.
@@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..
@@leif1075 ε corresponds to f(x), and δ to x.
Actually this is stuff we're just about to study. Sa damn thanks
Just wondering, r u in AP calc or calc 1 in a uni?
@@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.
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
This was so helpful thank you 😁😁🙏🙏
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