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.
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 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
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’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
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!
@@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
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 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!
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 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
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 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 TH-cam was of a quadratic the factored to a perfect square which comes out much nicer in these circumstances.
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
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
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
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!
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)?
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
The ultimate introduction to the εδ definition th-cam.com/video/DdtEQk_DHQs/w-d-xo.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
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'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?
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.
*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
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.
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 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!
more examples:
linear, square root, and quadratic 👉 th-cam.com/video/yC8Y50H6kw8/w-d-xo.html
1/x and x^3 👉 th-cam.com/video/7VSG9G6EXrU/w-d-xo.html
where did you get your shirt from????
Shouldn't delta be smaller than epsilon? Such as Delta = e/3 ?
@@mikevaldez7684 yeah it is smaller than epsilon in this case, but that really doesn't make any difference and is unrelated to the proof.
Best professor of all time♥️🔝
This is the best explanation I've ever seen. Every other Real Analysis lecture makes this way too difficult and confusing.
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 man just explained the hardest topic in limits in just 15 Mins. Hats Off!!
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
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!!!
I wish I had found this video during my first college year. It is so well explained!
this dude's actually the best i can't even put it into words how grateful i am for him and his wonderful content!!
Wouldnt have been ever able to grasp this concept otherwise without this video. Thanks.
"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. :)
Every Math professor should be simple, clear and paced as you are. Thanks a ton !
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
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!
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 😂
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.
DAMN! you explained it to me in just 15 minutes and I was struggling with it for last 2 hours . ......Thanks , man.
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.
I've never been thought this method. I'll try to practice with it!
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 ❤️❤️❤️
was waiting for this video thanks man ❤️
watching this 2 days before my calculus paper and suddenly it all makes sense...LMAOOOO
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 is kind of on me for not attending class after convo, but this man probably just saved me
Thanks so much, you helped me to understand easily and fully about limits with epsilon, delta, thanks so much for your videos
thank you bro you explained better than my lecture did in 2hrs
The last sentence of "We Are Done." is too satisfying!!!
كبيييير واصلي دوووود
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!
excellent video! It was the one that finally made it make sense!!!!!!!
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
Thanks, you explained it much better than my professor. It clicked!!
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
Bro you are nothing less than a life saver man thanks a lot bruh this video is amazing. .
You're a lifesaver. Thank you!
Thank you very much you explaination is very efficient
thank you sir you saved my exam !!
You're awesome mate!
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)
th-cam.com/video/AfrnYS5S8VE/w-d-xo.html
I've just started calculus. It's nice
That was a really nice video. Thanks!
taught better than our college professor..... do uploa more videos.....
Excellent explanation! You're a life saver, man!
Thanks teacher
You save my life
Thank you so much for your help sir.
This is an amazing video, thank you so much!!
thanks god I found you before my next week exam.
I got an A for real analysis (continuous/discontinuous functions ) just bcz of this 8 minutes video.. tnx blackpenredpen ❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤
From Srilanka
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.
It always amazes me how smooth and fast you can shift your pen colors..
You are the best man🥺🥺 thankyou
bro I am 14 and this is so nice and understandable, honestly you are the best teacher ever.
Thank you so much, i should have known this channel before
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.
What about for the cases when X approaches to infinity?🙏🏽
That Pokeball looks awesome 😁
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 TH-cam was of a quadratic the factored to a perfect square which comes out much nicer in these circumstances.
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
Thx thx really thx it took me several years to understand that damnned e-d stuff until I see your video.
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...
Excellent … thank you so much sir…
thank you from Zambia
thanks for clear explanation
Nice explanation, very clear
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
Very great explanation
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
great explanation, made a complicated topic seem easy and simple!
This dude is a legend
I actually understood it. My teacher is great but I just need a little more time to learn the concept.
Tnxs you are a savior it was fun 👍👍
Wow bro, u are so brilliant, I like u bro, u help me so much to understand
This was so helpful thank you 😁😁🙏🙏
Thanks, I understand this well
AY YO! Bro, my midterm is tomorrow, you just saved my ass.
thank you this is exactly what i needed
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
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!
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)?
th-cam.com/video/2xmKUBgWk78/w-d-xo.html
Even tho, I don't need this at school now, cool video.
that was so clear thanks
Awesome video, u know real numbers so good 👌👌
This is so much more understandable than how my professor explained it to me
can you please love this for no reason
I live them these problems about analysis of real
Thank u so much agreat teacher ... u were studying in university
Im sorry i means u remember were studying in university
Alhamdulillah , Akhirnya ada subtitle indonesia , sama ini hanya memahami dari angka dan tulisan aja :)
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
very nice presentation. Thanks man!