epsilon-delta definition ultimate introduction

Рет қаралды 351,778

Күн бұрын

My ultimate introduction to the epsilon-delta definition of limits in calculus! The epsilon-delta definition of a limit is commonly considered the hardest topic in Calculus 1 (it's also the important part at the beginning of real analysis). The best way to understand this precise definition of a limit is to actually use an actual value for epsilon first, then solve for the corresponding delta. When writing epsilon-delta proofs for limits, be sure to set it up: given, choose, suppose, and check!
εN definition (finite limit at infinity): 👉 • epsilon-N definition f...
Check out more examples of proving limits with the εδ definition:
linear, square root, and quadratic 👉 • limits with epsilon-de...
1/x and x^3 👉 • limits with epsilon-de...
"a taste of real analysis" 👉 • Proving x^2 is continu...
0:00 the εδ definition of a limit is the hardest topic in calculus 1
1:34 limit of sqrt(2x+1) as x approaches 4
4:14 if epsilon is 0.2, how to find the biggest delta
10:27 writing the εδ proof
Get an epsilon-delta hoodie: 👉 blackpenredpen.creator-spring... Use "WELCOME10" for 10% off
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Пікірлер: 530

@blackpenredpen 10 ай бұрын

Check out 24 more rigorous proofs: ultimate calculus: 24 rigorous limit proofs kzfaq.info/get/bejne/d8yiobyEmrmchnk.html

@redblasphemy9204 2 жыл бұрын

back when my fiancé and I were at our 1st year of university studying analysis, we were hanging out together and it was a classic romantic dusk moment... and then I screamed "I JUST REALIZED HOW EPSILON DELTA WORKS!" he is still mad at me lol

@blackpenredpen 2 жыл бұрын

😆

@verypotato6699 2 жыл бұрын

how is he still mad? if i were the reason anyone realised how epsilon delta works i’d be overjoyed

@fareschettouh 2 жыл бұрын

Hello Please can you resolve this équation not geometricly (2^×)+(3^×)=(5^×) I know that x=1 but how you can find this solution thank you

@iitguwahaticseairunder500r2 2 жыл бұрын

@@fareschettouh heyy, Use a function f(x)= 5^x -2^x - 3^x Then draw the curve using curve tracing The number of times it crosses x axis is the number of solutions of the original question. I don't know any other geometric soln.

@michellauzon4640 2 жыл бұрын

@@blackpenredpen It is quite easy to figure the contradiction which is There exist epsilon > 0 such that for all delta > 0, there exist x such that ABS(x-a) < delta and ABS(f(x)-L) > epsilon. If so, we can put delta(n) = 1 / n for all positive integer, and pick x(n) for each n. Then x(n) tends to a, and f(x(n)) doesn't tend toward L.

@JohnSmith-rf1tx 2 жыл бұрын

This is great. Could you also do a counterexample where the limit doesn't exist and show how it breaks using the epsilon-delta definition? I often find that showing a counterexample that highlights what goes wrong is often more helpful in building understanding than just seeing one more example where everything goes right.

@henriqueassme6744 2 жыл бұрын

That's what I was going to ask. I have no idea what happens when the limit doesn't exist using epsilon-delta definition

@kingbeauregard 2 жыл бұрын

y = sin(1/x)

@kingbeauregard 2 жыл бұрын

@@henriqueassme6744 I believe what happens is, you reach impasse with the arithmetic: you find yourself at a point where there is no way to get to an expression like "delta*constant = epsilon".

@popularmisconception1 2 жыл бұрын

It means that for some too small epsilon (desired output error margin), you just cannot find small enough input margin delta that guarantees you to fit into that desired output error margin epsilon. You can't, anyhow close on the input side, the output will always be too off. Think about a threshold function for example: Zero or grater -> returns one. less than zero -> returns zero. What is the limit in zero? There is none, because whatever anyone would claim it to be, the values of f(x) around the zero will still be zero on the minus side and one on the plus side. Even if you chose it to be one half, the minimum output error you can get is one half even for infinitesimally small difference from zero on the input side. Even if someone told you it is one (i.e. the value of the function by definition), if you approach that value from the left, you are still too off from the alleged limit.

@lostwizard 2 жыл бұрын

This is exactly where my calculus professors in university went wrong with the epsilon-delta explanation. They concentrated almost entirely on cases where it works and failed do more than a cursory "and we see how it doesn't work in this case" after a flurry of barely legible scribbling for a couple of counter examples.

@BoazNahumPlus 2 жыл бұрын

I learned 3 things today: 1. The definition isn't that bad, calming first does help. 2. That Pockeball has no use! the mic is just next to it. I'm shocked. 3. I noticed your huge stock of Expo's in the back for the first time. Thank you for your amazing videos and work, offering knowledge for free. Math can be hard as it is, and you help it seem reasonable.

@blackpenredpen 2 жыл бұрын

Thank you : ))

@christianchavez2202 2 жыл бұрын

I'm shocked too :0

@lakshya4876 3 ай бұрын

''pokeball has no use'' MY LIFE IS A LIE

@mikee-fl8ex 7 күн бұрын

it may act as a noise damper

@aiosuu3507 2 жыл бұрын

the king of math has uploaded :0

@agrajyadav2951 2 жыл бұрын

Euler or Archimedes?

@ojaskumar521 2 жыл бұрын

@@agrajyadav2951 Bprpmedeseuler

@yoursleepparalysisdemon9599 2 жыл бұрын

@@agrajyadav2951 gauss

@coreymonsta7505 2 жыл бұрын

For understanding the definition, it helped me to think about the absolute value parts as distances. Ie read |x - a| as "the distance between x and a". This even makes the more general definitions pretty digestible, because distance is what it's all about.

@greghansen38 2 жыл бұрын

I love these videos of yours -- short, focused on a specific problem. Helping me dive back into the math more than a decade after the homework is over. I just wish for an expanded domain, like multivariable, differential equations, linear algebra, all the stuff a physics student would know and love.

@blackpenredpen 10 ай бұрын

εN definition (finite limit at infinity): kzfaq.info/get/bejne/b7B9ea-rrdrQmnU.html

@dellta491 2 жыл бұрын

After watching this video several times, I finally understand your proof and also understand your itch to draw a square and shade it. I'm your fan from the Philippines. Excellent work, teacher!

@scottwitoff8932 2 жыл бұрын

The definitions I found confusing and tedious to memorize but once I saw a visual representation the concept was not too difficult. Thanks

@mlensenm 2 жыл бұрын

I've always thought that the reason the Epsilon-Delta is presented so early in Calculus I is to scare off those who unprepared. It weeds out many who just aren't ready to take the class. When I took Calc I many, many years ago, things go a lot simpler after slogging through the Epison-Delta problems.

@stephenbeck7222 2 жыл бұрын

Which is why it should probably be taught later in Calc 1 or just not at all. Maybe it could be saved for Calc 2. Let Calc 1 be a class that focuses on slope and area concepts and applications so people can understand why we even do all this. Honestly I appreciate the conceptual focus of the AP Calc exam over how the standard textbooks are normally used in a college Calc course (and I love how Stewart, Larson, etc. are written generally).

@imacds 2 жыл бұрын

I think it snuck its way into the curriculum because it's such a short and simple proof to memorize, despite the students probably not even understanding what ∀ or ∃ or proofs even are. So idk if its really that useful, especially if all it does is make kids flunk the class instead of helping them build a basic mathematical intuition.

@PJ.N3G4 Жыл бұрын

@@imacds what does not that proof mean

@TheXenoBrosMC Жыл бұрын

wait you do epsilon delta in calc 1?? genuinely shocked (learning it in analysis rn)

@MyOneFiftiethOfADollar Жыл бұрын

Right, a bunch college admins met at Starbucks one morning and thought "what can we do to lower enrollment" ? AND delta epsilon continuity notions immediately raced through their minds!!!! Brilliant insight man.

@outofnowhereboy8448 2 жыл бұрын

I have a masters in statistics and a degree in maths and at uni this was the only module (not exactly called calculus but the module that contained this element) I failed, retook and STILL failed. And I put it down to, my stats teaching was AMAZING (hence why I followed stats) and the “pure maths” teachers just did not care to try and show any kind of examples to explain things. My point is, all this time later, and I have finally seen some teaching where it goes outside of “here’s this definition, if you don’t understand, you be stupid” and has bothered to put some actual real world understanding to it, that I finally get it. This is an amazing video and I respect it soo much. What a great example of how maths should be taught!

@blackpenredpen 2 жыл бұрын

😊 and thank you.

@AdoptedPoo 2 жыл бұрын

i hate stats, but my stats teaching is garbage. sucked the life out of learning because it was so boring.

@julius6678 2 жыл бұрын

such a good-hearted guy, that also happens to be an amazing explainer. Thanks a lot for the video, I took a lot out of it!

@abhishekkumar4777 2 жыл бұрын

Best explaination of the hardest and elementary topic of Limits i.e. epsilon-delta definination ,I have seen on internet by any teacher😍👍

@marcelandrade5759 2 жыл бұрын

I'm a Brazilian engineering student and I'm learning calculus with a professor from another country who speaks better English than my professor at the university, who is also Brazilian and speaks my native language. This is amazing, this video helped me a lot. Thank you so much

@imademedikasurya3917 2 жыл бұрын

after seeing him without his beard, It is like he become 20 years younger

@matheusreidopedaco 11 ай бұрын

This is the only explanation of the delta-epsilon definition of the limit that I could understand and now I got addicted and can't stop proving limits! Thank you so, so much for this video.

@michaelsekeleti4652 3 ай бұрын

Great I can be glade that u can help me

@uvxv_ 10 ай бұрын

As a self-learner, your explanations are mind blowing, thank you sir

@kaylo1680 2 жыл бұрын

If only I had this available when I took calculus when I started my degree. We had an e-d-proof on our exam. Thing haunted my dreams for a good 10 days after said exam. Professors just couldn't explain it in a way that made sense to me. I went back to look at the same problem just now after watching the video and solved it in 5 minutes tops. Damn that felt good. For good measure, it was supposed to be applied on 1/(1+x^2) as x went to 0. I arrived at d=sqrt(ε). I reiterate, damn, that felt good.

@sadiakhan6500 5 ай бұрын

saying that "this is one of the hardest things in Calc 1 and a very difficult thing to explain" honestly made me feel so much better, and I actually gained an understanding through this video. All the videos that i've watched that try to build an understanding didnt help, even if they used visuals, but this video's explanation in a more algebraic format helped SO much, and just admitting that it's not easy just makes it feel more like I'm not alone in struggling to understand the logic behind this proof. Like I knew how to write it, but not what it meant. Now I know both. Thank you so much!

@alexj.9011 3 ай бұрын

Your video is the only video that truly goes into detail on this subject

@mathusaymathtutorial935 4 күн бұрын

Thank you so much Sir! Clear, simple language used, well-explained epsilon-delta definition, concept, and proof!

@MiracleMirror117 2 жыл бұрын

Yessssss he finally shaved , thank you for being the best online teacher I ever had, good to see you back to the previous look💖

@dipun4849 2 жыл бұрын

Thanks sir now I am very happy 😊😊 thanks for your explanation. I am from India and am a small student this was written in my book that delta should be taken as small when you have two values of delta. And that increases my tension. Thanks

@mrm6696 2 жыл бұрын

I love your vids man. I like to take some time off of my extra math studies on the weekends and these videos are a great way to relax and enjoy some math.

@jimbyers3092 2 жыл бұрын

Very clearly stated process to help one learn to prove limits! Thank you.

@FirstReconClan 2 жыл бұрын

I'm actually in a course right now that is all about limits and infinite series, so this couldn't have come at a better time. I have to do so many limit proofs and I didn't really understand what was going on until now, thanks!

@treasure-tf5es 6 ай бұрын

You are such a great teacher . Thank you so much. I appreciate your effort

@aryansudan2239 Жыл бұрын

thanks bprp. I suck at real analysis and score the lowest in all quizzes. I have challenged myself to become the best in class at it this semester. This is one step forwards in a long journey

@williejohnson5172 8 күн бұрын

1:15 An absolutely perfect response. You could not have expressed the frustration of trying to explain this con any better. The epsilon-delta proof simply says no matter how close you get to the limit I can get closer. That's it. But the con comes in when they try to convince us that its proof of the limit. It isn't. Conventionally, division by zero is still implied when deriving the limit and the e-d proof has been an inscrutable fig leaf passed around to cover up this flaw.

@kingbeauregard 2 жыл бұрын

I've spent a lot of time chugging through epsilon-delta this past month, and I think I figured it out AND the explanation that would work for me. The trick is to stay away from the numbers until the concept is firmly in place. SO: imagine that you're trying to prove the limit of a given function at (a, L). Can you draw a rectangle around (a, L) that is tall enough that the function never touches the top or bottom edges? And, can you scale that rectangle all the way down to nothing such that the function never touches the top or bottom edges? If you can do that -- if you can derive dimensions for the rectangle that make it possible -- then since the rectangle scales down to converge on (a, L), the function must too, and that proves the limit. Our rectangle has a height of 2*epsilon and a width of 2*delta. So the math is all about proving that you can write epsilon in terms of delta, and probably as a straight linear function. You will start with two inequalities: |x - a| < delta, and | f(x) - L | < epsilon. Then you get to work on the latter. From there is it mostly a matter of basic math operations involving inequalities, but with one additional thing you can do: you can replace any term on the left with a simpler expression that always makes the left side larger, or at least never gets any smaller. So we are treating epsilon as an elastic term that we can make as large as we need to, to compensate for whatever shenanigans we're doing on the left. It is also usually necessary to restrict our x values to a narrow region around "a", which is fine, because we're primarily interested in what happens close to the point (a, L). Very often the "simpler expression" and "restrict x" steps happen together: "I can swap in suchandsuch simpler expression, but with the understanding that x will stay within a narrow region that makes it mathematically valid." Now, remember that the goal is to write epsilon in terms of delta, and we've already said that |x - a| < delta; so, when you've got things to the point where it's |x - a|*(some constant or other simple expression) < epsilon, you can swap in delta, and it becomes delta*(some constant or other simple expression) = epsilon. Once you do that, you've got your simple relationship between delta and epsilon, and you've won. You have proven that it's possible to draw a rectangle around (a, L) with dimensions such that, when you scale it down, the function will never touch the top or bottom edge. From there, use simple algebra to express delta as a function of epsilon. And again, we probably had to restrict our x values to a narrow region around "a", so delta needs to be written as a minimum of that narrow region and the function of epsilon.

@TimothyLowYK 2 жыл бұрын

Why can't the function touch the top and bottom edges though? Just scaling down a regular rectangle with no boundaries should work just fine to prove it wouldn't it?

@kingbeauregard 2 жыл бұрын

@@TimothyLowYK I'm just adhering to "| f(x) - L | < epsilon"; notice how it's "

@youkaihenge5892 2 жыл бұрын

This is similar to the concept of Existence and Uniqueness of solutions. If your solution is unique it must not have any form of overlap inside it's small "neighborhood" at the point, and for it to exist it has a solution. To be both unique and exist implies it is linearly independent and has a "nice" form. These ε,δ proofs can show this concept and for more difficult situations you can use Wronskians. Wronskian is the determinant of functions and its derivatives and if it equals zero you do not have a unique solution and it has dependency somewhere. So, if W≡0 then your solution does not form a basis for your function space. Try this example out with sin(x) and cos(x) to see the beauty of it.

@tonyhaddad1394 2 жыл бұрын

Wooww good job , youre comment is helpful for deep understanding

@kingbeauregard 2 жыл бұрын

@@tonyhaddad1394 Thanks! Lord knows I wrestled with it enough; it nearly broke me.

@thebeedy5 2 жыл бұрын

Videos are awesome. First place I come when I'm stuck is here. Great work!

@RADARTechie 3 ай бұрын

This makes more sense than how my course explained it. Thanks! Now to practice this a few dozen times so I retain it....

@douglasmagowan2709 2 жыл бұрын

It is definitely the toughest concept in Calc I and is usually taught in the first week. I will say that I didn't really understand it until I was in Real Analsys. I spent about 20 minutes considering the significance of each symbol in the definition before it clicked.

@yassako2496 Жыл бұрын

HOLD UP, did blackpenredpen just use a blue pen?

@DaniloSouzaMoraes 2 ай бұрын

best lesson yet on the subject

@ionikre 2 жыл бұрын

I still remember how I struggled to understand the epsilon delta at my day 1 college life... I believe the reason is that ppl were doing "real" maths before, so it's hard to understand a abstract definition. So a visualized explain would help to get through this. Very good work!

@navjotsingh2251 2 жыл бұрын

Luckily, I studied computer science and our course wasn't too bad. But, we did have to learn this definition and what helped me was to model it in a programming language like MATLAB and try many different problems, as weird as they can be, see if I can solve the epsilon and delta limit. If not, I'd research why that function didn't work and that's kind of how I got used to it.

@user-vs2wm7zh3o 2 жыл бұрын

I am a student who takes analysis in Korea. I understand that example very well. Thank you for your good video.

@bariumselenided5152 2 жыл бұрын

I can’t wait til I finally understand this. My professor did the epsilon delta region thing (he called them “tubes” which I quite liked) , and I get that. Like understanding what delta and epsilon are is easy, and finding one given the other is easy too. But the proofs... I just can’t seem to grasp how it actually is being proven. I can do the work and say the words and get the answer, but I just have no clue what I’m _actually_ doing. Hopefully it makes more sense as my brain marinates in it over the semester. Proofs never were my strong suit anyways, it’s why I wasn’t great at geometry

@bamdadzareh6178 2 жыл бұрын

Simply amazing!!! Loved the explanation!

@wackeydelly2016 2 жыл бұрын

Finally somebody did an EXAMPLE do show this. I dont know why none of my teachers did this. It pops out so fast with an example and the main idea is pretty simple. Most students get confused because they forget x approaches a limit but will never BE that number and thats why e>0, not equal. Also, even if a function is discontinuous everywhere (see thomae's function) it can still have a limit at a given a value.

@user-eh2ec3rn6w 2 жыл бұрын

Thank you very much . Your clip is very clear. Now I understand the definition of limit.

@businesscalculusandbusines8574 2 жыл бұрын

Very nice step by step proof - yes, example is the best approach.

@B-Mike 2 жыл бұрын

Great!!!! Loved it. First time I really understood the delta-epsilon concept.

@blackpenredpen 2 жыл бұрын

Glad to hear!!

@GreenMeansGOF 2 жыл бұрын

Small issue with the proof. We also need x greater than or equal to -1/2. Thus it should be δ = min(ε/2, 9/2).

@blackpenredpen 2 жыл бұрын

Very good point!

@Sahan_viranga_hettiarachchi 2 жыл бұрын

Yes , its true 👌

@dijkstra4678 2 жыл бұрын

Where did the -1/2 come from

@GreenMeansGOF 2 жыл бұрын

@@dijkstra4678 You have to pay attention to the domain of the function. We cannot take the square root of a negative.

@self8ting 2 жыл бұрын

@@GreenMeansGOF We don't have to do that : when we study limits we do it on the domain, or on the border of the domain. So it's redundant.

@michellauzon4640 2 жыл бұрын

It is very easy to prove the equivalence of the epsilon-delta formulation and the sequences formulation. Which is for all sequences x(n) converging to a the sequence f(x(n)) converges to L. The sequences formulation is very intuitive.

@douglasrauber2040 2 жыл бұрын

I remember when I got my calc book BEFORE my Calculus classes begun, the moment I understood this definition a mathematical tear dropped off my eye

@gabrielfonseca1642 2 жыл бұрын

This video would have been a lifesaver a couple years ago, but even watching it now I have a better sense of what the proof actually says

@comingshoon2717 2 жыл бұрын

gracias por darte el trabajo de explicar muy bien este tema. Coincido contigo en que es el tema de C1 mas dificil. Poder entender esto cuesta mucho tiempo e intuición.... gracias .. y "me salvaste el pellejo" como decimos acá en Chile... eres un maldito crack

@lordstevenson9619 2 жыл бұрын

Would love if you could do more ε-δ definitions, maybe from sequences, series, continuity and such. I’m finding your explanation and thought process very helpful, especially with how to go about doing the proof and how to formulate a valid proof. I’ve got exams on Analysis in a couple weeks so hoping it goes well. 👍

@citizencj3389 2 жыл бұрын

Its all the same definitions just dofferent arrangement of quantifiers.

@flobah 8 ай бұрын

This helped me understand a lil more! Thank you!

@stumerac 2 жыл бұрын

Very nice lecture! I really like the progression.

@blackbeanboi 4 ай бұрын

This video really helped me. You are a great instructor and I really appreciate your way of teaching! Also I love the pokeball, kirby in the backround and the flannel! I love all of those haha!

@MathTutor1 2 жыл бұрын

This is great. Keep up the good work.

@Alians0108 9 ай бұрын

I love this channel so much

@drpeyam 2 жыл бұрын

Omggggg welcome back 😍😍

@blackpenredpen 2 жыл бұрын

😆

@user-th3ty7dg1d 8 ай бұрын

thank you god for putting this video and in my recommendations and thank you professor for making this video

@alishehab190 2 жыл бұрын

Thank you for a beautiful explanation!

@nadiach1271 Жыл бұрын

Thank you, this was helpful! 😁❤ I'd been looking for this video for a while 😅

@sandorrclegane2307 2 жыл бұрын

Why is nobody talking about the fact that he shaved his beard! Grats on the new look

@haasjeoverkonijn6961 3 ай бұрын

Wow. I actually understand now. Thanks mate!

@richhamster24 Жыл бұрын

you are a brilliant teacher thank u very much

@mesganawoldeselassie4267 4 ай бұрын

I finally understand the definition thank you bro

@abdullahnusretkor4299 2 жыл бұрын

Oh thanks, I'm really gonna need this.

@abhishekshukla2570 Жыл бұрын

Lots of love and respect from India. There is a minor issue of way of talking but I understand ur feelings and concepts also.

@vishakasewwandi7911 2 жыл бұрын

Great explanations..really love it.my fav😍

@gerald5687 5 ай бұрын

Thanks, that's very helpful for me.

@blakedylanmusic 2 жыл бұрын

I’ve watched video after video on this, and I’ve banged my head against a wall trying to understand it. (For context I just finished Calc 3 and I’m taking my Linear Algebra final) I always wondered why this definition still works with holes in the graph at x=a, and why we write the 0 in 0 < |x-a| < delta. This video answered both of those questions elegantly and now I FINALLY get it! Thank you!

@blackpenredpen 2 жыл бұрын

Glad to hear 😃

@citizencj3389 2 жыл бұрын

Once you get into Real Analysis I and II...you will see epsilons and deltas EVERYWHERE.

@davesmyers 2 жыл бұрын

Around 9:20 you might discuss more deeply that sqrt(2x+1) does not give a symmetric window for delta, and you might indicate which is a better choice for summarizing the inequality: 0.58 vs. 0.62. I know this does not end up mattering in the end, but it is interesting perhaps and then you can mention how it does not matter when eps/2 is so small by comparison. Just a thought.

@sebsplatter914 2 жыл бұрын

Got an exam on this in 2 weeks! Thanks, this was helpful and love your style :)

@lordstevenson9619 2 жыл бұрын

Same here. Analysis is a struggle and I love bprp’s thought process. Good luck 👍

@DaMeowster 2 жыл бұрын

Good luck!

@nvapisces7011 Жыл бұрын

Thank you so much for this video! It is so much easier to understand than my lecturer (he's not bad as well but you're better). And the proof is so much shorter. I have to write the part about how you figure out the choose delta. Then write what you wrote. (will ask my lecturer if i could present it your way because he just mentioned that he only requires the part before the proof about getting the delta value in terms of epsilon)

@user-tr9ns6rc3f 2 жыл бұрын

The definition at first time is so difficult in the meaning and relation to our understanding to the limit concept and also in the calculation or its application. You can also talk about the Riemann integral definition.

@ayutac4056 2 жыл бұрын

Excellent explanation! Already linked for my students ;)

@dafta31 5 ай бұрын

I studied the definition using neighborhoods from "Vectorial Calculus" (Marsden, Tromba) and it helped me a lot. Please do an example proof when the limit does not exist.

@philj9594 26 күн бұрын

Okay I feel a little bit validated now as I dropped my calculus 1 course this summer partly because when I got to the epsilon-delta part of the textbook it made me feel like an absolute idiot completely out of his depth. Everything outside of that was coming to me fairly painlessly (struggled a little with related rates). Going to give it another try this fall. Thank you!

@taljune142010 Жыл бұрын

Thanks a lot for your excellent tutorial!

@jackcoleman6449 2 жыл бұрын

This actually saved me I understand it! thank you !!!!!!!!

@anshumanagrawal346 2 жыл бұрын

I make sense of the definition as: "If x is close enough to a, then f(x) is close enough to f(a)"

@popularmisconception1 2 жыл бұрын

yes, and including the quantifier part, it says "you can always get f(x) close enough to L, just by getting x close enough to a"

@anshumanagrawal346 2 жыл бұрын

@@popularmisconception1 Yes

@SyberMath 2 жыл бұрын

Very nice explanation! Great proof! 👍😍

@blackpenredpen 2 жыл бұрын

Thanks!!

@OmerAgmon 2 жыл бұрын

Great video as always. I especially enjoyed seeing you moving the mic away (5:43) for what might be the first time

@blackpenredpen 2 жыл бұрын

😆

@Qalpsy 2 жыл бұрын

Thank you so much for helping us

@alpmuslu3954 8 ай бұрын

Thats really helpful, thank you!

@ditang1162 2 жыл бұрын

My professor Dr Grizzle used to tell me that “you tell me how small ε is” when he explained the limit(of series). This is the clearest and easiest explanation I’ve heard.

@ditang1162 2 жыл бұрын

And yes it was in he’s nonlinear control theory course. You know, Lyapunov.

@simonecoppola8149 2 жыл бұрын

I'm italian, I understood this better than explained by my analisi 1(calculus 1 name in italy) teacher in my language

@vinayakghadge6869 2 жыл бұрын

Kudos!!! Neat and thorough.

@agustinlawtaro 2 жыл бұрын

You're great, many thanks !

@viviancici3936 2 жыл бұрын

a real good teacher!!🤩

@vasusareen8990 2 жыл бұрын

Looking great!

@tubeman5987 2 жыл бұрын

I remember epsilon-delta thing being really confusing and I didn't understand it for a long time untill it finally clicked. It was like when I was a kid and said, that telling time by analog clock is hard and I'll never understand it, but then one day I just magically understood it

@rg99999 2 жыл бұрын

Awesome explanation! Do you have anything on continuity and uniform continuity?

@orenfivel6247 2 жыл бұрын

i think we can choose δ=min{|(3-ε)^2-9|,|(3+ε)^2-9|}/2 as a tighter choice for δ, basically via solving for x-4 in 3-ε

@friendlyneighbourhoodduck1677 2 жыл бұрын

Had this last semester, wish I saw this video back then

@TranquilSeaOfMath 7 ай бұрын

You give a nice lesson here.

@blackpenredpen 7 ай бұрын

Thanks! 😃

@crash_programmer1426 2 жыл бұрын

Why did the beard had to go?! 😭 Nice content as always :)

@genius5625 2 жыл бұрын

Yes , it is the hardest topic in calculus1. But we have you to make it look so easy . Thank you for all your efforts. 🙏

@fix5072 2 жыл бұрын

You could also just say that the Funktion is obviously contious so lim f(x)=f(a)

@MADEBYLAC 2 жыл бұрын

just had today mi final exam of calculus 1. I study at spain. That explanation was really good, but i had the luck that i didn’t need to use that definition in my exam

@ahcenecanpos9463 2 жыл бұрын

nice and logical explication .............. very good

@anaselmanaa5035 Жыл бұрын

thank you so much that was so helpful

@ampisiades 2 жыл бұрын

Big fan of your videos.Could you please make some videos about integrals of f(x)g(x) or f(x)/g(x)?? Wish you the best!

@herbie_the_hillbillie_goat 2 жыл бұрын

You tell me how close you want f(x) to be to L and I'll tell you how close x needs to be to a. The idea is that there is always some range of values around a that will bring f(x) within any given tolerance to L. This definition solved a long time problem in calculus. While terms like "close to" and "approaches" make intuitive sense, they're vague and don't make mathematical sense. You'll notice that this definition defines the limit entirely in terms of absolute values and inequalities. Thus, we can use mathematics we already know to PROVE the limit is what we claim it is BY DEFINITION.