Lmao idk how you'd prove a definition. I guess you could rigorously prove all the algebraic manipulations you did from the field axioms or something
@CharlyCrazy2000
3 жыл бұрын
Nah, a definition can't have a proof. Or well, you can prove it by definition hahaha
@hybmnzz2658
3 жыл бұрын
At that point you are doing more proving properties of algebra than calc1 lmaooooo
@ianmoseley9910
3 жыл бұрын
I think you start fading into philosophy by then
@Mauricetz
3 жыл бұрын
String theory
@powerplayer75
3 жыл бұрын
This is the equivalent of a child asking "why?" for every answer given
@DarthShpan
3 жыл бұрын
yeah, that is actualy what calculus is about. Or what is math about. Or every single science.
@realbignoob1886
3 жыл бұрын
@@DarthShpan yes
@yuveex
3 жыл бұрын
I did it when I was a child then I now realize it's tremendously annoying
@chappie3642
3 жыл бұрын
@@DarthShpan why?
@aleph6707
3 жыл бұрын
@@DarthShpan You got it backward, maths is about assuming a few axioms and then take those to their logical conclusions
@drpeyam
3 жыл бұрын
(d) Do this with your left hand
@utkarshsharma9563
3 жыл бұрын
Or right, for left handed people
@Gennadi149
3 жыл бұрын
(e) Do this with both hands simultaneously :D
@hassanalajmi155
3 жыл бұрын
(f) Try to solve this without writing anything
@rodrickzapanta7197
3 жыл бұрын
(g) use the force, Luke.
@realbignoob1886
3 жыл бұрын
h) prove part g
@thedoublehelix5661
3 жыл бұрын
Proof for part b and c are trivial and left as an exercise to the grader :)
@TheLucidDreamer12
3 жыл бұрын
Okay engineer
@thedoublehelix5661
3 жыл бұрын
@@TheLucidDreamer12 lmao I feel like this community is the only community that uses engineer as an insult. Btw I'm pretty sure an engineer wouldn't say the proofs are trivial
@gabriel7233
3 жыл бұрын
@@thedoublehelix5661 IT WAS A JOKE
@mgancarzjr
3 жыл бұрын
sin(very small angle) ≈ 0 duh
@thedoublehelix5661
3 жыл бұрын
@@gabriel7233 I know lol
@OmicronGaming
3 жыл бұрын
ah yes epsilon delta, the kryptonite of my collegiate mathematics adventures
@roberto3414
3 жыл бұрын
lmao
@tubax926
3 жыл бұрын
Agreed man. When I first saw it I just started crying because I encountered yet another greek letter, but then I started screaming because it's the most complicated out of all them
This man really was trolling me 40seconds in the video
@xthomas7621
3 жыл бұрын
got me too :D
@godson200
3 жыл бұрын
Lol xd
@godson200
3 жыл бұрын
Hehe noobs
@executorarktanis2323
3 жыл бұрын
Has he wrote 1/3 I sighed and said not again then started laughing
@skpcboy
3 жыл бұрын
nearly had a hear attack damn
@lagrangiankid378
3 жыл бұрын
Yeah but in part c you assumed all the properties of fractions, multiplication, sum, subtraction: you have to prove all of that too...
@multitude1337
3 жыл бұрын
hahahhaaha
@lagrangiankid378
3 жыл бұрын
@VeryEvilPettingZoo I personally find the same thing true even for points b and c
@ahouais5620
3 жыл бұрын
Then he also has to introduce the concept of relations between two objects Also sum and substraction are the same operation, and multiplication and fraction are too :x
@lagrangiankid378
3 жыл бұрын
@@ahouais5620 yeah, you are right
@Ferraco05
3 жыл бұрын
XD
@mycroftholmes7379
3 жыл бұрын
Teacher: Prove the proof *shows the history of derivatives from Leibniz and Newton
@stapler942
3 жыл бұрын
I think the whole reason we have the epsilon-delta proofs is because mathematicians were not satisfied with Leibniz and Newton.
@evansmith6216
3 жыл бұрын
I would've gotten a single point. I shall ensure that this video never reaches my calculus AB teacher.
@chimetimepaprika
3 жыл бұрын
Approximately 45 seconds: "...Just kidding." "Awwww, you got me!" "..just kidding again." "EVERYTHING I KNOW IS A LIE."
@blackpenredpen
3 жыл бұрын
: ))))
@flowerwithamachinegun2692
3 жыл бұрын
Turning around and revealing that you have the rest of the definition on your back was *the* biggest plot twist I have ever seen
@not_vinkami
2 жыл бұрын
(a) Find f(x) [1 mark] (b) By using the Set Theory, define f(x), x^2, limit, and all arithmetic operations that you need [49 marks] (c) Hence, prove the result you got in (a) [50 marks]
@blackpenredpen
2 жыл бұрын
Could you reserve one point for just writing my name on the test? 😆
@tank2256
Жыл бұрын
@@blackpenredpen 😂
@skeetplayz
8 ай бұрын
Man said find f(x) 💀
@kallethoren
3 жыл бұрын
Me still studying high school math: part a) “Alright, this is easy”, part b) “Oh yeah, I remember that definition. Fair enough”, part c) “Panik”
@jasonvanmeir3978
3 жыл бұрын
Yeah we didn’t cover this in high school calc 😭
@yuveex
3 жыл бұрын
It's all good and well till we reach part c
@oliverbrubacher9608
3 жыл бұрын
Im in uni and still panik'd when I saw prove your proof T-T
@tubax926
3 жыл бұрын
@@jasonvanmeir3978 yup you learn the proof of the proof in advanced uni maths
@targetiitbcse1761
3 жыл бұрын
same here
@jehmarxx
3 жыл бұрын
The hardest part of any exam ever is the basic lesson from years ago that you already forgot.
@austinemmons2647
3 жыл бұрын
"Write 'choose delta = ' and leave it blank" It's a surprise tool that will help us later
@colleen9493
3 жыл бұрын
Part c: Since they are asking us to prove part b, it must be true. Done!
@1234567qwerification
3 жыл бұрын
This is so meta ^_^
@rosschurchley2070
3 жыл бұрын
Great presentation! It's probably worth noting in part (c) that the cancellation of h in (2x+h)*h/h relies on the fact that the epsilon-delta definition has us assume that |h|>0. (If h=0, we'd be cancelling 0/0 which is no good.) This is the reason the epsilon-delta definition is more rigorous - we're proving that the cancellation you did in part (b) was justified.
@blackpenredpen
3 жыл бұрын
Very good point, thanks.
@hevidu4896
2 жыл бұрын
Is it wrong to say that delta is an infinitesimal? If so we're not doing division right?
@elweewutroone
2 жыл бұрын
Infinitesimal = infinitely small which is the same thing as saying 0 (0.9 recurring = 1, for example) Limits = what happens as some variable approaches, but not gets to that value They are not the same
@uklu
Жыл бұрын
@@hevidu4896 it's not wrong per se. It's a good way to get intuition, infinitesimals are just not mathematically rigorous
@barakeel
Жыл бұрын
@@uklu infinitesimals can be rigorous, it's called non-standard analysis.
@markcross109
3 жыл бұрын
x^2 be like that nerd boy in middle school then suddenly get buffed in college
@greg77389
3 жыл бұрын
Then you have e^x^2, it's father on steroids
@lp9931
3 жыл бұрын
Haaaa
@swanhtet1
3 жыл бұрын
Came here for the beard. Stayed for the math.
@blackpenredpen
3 жыл бұрын
Appreciate that!
@Geo25rey
3 жыл бұрын
Part C gives me flashbacks to Real Analysis :(
@arequina
3 жыл бұрын
I failed real analysis. Still gives me nightmares to this day. That was over 30 years ago. Hated real analysis ever since.
@Geo25rey
3 жыл бұрын
@@arequina yeah I think I got a D in it. It was just so awful
@arequina
3 жыл бұрын
@@Geo25rey That's what I actually got. But it's still considered a failure since I did not really learn anything. My professor wrote his own manual that was full of errors that he admitted but made us buy anyway. It left a really bad taste in my mouth that I still remember it today.
@АзХашми
3 жыл бұрын
@@arequina Oh man. I hate professors like that
@stevengu1253
3 жыл бұрын
Interestingly enough, I loved Real Analysis.
@knutritter461
3 жыл бұрын
The shortest math-joke ever: Let E < 0 :-D
@colleen9493
3 жыл бұрын
I don’t get it. Can you explain?
@blackmamba1261
3 жыл бұрын
Negative. I refuse
@novidsonmychanneljustcomme5753
3 жыл бұрын
@@colleen9493 "E" means "Epsilon" here and in "classical" math proofs it's actually always "Let E>0." (and never negative). So simply a nerdy insider joke. :P
@heth8225
3 жыл бұрын
Let E be any large positive number :)
@LabMember-lq1ul
3 жыл бұрын
Write ϵ
@kotarojujo6365
3 жыл бұрын
He used to look like my big brother and now he looks like me dad.
@wise_math
3 жыл бұрын
Lol. Bcos of long beards..?
@fgvcosmic6752
3 жыл бұрын
What, like Jigashitaka Hosuke?
@sueyibaslanli3519
3 жыл бұрын
This was our first lesson when we had begun to calc.
@erik19borgnia
3 жыл бұрын
When I saw C, I thought that it means to prove that the limit used in B is really the derivative, so I was thinking in the graphical definition of derivative. I wasn't expecting the proof of the friggin definition of limit xD
@micheledejana7849
3 жыл бұрын
Hi from Italy 🇮🇹🇮🇹❤️
@ettorefagioli1012
3 жыл бұрын
hi from zona gialla
@salvatorebonanno860
3 жыл бұрын
hi from zona arancione
@diego_1619
3 жыл бұрын
Hi from Sacro Campano Impero
@micheledejana7849
3 жыл бұрын
@@ettorefagioli1012 hi from la zona più rossa d'Italia
@filippomaccarini9754
3 жыл бұрын
Hi from gabbio
@djgulston
3 жыл бұрын
Hold up! How long have you been growing the facial hair? This is the first time I'm seeing it.
@blackpenredpen
3 жыл бұрын
Lol, since March after schools closed down.
@godson200
3 жыл бұрын
@@blackpenredpen youre growing a beard, and I am growing my hair. Facial hair just isnt my thing. Last time I had a haircut in march, too
@muskyoxes
3 жыл бұрын
The way to solve this is to think of some intermediate "proof" for part b such that you can use the real part b proof as the part c proof.
@valar_dohaeris7387
3 жыл бұрын
That's actually pretty smart, like fr.
@ukas8343
3 жыл бұрын
At 0:49 "and if you got this question wrong then..."😅😆
@claxvii177th6
3 жыл бұрын
I wouldn't worry, it just means you don't know calc
@claxvii177th6
3 жыл бұрын
you as anyone in general. I am just arguing against whats said in the vid. just don't like anyone to feel bad about math in anyway
@josephquinto5812
3 жыл бұрын
I would have gotten 5/15 on this test 😂
@ashtonsmith1730
3 жыл бұрын
i would of had ⅔ points.
@damiankaleomontero496
3 жыл бұрын
Same
@UltraStarWarsFanatic
3 жыл бұрын
5/15 for me now, but I feel it would have been easy to guess ahead of time that a proof for a derivative would be on the exam, so I imagine I would have prepared in advance when I was in calc... so 10/15. Never even heard of anything from part C though. Literal gibberish. 🤣
@AboodXD
3 жыл бұрын
@@UltraStarWarsFanatic doesn't that still mean you would get 5/15?
@thegamerfromjuipiter7545
2 жыл бұрын
@@UltraStarWarsFanatic Really? While we didn’t use epsilon delta proofs for this purpose, at least not yet (in calc 1 rn), we did use epsilon delta proofs in the first quarter of calc
@talkingmango8658
3 жыл бұрын
Literally just had a test almost exactly like this a few weeks back.
@blackpenredpen
3 жыл бұрын
Nice, how did you do?
@PixelThorn
3 жыл бұрын
@@blackpenredpen not so well it seems
@370GameOver
3 жыл бұрын
In my 1st year of university i went to calc 1 monitoring, asked the monitor how can i prove a limit using this definition. He tried for 50 minutes and failed miserably.
@TautBrigas
3 жыл бұрын
He looks like a Chinese movie monk you confront when you reach a dojo on the top of the mountain during your training
@effanineffables
3 жыл бұрын
An excellent quick example for revision of First Principles and epsilon-delta. A confidence booster for sure.
@blackpenredpen
3 жыл бұрын
Glad you enjoyed it
@carultch
2 жыл бұрын
Is there a practical application for knowing how to find derivatives through first principles and epsilon-delta, now that mostly every function you'll ever use in practice already has derivative you can solve through differentiation rules?
@thefremddingeguy6058
3 жыл бұрын
*part a* yeah i can do that *part b* great a little more work i guess i can do that *part c* no
@MathAdam
3 жыл бұрын
I love this. I'd like to do a whole course on the Basel Problem. Suck the marrow out of one single expression.
@user-nb6zu3rk4f
3 жыл бұрын
Proving that the Taylor series is valid would take quite long
@ArcsMX
3 жыл бұрын
good old times when all 10 questions were epsilon-delta exercises :)
@chimkim
3 жыл бұрын
I forgot the limit formula for part B, so I used FTC to say that if the integral of 2x is x^2, then d/dx x^2 = 2x. I then said the area under the graph of 2x can be described as a triangle with a base length x and height 2x, so to find the area at a given point you can use the area of the traingle 1/2 bh and replace b for x and h for 2x, giving the formula 1/2 * x * 2x or x^2. I have no clue how I would answer part C though. Maybe a proof of the triangle area formula?
@skolmatematik2729
3 жыл бұрын
I find his T-shirts really fantastic thank you for your videos and your enthusiasm makes you want to do math. I teach mathematics in France and I run a SKOL MATEMATIK KZitem channel You are a real source of inspiration for me good luck👍👌🙏
@mgancarzjr
3 жыл бұрын
I actually remember the concept if not exactly the formal definition. It helped me understand why a unified limit from both sides doesn't exist at certain types of asymptotes such as 1/x as x -> 0. I recall the example of this being a function which oscillates infinitely as x-> 0: sin(1/x) but had to look that one up.
@IISH4RKZzII
3 жыл бұрын
how to use delta epsilon definition to disproove something, I only see it prooves every limit i encounter.
@danielbee
3 жыл бұрын
I think you do something like: Suppose f(x) has a finite limit at x=a.... And then show a contraction in the proof
@hybmnzz2658
3 жыл бұрын
A limit is not equal to L if there exists epsilon such that for any delta, |x-a| epsilon. Then if you can say this statement for any L you can say the limit does not exist in general. Keep in mind a limit equal to infinity is a special type of does not exist but is often seen as something that needs proving.
@JackRule16
3 жыл бұрын
In college, I probably get 10 points. Now I get 5 by barely remembering the limit definition of a derivative. When I'm 40, god help me.
@divisix024
3 жыл бұрын
For part (c) "check" most of the work is essentially the exact same as in (b) except for the last line, which is trivial. So I think it would be fine to just write "Given any epsilon>0, choose delta=epsilon. By (b), |f'(x)-2x|=|h|
@JustinsRealmMC
3 жыл бұрын
0:40 2x+C where C=0
@zfam99
3 жыл бұрын
Definitions be like: I've got your back
@vladthe_cat
3 жыл бұрын
Ha! Its funny cuz he has the definition on his back!
@MsPocketMonsters
3 жыл бұрын
I love these, man. Your videos are so much fun I got an erasable notebook just so I can do and do calculations with a pen without worrying about the paper after I'm done
@takyc7883
3 жыл бұрын
you actually scared me with that integration instead of differentiation lmao
@blackpenredpen
3 жыл бұрын
You mean the integral of x^2 without the power rule?
@Mark-uk8wz
3 жыл бұрын
Prove part A, prove part B, prove part C, prove part D, prove part E, prove part F, prove part G, prove part H, prove part I, prove part J, prove part K, prove part L, prove part M, prove part N, prove part O, prove part P, prove part Q, prove part R, prove part S, prove part T, prove part U, prove part V, prove part W, prove part X prove part Y, prove part Z, prove par...oh wait nevermind
@mikuculus3720
3 жыл бұрын
Prove part π, prove part ∫, prove part ∭ PROVE PART, ∰
@plislegalineu3005
2 жыл бұрын
Prove part 一, prove part 二, prove part 三, prove part 四, prove part 烤, prove part 中 and prove part 國
@seanvogel8067
Жыл бұрын
Did you write a program to write that comment? I would’ve. 😂
@yassineseghrouchni8175
3 жыл бұрын
I hope there are no teachers watching this
@wise_math
3 жыл бұрын
Lol
@Zulfar-bd9tc
2 жыл бұрын
As a student who took AP Calculus AB and BC (Calc 1 and 2) in a Florida High School, I can tell you right now. There's no way I'd get more than 5 points. Part C was never taught, nor did it ever show up in any AP exams, ever. There's no way I could get part C correct, I wouldn't even know where to start.
@blackpenredpen
2 жыл бұрын
The epsilon delta proof is not on the AP test. It’s usually taught at university calculus.
@imperialrecker7111
3 жыл бұрын
I could have done the first 2 problems. The last one, I have never seen it before. I am glad that I learnt something new today.
What is written ? I only read epslon and Delta from the comments section
@DarkRedZane
3 жыл бұрын
0:28 I thought I was high and mistook the derivative as integral
@blackpenredpen
3 жыл бұрын
It happens : )
@MathswithMuneer
3 жыл бұрын
Respect from one math teacher to another math teacher ❤️
@rexreinke9565
3 жыл бұрын
This was literally in my maths A-Level this year
@devan2604
3 жыл бұрын
Do we have the first principles and epsilon-delta for A levels? I don't think so right?
@rexreinke9565
3 жыл бұрын
@@devan2604 first principles. 7 or 8 marks for the question i think i got it right
@devan2604
3 жыл бұрын
@@rexreinke9565 Which paper is that?
@rexreinke9565
3 жыл бұрын
@@devan2604 paper 2. OCR mei b
@joshuamitchell5530
3 жыл бұрын
@@rexreinke9565 Ayy finally someone else that did OCR MEI.
@jasserramos1512
3 жыл бұрын
First comment gets a like they said
@Xeotroid
3 жыл бұрын
Everybody gangsta until the calc prof starts writing code.
@StuartSimon
2 жыл бұрын
I wish that in my Cal I class I was actually given epsilon-delta proofs. We were merely required to memorize them in the definition of the limit, and I was constantly confused by their roles in the definition. It would also be useful to use the negation to prove that a limit does not exist.
@patricioluzuriaga9292
3 жыл бұрын
Creo que soy el único hispanohablante que ve tus videos. O al menos quien comenta. Simplemente, muchas gracias. No sabes cuántas horas me quedaba estudiando tus videos. Muchísimas gracias!!!
@EntaroCeraphenine
3 жыл бұрын
So, if someone gets part a wrong but they somehow manage to prove their logic in part b, do they get 4 points? Cuz it says to prove the answer in part a :p
@jcnot9712
3 жыл бұрын
Any professor worth their salt would give partial credit in that instance. There exist petty authoritarian professors who would deduct half or more but those people shouldn’t even have a job.
@fernandosampalopino1597
2 жыл бұрын
Everypeople can pass with a and b question 😊
@Grassmpl
3 жыл бұрын
you're wording of b, c, are vague. How do we know not to answer the part c already when we are doing part b?
@aleladebiri
Жыл бұрын
The Power Rule is already proven so referring to it is as valid a proof as using the definitions. I think the question ought to include "prove part a using the definition of derivative" and "prove part b using the formal definition of limit"
@shashwatd03
3 жыл бұрын
0:30 that literally stunned me
@dequariusforester8081
3 жыл бұрын
I was like, why’s he taking the integral did I miss smtn? Only to find out I have been bamboozled
@Firetech2004
2 жыл бұрын
For part c, I actually thought you’d use first principles to prove that the derivative of x is that formula you use in part b. I learnt this in class 11 and I was required to write all of this to find a derivative of a function for 5 marks- Let y = f(x) y + delta(y) = f(x + delta x) delta(y) = f(x + delta x) - y = f(x + delta x) - f(x) Dividing both sides by delta(x), delta(y)/delta(x) = [f(x + delta x) - f(x)]/delta(x) Taking limits on both the sides, dy/dx = Lim (h -> 0) [f(x + h) - f(x)]/h And now write whatever you wrote in 2 to find the derivative of x^2 = 2x
@mohammedsalouani7672
3 жыл бұрын
0.30 this what really happens when you are in the exam 🤣🤣🤣
@mazingzongdingdong
3 жыл бұрын
thank you Confucius
@lelouchlemprouge6380
3 жыл бұрын
Dude give us Amazon links for those tshirts 🙏🙏🙏 Edit:-I saw link in discription sorry to bother ya 👍👍
@blackpenredpen
3 жыл бұрын
No worries. 😃
@jeanmerguz2792
3 жыл бұрын
I don't understand around 7:30 when we want to prove that |f(x)-L|
@dudono1744
3 жыл бұрын
When i saw the thumbnail i thought bprp was trolling, then c part came in
@blackpenredpen
3 жыл бұрын
It happened in real life before...
@JSSTyger
3 жыл бұрын
Now find the area under the curve using Riemann sums.
@asamet2007
3 жыл бұрын
Why do I find that the epsilon-delta definition is obsolete?!! It doesn’t add any new information beyond the proof of part (b)!!
@Bingcenzo
3 жыл бұрын
It's trivial for this problem but the steps are necessary with a more complicated problem. All about the steps.
@asamet2007
3 жыл бұрын
VincenzOK Can you give me an example please? I mean an example where using epsilon-delta definition will add a new level of depth (insight/ knowledge) in our proof? Because, I really think it’s an equivalent to the Limit definition .
@mgancarzjr
3 жыл бұрын
There's a function, I believe it involves sin, where the function oscillates an unlimited amount of times as you approach zero. Therefore, the closer you attempt to get to the derivative at zero, the less close you are to a value. It's also why limits of asymptotes exist only from one direction unless it's a, for lack of a better term, spike. Lastly, the definition allows for a limit to exist at a removable discontinuity as the closer you get the inputs from both sides, the closer the resultant value is.
@asamet2007
3 жыл бұрын
Maciej Gancarz Jr. you meant Sin(1/x).. but still I don’t see how using epsilon-delta definition helps or gives a more insight (for this case) than the definition in part (b) in this video
@angelmendez-rivera351
3 жыл бұрын
@@asamet2007 Well, why don't you try proving that the limit doesn't exist by using the definition? You haven't shown any semblance of an attempt
@benitimur2788
3 жыл бұрын
U look like the Chinese version of al khawarizmi
@eduardovega3591
3 жыл бұрын
Please solve an IB math hl exam
@andyramirez6016
3 жыл бұрын
I would love that. Please bprp!
@korbinmdavis
2 жыл бұрын
Real Analysis killed me. I died. I am dead.
@elijahcota2408
3 жыл бұрын
my first calc 1 midterm at Dartmouth had a question like this.
@dragofand
2 жыл бұрын
Thankfully the first time I heard about the epsilon delta definition was when I took a class called "Foundations of Higher Mathematics".
@alexisr1006
3 жыл бұрын
Oh my god i love this kind of "theoretical" video!
@vyommodi811
3 жыл бұрын
During 10:00 th minute how can we say delta = epsilon by an equality sigh as for instance 0
@multitude1337
3 жыл бұрын
i laughed super hard at the first part hahaha
@blackpenredpen
3 жыл бұрын
Glad you did 😆
@戴劭名-z8p
2 жыл бұрын
It feels like someone deliberately tells you to write something in C program. And then tells you to do the same thing in assembly. And lastly, connect an actual circuit that does the same thing by hand. Completely unnecessary but the professors just wants to mess with you.
@ajetsai1199
3 жыл бұрын
I used to watch your videos in 2016, remembered how much I loved them and came back just for them. Love your work. Keep rocking.
@blackpenredpen
3 жыл бұрын
Thank you! Highly appreciated 😃
@pharynx007
2 жыл бұрын
for anyone except a math major, the epsilon delta definition of a limit is worthless -_- my first calc 1 teacher was obsessed with it, and actually had us use it on tests. i did not pass that class and had to retake it with a calc teacher that knew the above statement is true, and got an A.
@lucasyoungers
3 жыл бұрын
gonna be real i didn't even remember the definition of a derivative. also my calc 1 final was super easy so maybe i just got off easy or something, I never learned the epsilon delta thing
@chenkoguenas9665
3 жыл бұрын
You really only need to know it if you are a math major tbh. It reiterates something that is already extremely intuitive
@thedoublehelix5661
3 жыл бұрын
Bruh it's just lim change in y / change in x as change in x goes to 0
@amitir22
3 жыл бұрын
@@chenkoguenas9665 or a CS major :,(
@ianmoseley9910
3 жыл бұрын
I didn't even learn that "for all/exists" notation until a year or so ago. Still not sure I follow the concepts here but shall try again.
@rikhalder5708
3 жыл бұрын
Your beard like Lim h=0 sin(π/x)
@johnathanleung7500
2 жыл бұрын
This is basically my university's real analysis course, but we could go further to derive real numbers from the axioms!
@SashaTownsendTulsa
3 жыл бұрын
This makes me happy. Great question for Honors Calc I!
@Chaosdude341
3 жыл бұрын
I feel that the depth of a mathematician could be judged by how many (prove the previous statement) statements they could satisfactorily complete. Very interesting idea.
@siri7311
2 жыл бұрын
Roju and then delete this communication including attachments. And then delete and destroy any questions please contact
@chandansuman6362
3 жыл бұрын
Can u solve JEE - Advanced Exam of India?
@marcallengonzalvo687
3 жыл бұрын
Up
@drunkgoblinpainting9223
3 жыл бұрын
I'm in my final year of a physics degree. I got 1 point...
@frozenmoon998
3 жыл бұрын
I thought you had to do derivative by part.. such a hard derivative, for a first grader of course, but such a great video, for all maths viewers - no matter the level of math they are at.
@dandrost646
2 жыл бұрын
@:40 i was questioning literally all my calculus knowledge
@hiepomegahiepomega485
3 жыл бұрын
You can set caption Vietnamese. Please ,I don't understand you talk
@woody4456
2 жыл бұрын
i love watching these thinking that i know what i’m doing
@ekakiman
3 жыл бұрын
anyone notice he's not even holding his mic any more, its just a pokeball
@The1RandomFool
3 жыл бұрын
Part c is a question you'll find in a real or complex analysis course, haha. Part of the reason I'm glad I'm self-taught is that I don't have to memorize epsilon-delta proofs for exams.
@Pseudo___
3 жыл бұрын
that beard is gross
@empoleon7750
3 жыл бұрын
I should keep this video in mind for when I get to Calculus 1.
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