Check out the εδ definition ultimate introduction 👉 kzbin.info/www/bejne/epXXdoShlKl7h9U
@thatomofolo452 Жыл бұрын
Right 👍👍
@scottleung9587 Жыл бұрын
This was my absolute worst nightmare while taking Modern Analysis in college! But many thanks for walking us thru the steps of how this proof came to be.
@shiftsync9988 Жыл бұрын
This is just what I studied for an upcoming exam, great to refresh my memory. Thanks 🙏
@yassinelaouadi305 Жыл бұрын
Thank you for making this demonstration waaay easier than what I learnt in school. Time to flex it on my teachers 😜
@lawrencejelsma8118 Жыл бұрын
As an engineer working on engineering precision mathematics we find the x equivalent in like time measurements all the time when 2x + 1 approximates to 2x with no significant error in precision. 3x + 4 would need a larger x to equal the same low error approximation as 2x + 1 approximate 2x replaced as 3x + 4 approximately is 3x for x >> 1 for large x. For example, x = 10^4 then the function approximates to 2x/(3x) or x in numerator and x in denominator show we are so close to 2/3 no matter if you have a ripple 1 in the numerator and a ripple 4 in the denominator compared to the 2x value / 3x value ... Not the 2 value / 3 value limit mistake in thinking.
@dmitrybak9372 Жыл бұрын
For epsilon-delta proofs, when speaking through the proof out-loud, it becomes way more obvious for the student if the speaker says not just “for all epsilon greater than zero, …”, but “for all epsilon, no matter how small you decide to choose it, …” - i.e. emphasizing that our intent is to “make” epsilon “smaller and smaller”. Also “given arbitrary epsilon greater than zero” -> “given arbitrary small epsilon greater than zero”.
@yanceyward3689 Жыл бұрын
This is an important point that often gets lost in these discussions- you can make epsilon as small as you like and will always be able to find a delta or N that satisfies the delta/N inequality, and vice versa, if the limit is in fact L. If the L is not the limit, then you will get a contradiction.
@nayjer25765 ай бұрын
@@yanceyward3689to be exact, for all n > N that has to satisfy, otherwise it's a limit point
@varun3282 Жыл бұрын
Good that you gave this video I'm about to start limits in my calc course
@haasjeoverkonijn69615 ай бұрын
First time I understand. Great explanation. Thanks
@basilbrush78785 ай бұрын
Man, you bring out the inner math genius in me, and I'm 62. I follow your logic perfectly
@nonentity16810 ай бұрын
Damn, I appreciate your videos even more given my professor couldn't explain it properly in 3 hours.
@ItsMeTheUser Жыл бұрын
Welcome back man!
@helphowdoinputusername357111 ай бұрын
Could you do a video on how to do the proof backwards/both ways?
@Ninja20704 Жыл бұрын
My teacher gave us some simple limit proof qns in my proofs class when teaching us proof by construction. And this was one of them. Quick question, if we wanted to prove a limit as x->-inf, do we just change to N
@CatchyCauchy Жыл бұрын
I think there are many ways to define it for example: lim x-> -inftx f(x) := lim x-> infty f(-x) if it exists Or using sequences: For all sequences (xn)n with xn -> -infty, then we say lim x->-infty f(x) exists if and only if lim n->infty f(x_n) exists and is the same for all sequences I think yours is probably aquivalent
@Xorven2 Жыл бұрын
@Ninja20704 Yes. A usual definition of the existence of a finite limit L of a real function f at -∞ is : For all Ɛ>0, it exists N
@thatomofolo452 Жыл бұрын
To infinity and beyond 🚀🥳🤸♥️💫
@BusyBlueLion10 ай бұрын
Thank you!
@user-nw6cw7vf8r Жыл бұрын
L'hospital: it that even a question?
@user-qj3rv2mo1b6 ай бұрын
I have seen an example where the δ chosen was greater than ε. I was wondering would it not throw δ outside the ε window. Can the chosen δ ever be greater than ε? Thank u
@hritamkashyap5 ай бұрын
Very Very Thank you sir ❤
@jaylinkim19Ай бұрын
beautiful
@teddy05p11 ай бұрын
Lovely video, though I would like to point out a correction that for epsilon-N it should be stated as a defined sequence lets say a_n, so rather a set of a sequence than as you said a function:) But both work fine I guess! Ty for the videos!
@ziro4614 Жыл бұрын
I asked myself what the limit of (1+1/x)^(1/x) when x goes to infinity. I think it goes to 1 but I don't have a way to show it and when I asked Wolfram Aloha it says 1 but the Step-by-step solution kinda goes like e^(0/infinity) equals 1, which it say is the solution. Can someone help me?
@asifthatwouldeverhappen Жыл бұрын
Write the expression as exp((1/x)*ln(1+1/x)) As x tends to infinity, 1/x tends to 0 and ln(1+1/x) also tends to 0. Therefore, the limit is equal to exp(0*0) = e^0 = 1 You can then write the proof it in the epsilon N form.
@ziro4614 Жыл бұрын
@@asifthatwouldeverhappen thanks
@Ninja20704 Жыл бұрын
A simpler way to calculate the limit is that 1/x goes to 0 as x goes to infinity. So the base approaches 1 and the power approaches 0. This is not an indeterminate form, so we can legitamately conclude that the limit is 1^0=1
@Shaan_Suri7 ай бұрын
Hi, what do you do if you have a minus sign in the denominator, so you can't get rid of the absolute value??
@etcthedeimos Жыл бұрын
Nice video
@IloveTwinkies41210 ай бұрын
respect from bmstu
@Happy_Abe Жыл бұрын
Do you have to use the max? What’s wrong with N being negative?
@spiderjerusalem4009 Жыл бұрын
"approaches infinity"...
@Happy_Abe Жыл бұрын
@@spiderjerusalem4009 of course, but I’m saying if such a small N works that it’s negative should still be fine if the inequalities hold, same way N can be a random small positive real number that isn’t close to infinity
@stlegendff739010 ай бұрын
Did you get the answer to your question? Cause I have the same doubt
@Happy_Abe10 ай бұрын
@@stlegendff7390 nope unfortunately not
@thebestchemicalelement4455 Жыл бұрын
hey blackpenredpen, can you solve x = i^x as in, an infinite power tower of i's.
@nickulman9739 Жыл бұрын
i^i^i^…..=x x=i^x x=e^(ln(i^x)) x=e^(xln(i)) note: (ln(i)= (pi*i)/2 for the complex logarithm principal branch, this can be observed also through rulers identity e^(pi*i) = -1 as putting both sides to the power of 1/2 results in e^((pi*i)/2)=i.) x=e^(x*i*pi/2) x/(e^(x*i*pi/2)) = 1 x(e^(-x*i*pi/2))=1 x*(-i*pi/2)*(e^(-x*i*pi/2))=(-i*pi/2) W(x*(-i*pi/2)*(e^(-x*i*pi/2)))=W(-i*pi/2) -x*i*pi/2=W(-i*pi/2) x=(2i/pi)*W(-i*pi/2) Sorry for bad formatting, am commenting on phone.
@sadi_supercell21322 ай бұрын
How to do it with negative infinity
@neekunjchaturvedi Жыл бұрын
Can we not do taking 1/x tend to 0 if x tends to infinity
@sivanaidoo5602 Жыл бұрын
Not calculate but prove it is 2/3. So the limit definition is applicable.
@Ninja20704 Жыл бұрын
You can use this definition to prove that. Given any epsilon>0 Choose N = 1/epsilon Suppose x>N. Check |1/x-0|=1/x (x>0 so 1/x>0)
@neekunjchaturvedi Жыл бұрын
@@Ninja20704 thanks brother
@broytingaravsol Жыл бұрын
still appealing to the version in English
@mihailangelov6 Жыл бұрын
When I will have access to America?
@ceo1OO11 ай бұрын
The blackPenredPen guy is putting on weight: ... he must be eating alot of general Tso's chicken... lol.. it's alright, I eat general Tso's chicken also... 😎
@MikiMiusA8 ай бұрын
Don't we need to write the conclusion at the end?
@naxnusternann332 Жыл бұрын
Are you not allowed to use L’Hopital for a prove?
@SimsHacks Жыл бұрын
Of course not. That's not a proof, that's a calculation technique. Furthemore, these easy limits are usually covered before derivatives.
@photophone5574 Жыл бұрын
@@SimsHacksI think you are right on it coming before derivatives, but calculation techniques do work in proofs. Calculation techniques in proofs is just called algebra
@SimsHacks Жыл бұрын
@@photophone5574 it's allowed if you had previously proved l'Hospital's rule. Which I don't think is the case.
@zarkuz8702 Жыл бұрын
No you definably can’t due to the lack of proof and evidence
@spiderjerusalem4009 Жыл бұрын
please stop bringing this overly used method up, notably whose validity is beyond your question. Utter tiresome.🙄
@Douae11119 ай бұрын
3:36
@JB-ym4up Жыл бұрын
I just multiply the top and bottom by (1/x).
@AdityaKumar-gv4dj Жыл бұрын
Please solve this question for me: Let f(x)=(x²+x+1)/(x²-x+1), then the largest value of f(x) for all x belongs to [-1,3]. Can you please teach me how to apply x's bound over such f(x)?
@arkodasgupta04129 ай бұрын
is it 3 ?
@SamsungA04e-dp7kj5 ай бұрын
dalil d La Hospital Undefined : Proof Theory Graph Trayektory
@siamchowdhury3987 Жыл бұрын
This chanels name starts with my favourite k pop bands name.
@picup30296 Жыл бұрын
the one who copy la campanella?
@ussr8410 Жыл бұрын
Use L'Hopital's rule what's the problem bruh😅
@tiangong6616 Жыл бұрын
But this is about how to write a formal rigorous proof, not obtain the final answer, L'Hopital's rule is more like a calculation technique
@willthecat3861 Жыл бұрын
My cat, and I, have watched a lot of BR's proof vids. My cat is much better than me at giving all the proofs... just copies BR's proof. I don't think my cat understands math... do you?
@ingramr8811 ай бұрын
If the first thing you comment it L’Hospitals, we already know that you’re not going to get out of this video what you need to get out of this video. It’s very telling. Come back after a discrete math class then look at this video lol
@jotajaviergonzalezgarcia7504 Жыл бұрын
Lhlpital 3secs
@cagryldz40895 күн бұрын
hayatımda bu kadar rezalet bir anlatıma şahit olmadıım.