Thankfully, they removed them from the AP exam.

@@primoop9881 Wow, I didn't realize that they had them on the exam at one point. That would be pure pain.

delta eplsion proofs are so henious

It means that they didn’t think you could do it. But you can, in fact, do it.

its literally the opposite bro

I agri

​@@w8floosh281Only if ε > 0 though.

I always thought the same

In my experience of getting a minor in mathematics, epsilon delta proofs of limits only really comes into play later in the upper level classes. The first time I looked into them in detail was Real Analysis. This was after calcs 1-3, Linear algebra, and abstract algebra.

@@gregsavitt7176 could i ask the reason for formalising such concepts? I mean i know it's standard practice to have everything rigorously defined, but is That really necessary?

​@@Qrudi234 To answer your question, yes it is, but not for exercices like this video and very rarely for computation purpose. I see 2 reasons. 1) It is necessery to have a proper limit definition in order to generalize limits to metric space as they are often not as intuitive and 2) at some point, results in analysis are not as trivial and need epsilon argument to properly prove them.Just to name a few, results tied with Cauchy sequence, uniforme convergence, compactness and completeness often need such argument (but not necessarily in more general topologycal context, but that's another story).

@@francoislaniel868 Okay, i already figured the first reason, being that it gives way to generalising the definition. Thank you for your time

Idk why but your profile pic somehow matches your comment

Welcome to blackpenredpen

bro I know how to get simple definite and indefinite integrals. by simple i mean something like no fractions or trigonometry in the equation but still while solving it it can have trig

That's not something you should be proud of tho

@@sherueatyourbestfriend6791 Learning makes everyone happy and being proud of it makes sense..instead of eating your best friend,you better learn how to appreciate even small things in life:)

​@@sherueatyourbestfriend6791 gtfo

​@@sherueatyourbestfriend6791 ofcrse🐒

@@sherueatyourbestfriend6791 stfu

Hey guys, did you know that I hate the epsilon delta definition of limit

Yes we get the gist

🤣😂

Do you want to know the dark side, where you can just show that if x is infenitesimaly close to 2, then 3x-1 is infenitesimaly close to 5 and it will be formall proof? Take d -any infenitesimal f(2+d)=3(2+d)-1=5+3d≈5 qed

Facts

Sequences were taught in calculus where I'm from, but they were after almost everything else which I agree makes no sense

It comes from practice and noticing things carefully

He is not really choosing it to be that. For an epsilon-delta proof you need to show that for any given epsilon there exists a delta (both positive), such that the statement 0

x is approaching 2, so we need |x-2|, the distance between them, to be arbitrarily small.

U are basically proofing that 3x-1 is continuous in 2 that’s why we look at abs value of x-2

It follows from the definition

It's the formal definition of a limit. In the first method, he just plugs in x=2, and evaluates the expression to find the limit as x approaches 2. For this example, it's just a simple linear function, and we have no discontinuities, so there's no need to do anything more than that to find the limit. The second method formalizes the process, in what we exactly mean by "approach". Send x arbitrarily close to 2 without being 2 exactly. Does (3*x-1) continue to get closer to 3*2-1, as x approaches 2? That's what he's calculating. They call it the epsilon-delta proof, because epsilon and delta (the Greek equivalents of e and d) are the traditional symbols that are used for this process.

huailiulin Teenage calc has epsilon delta? 😵‍💫

its on his main channel, epsilon delta definition.

Epsilon Delta 👍

Let's introduce polar graphs and form

In non-standard analysis equivalent definition of limit is: lim_x -> c f(x)=g if and only if x≈c => f(x)≈g where a≈b means that b-a is infenitesimal

based nonstandard analysis

Real Analysis by Bartle and Sherbert is a good place to learn these kinds of proofs and others that are honestly much more interesting. Any other real analysis text would work too. Maybe even start with How To Prove It: A Structured Approach, if you've never encountered propositional logic and basic proof techniques. This level of math doesn't require any real "genius". It's accessible to anyone willing to put in some study. Take some Calc, learn proofs, and bam real analysis is your oyster. Then you get to do complex analysis which is far more fun.

Proof by look at the graph

​@@wavez4224 i dont need to lift my pencil. QED

Proof: Obvious

it's very easy to show x is continuous and then use limit laws to show all polynomials are continuous. anybody doing math at a higher level would just plug in x=2

Not sure about algebriacly but since |x-2|

Cries in proving limits of a quadratic function

Also the suppose part

Well if you were to choose another number it wouldn’t work, so you need to choose the one that does work

Yous need it as proof of the limit, not necessarily to evaluate the limit.

Evaluation and proof are different processes. In this type of proof delta is chosen depending on epsilon. This choice is often found by working backwards from |f(x)-L|

the epsilon delta proof can only prove that a given limit exists, you can't use it to find the limit. for your question, you could use l'hopital's rule to solve it. however, there is also another way using geometry which relies on finding the area of triangles and a sector from the unit circle and then using the squeeze theorem. either way you'll get that the limit is equal to 1

@@Blobfish3561 do you mean here that, using l'Hopital's Rule as a way of getting an idea of what the limit might be? And then use that finding to inform the Geometry Approach that has no circular logical fallacy to actually prove that the limit is 1?

@@AngeloLaCruz l'hotpital's rule can be used to directly find the limit. if we try to solve the limit by plugging in x=0 we get sin(0)/0=0/0 which is indeterminate. So we use l'hopital's rule, which tells us that that limit of sin(x)/x is equal to the limit of the derivative of sin(x) / the derivative of x. The derivative of sin(x) is cos(x) and the derivative of x is 1. So the question can be rewritten as lim[x->0] cos(x)/1. then we can plug in x=0 and we get cos(0)/1= 1, so the limit is one. For the geometric approach, its hard to explain using text without a diagram but basically, you will find that the value of sin(x)/x will always be greater than cos(x) and less than 1/cos(x) (you can prove this by using the areas of triangles and sectors within a circle). and since the limit as x approaches 0 of cos(x) and 1/cos(x) are both 1, by the squeeze theorem, the limit of sin(x)/x must also be 1. you can just search on KZfaq or google for a geometric proof of the limit of sin(x)/x and i think you'll, understand better

​ @Blobfish entertain for a moment the following "thought mathematical experiment": During the first class on the subject of calculating / finding the derivative of the functions: ► f(x) = sin(x) and ► g(x) = cos(x) using limit approach / the limit definition. Would You use l'Hopitals Rule?

@@AngeloLaCruz for those questions i wouldn't cause you can find the derivatives of sin and cos by directly plugging them into the definition of the derivative. l'hopital's rule is only for indeterminate form such as 0/0 or infinity/infinity.

my thoughts exactly! lol. i think the epsilon-delta proof is "teenage calculus" and then adult calculus circles back to plugging in 2, but with the understanding of why you can