this was actually so helpful. thank you so much! ive been watching a lot of epsilon delta videos since my teacher’s lecture made no sense and this is definitely the clearest one i’ve found so far

I watched this twice and I now understand half of it. Progress!!

Oh thank god, my prof just sort of dropped this on us last week and I had no idea what I was doing. Its really helpful to hear the _context_ in which these problems exist so that I know what I'm looking for and why I need to do certain things.

Thanks! Extremely clear and concise explanation.

Easily the best epsilon delta on youtube, I would say even better scripted than 3B1B's brief explanation. Well done.

That was a truly brilliant explanation.

I have a comment to make. When solving the questions we find a value of epsilon from |f(x)-L|, such that, it is in terms of |x-c| and some other constant term(s). This establishes the connection between the |f(x)-L| interval and |x-c| interval. Now if we squeeze |x-c| interval then |f(x)-L| interval gets squeezed too, since those two are connected. When we can establish this connection through algebraic manipulation we say that the limit exists. Geometrically this makes sense. When we narrow the interval around c the interval around L gets narrow too. Also remember: |f(x)-L| and |x-c| are intervals.

the fact that his shirt says the video is just really cool

YOU JUST SAVED MY LIFEEE !!! Thank you so much x

I had to watch some parts multiple times but it was worth it, I think I finally got it :D

Thank you. What a clear explanation! Amazing teacher!🙏🏻

By far the best video on this topic.

Kudos to our distinguished young man! I never had this concept in calculus, and the Schaum outline series didn't help. Why don't they teach it with visuals? I am visual, and this approach helps tremendously.

Thank for this vid. Really need this😍

I watched like so many videos and this is the only that is good to explain

You explained it really well

Superb explanation :)

0:25 - 0:50 was especially impressive, the word choice was very clear and concise. I could tell that took a few takes, and not just cuz of the jump cuts. How much time do you spend on "scripting" these videos?

@MuPrimeMath

4 жыл бұрын

I spent a lot of time on this video in particular because I was trying to keep it short while still giving good intuition. In general, for my concept explanation videos, like this one and stuff in the vector calculus series, I spend about 1-3 hours on the "script" before I start recording!

how do we shoh that limit approaches to infinity is undefined

Thank you . Maths I get. The language of maths scunners me.

really cool explanations. need your shirt ;) tks man

Hi, where did you get that tshirt?

Thanks dude!

When we are explaining the problems with it and we suppose the limit is m instead of L, are we considering |f(x)-m| instead, and saying that there will be an epsilon such that |f(x)-m|

@MuPrimeMath

4 жыл бұрын

Yes!

Thank you ♥️🌺

Where did you study math?

thank you so much!

How do we show that lim(|x|+1)=1 as x approaches to infinity?

@rokettojanpu4669

3 жыл бұрын

i assume you mean x->0 not x->infty. we must find a delta in terms of epsilon that satisfies the implication in the definition. doing some scratchwork shows that a suitable choice is delta=epsilon

Well I understood but I needed more than You 4 minutes. That's what replay is for.

This stumps so many first year students that it's brushed over in many colleges.

@RealMathematician21stCentury

2 жыл бұрын

It's worthless garbage that has no place in any study of calculus.

This guy's vid is perfect 4:00 mins

So you’re saying that this formula helps find a range of numbers that you need to locate something?

@MuPrimeMath

4 жыл бұрын

The purpose of the limit is to describe the idea of what a function's value approaches as the input approaches a certain value. For example, f(x) = x^2 approaches 4 as x approaches 2. It's useful because we can describe what a function approaches even if it isn't defined at the limiting input!

ur a hero

Thank you

1:00 why do you say 0.1 or 0.01 ~of L~ , I am not sure I understand why should it be multiplied by L

@MuPrimeMath

4 жыл бұрын

I wasn't talking about multiplying by L; when I said "a value within 0.01 of L", I meant an output f(x) where |f(x) - L| or, in other words, a value with a difference from L of less than 0.01. You're right that multiplying by L would be a little strange!

@sudheerthunga2155

4 жыл бұрын

@@MuPrimeMath Thank you so muc for replying, thanks!

is your white board a wall painted with a "Whiteboard-like" material?

@MuPrimeMath

4 жыл бұрын

I'm using a board from writeyboards.com/products/premium-whiteboard

Try cutting the video less, otherwise a super great video

Very helpful!

God thanks, gonna watch this 10 times though cuz this is really not registering with me.

I like it

... well goddamn, I think it finally makes sense! Maybe? I need to roll it around in my head some more.

@kingbeauregard

2 жыл бұрын

I've done a ton of thinking about this, and I feel like what makes epsilon-delta so difficult is that we students don't properly internalize the concepts and basic thrust before jumping into the math. All those inequalities get really confusing if you don't have the basic road map in mind first. After a lot of thought, I've written up the explanation that would have helped me; it omits details but then again so do all road maps. --- In concept, limits are simple: the closer you get to a given “x” value, the closer you get to a given “y” value. The trick is proving the existence of a limit in mathematically rigorous fashion. Imagine drawing a rectangle around the point that you’re testing for a limit. The rectangle needs to be tall enough to vertically contain the function over the entire width of the rectangle; in other words the function never crosses the top or bottom edges. And you also want to set proportions of the rectangle such that you can scale the rectangle down to nothing, and the function still never crosses the top or bottom edges. If you can make a rectangle that satisfies those criteria, you’ve proven the existence of the limit. You have a great deal of control over the dimensions of the rectangle to make this happen. For starters, you may need to cap the width for your rectangle, so that you can focus on a “well-behaved” part of your function without humps or singularities. Putting a cap on the rectangle’s width is fine, just so long as it can scale down to nothing. And the rectangle can be however tall you need it to contain the function at every scaling, all the way down to zero. In fact, the rectangle can be LOTS taller; taller is always fine, the only problem is if it’s not tall enough. SO. If you are trying to prove that the limit of function y(x) is L at x=a, imagine that your rectangle covers the horizontal region between a-δ and a+δ (not inclusive), and the vertical region between L-ε and L+ε (not inclusive). Your job will be to establish a linear relationship between δ and ε, specifically δ as a linear function of ε. And if you have a cap, your δ will be the minimum between the cap and your linear function of ε. If you’re lucky, your y(x) will lend itself readily to showing a linear relationship. If it’s a little more complicated, you may have to employ tricks like representing your function in an unfortunate way (for example, replacing an exponent with one of the definitions of exponents). Sometimes, you will need to take your y(x) and turn it into something guaranteed to be bigger than y(x), and establish your linear relationship against that.

in the definition it says for all epsilon greater than 0 that includes values that are not small

@MuPrimeMath

4 жыл бұрын

That's correct!

@mariashafayat8371

4 жыл бұрын

@@MuPrimeMath So can u answer this question: math.stackexchange.com/questions/3723800/epsilon-delta-definition-for-restricted-epsilon

@MuPrimeMath

4 жыл бұрын

There is a mistake when squaring both sides. a only applies necessarily when a and b are both positive. For ϵ>4, 2 - ϵ Putting an upper bound on ϵ works because the inequality |f(x) - L| describes a range of values for f(x). Increasing ϵ makes the range larger. If there is some delta that restricts f(x) to a small range, then it will also fit in a larger range.

@mariashafayat8371

4 жыл бұрын

@@MuPrimeMath Thanks, I have corrected it.

@mariashafayat8371

4 жыл бұрын

@@MuPrimeMath There is another way to reach the same conclusion (delta=4*epsilon - epsilon^) without any squaring see: math.stackexchange.com/questions/3734406/multiple-possible-delta-in-epsilon-delta

Man, explain the Leibnitz trick

@MuPrimeMath

4 жыл бұрын

If you're talking about the Leibniz rule for integration, I have two videos on that: kzread.info/dash/bejne/i2qOs6-gm5anaNY.html kzread.info/dash/bejne/eYtsmLWMmMa_krA.html

@giovannimariotte4993

4 жыл бұрын

@@MuPrimeMath oh, awesome, You gain one sub

o i get it thanks

lol this is kind of convincing me I should not go into a stem field

Return after a year

My brain hurts

Why use s blackboard when you have shirt, just hang the shirt there and teach 🤣

δ

You talk a bit too fast for me :d

@MuPrimeMath

4 жыл бұрын

I was trying to go fast for this video because I wanted to stay under 4 minutes, but most of my videos are a bit slower!

@nuklearboysymbiote

4 жыл бұрын

0.75 replay speed

@pinklady7184

4 жыл бұрын

Switch on caption or adjust video speed. My studying technique, I usually watch some videos *three or four times.* This works for me. *First time,* I listen only attentively, no matter how difficult the tutorials. Sure, you miss something, if you think that. Unconsciously, your memory bank is absorbing what you see and hear. *RESIST notetaking or pausing allowed during first time listening to tutorial.* Just watch attentively - no stopping the video. At the end of video, take a break of 30 minutes or better an hour or few. Have a snack or do something else. Break helps brain process memory unconscusly. Return and watch video all over all again. Second time listening, still *NO* notetaking or pausing. Listen attentively. Break of 30 minutes or longer. Third time listening to tutorials, you may now pause or rewind video and make notes. You can do that next day, if you like. Sometimes, you remember better at later times.

@-danR

4 жыл бұрын

@@pinklady7184 " take a break of 30 minutes" That misses the issue of the OP, and this is a 4-minute video.

the way you hold the marker is very distracting

The boy was too technical.

This went way too fast

handsome 🥹

thanks bro!