Precise Definition of a Limit - Understanding the Definition 

I have a calculus exam tomorrow, i may fail. But finally being able to understand this gave me some comfort. Pray for me y'all!

When I graduate and start my career I'm going straight to patreon and giving you the biggest donation ever!

“You tell me how close you want to be on the y axis, and I tell you how close you need to be in the x axis. If that is possible, then we say the limit exists.”

i wish you were my math professor.

Great explanation. I bought a supplemental calculus book which omitted this section because it's based on "high level mathematics." Think people underestimate our ability to learn sometimes. Will definitely be supporting your videos!

I no longer go for lectures. ever since i discovered the legend...patrickjmt!!

Thanks for the video :) I didn't really understand the definition of a limit before, I just memorised it

10/10. I read through my textbook, and all of the resources my instructor provided and got nothing but this really put it all together in words I could understand!

This is a massive help! My professor is used to teaching grad level calculus, so he gets easily frustrated with us even though it's the entry class 😅

Patrick. You are awesome. Understood this definition after a year. I wish you could make real analysis videos. Such explanations are very clear. Your teaching style is unmatched. Thank you!

THANK YOU! idk why my professor started teaching the entire concept of limits by throwing the definition at me but you just saved me so many tears

6 years later and you’re still helping poor confused college students. thank you for your service brother

This actually really helped me! Thank you so much! I tried to learn from watching Sal from Khan University but it just wouldnt click. You are a much better teacher, thanks again! :)

Thank you for explaining the variables epsilon and delta in simple way. Now I know that epsilon correlates to the limit (L) on the y-axis and delta correlates to the x value it is approaching (c) on the x-axis! I hope you have a nice day!

Thanks mate! This made perfect sense. Props for teaching it in such a way that you encapsulated the definition into pieces that actually make sense to the average person.

You made the whole concept clear to me ... My teacher should learn from you 👍👍👍

U LITERALLY JUST SAVED ME FROM BREAKING DOWN. GOD BLESS

Never seen this concept explained so well, thank you

I've been watching your videos for a few years now. I would not have passed any of my classes without you. You're the best teacher I have ever had. Thank you so much Patrick.

My man... you have a way with words... best video ever. Thank u

At 8:15 really helpful to me, and therefore maybe to you, around the time where he starts the sentence with: "and thats the whole point....."

Man i didnt understand this since last 2 weeks.This video helped me alot understanding ....thanks👌

Yes you should be impressed with your self. Thank you for this!

It's intuitive while still maintaining the rigor, thank you!

Thank you for the video! This is the section we are working on in Calc 1 and you cleared it up so well. Keep doing these!

I watched your video after trying Khan academy. Yours honestly helped me out way more. Definitely using your videos in Calculus next semester. Thanks! ^-^

So great at explaining, wish you were my professor!

Got it in the first watch , you're brilliant .

why can this be explained this way in university i mean this is GOLD.

To be honest the lecture handout we had seemed a bit convoluted and it was almost a whole page of notes. I tried to do some visual representation initially, but then just left it because the technicalities of it were not going to be discussed in that particular module anyway. But I've started to look back and refresh my memory while I'm on a break from college and decided to break it down into small chunks and draw diagrams, and, taking it a little bit each time, over a few days it turned out that it's actually not that difficult to at least grasp what the definition means and to see why it works. Sometimes things seem more intimidating than they are, but taking it in smaller chunks might make things less daunting. I think I was making it harder than it actually is. Came to your video for a different perspective and like your concise, easy to follow explanation. I think intimidation is such a significant factor in college math; it can really be debilitating if you let it get to you; it certainly caused me to skip over some essentials in the past.

A PICTURE IS WORTH A 1000 WORDS.SAYING THE DEFINITION OF LIMIT WITHOUT A PICTURE, IS VERY HARD TO UNDERSTAND IT. A LOT OF SYMBOLS IN THE ABSTRACT IS VERY CONFUSING. THANK YOU MR PATRICK JMT FOR YOUR EXPLANATION.

Hey Patrick, I was wondering if this would be a valid way of interpreting the limit definition: - Let epsilon and delta be arbitrary small numbers. -When we say "The limit of f(x) as x approaches a is L" we mean this: There exists a delta such that the interval (f(a - delta), f(a + delta)) is inside the interval (L - epsilon, L + epsilon), regardless of the value of epsilon.

Dude u r a lifesaver....hats off... would really appreciate if you could do a series on Real Analysis 😊😊

THANKYOU SO MUCH!!! just saved me on my calc test tomorrow!!

Thank youuu you’re the besttt

Thank you so much Patrick

you are a lifesaver

I really love the way he explains it

Thank you thank you thank you ❤️ watching you from Kuwait 🙏🏻

My professor explained that in class, and I was like "I have no idea what that definition is trying to say" then I watched this, and now I'm good hahaha... Thank you!

Read it three times then got it on the first watch, the concept had already started to build tbh

Thank you for this video! it made the concept so much clearer. all those symbols make it look harder than it is

by hearing your explanation on this, you literally saved my ass.

Man you're a legend , thanks for simplicity!

U explained it so differently, gr8. Thank you

Shouldn’t |x-3|

Thanks man. This is so well-explained!!!

bro you seem nice as hell thanks for saving me rn

After watching these videos I can't tell if my professor is just a buffoon or what. Thank you!

Why do we give epsilon on y axis first but not the x axis in the definition? In your example you started with the x axis, you took a small range around the number 7 first.

i understood this, thanks mate

Keep it up! plz keep making more videos

thank you so much. Maybe not an expert yet but I really appreciate it

you are saving my life *500000000000000000000000 batter then my teacher

finally, I fully understood this formula

This video helped a lot thank you

Great video! Now I understand haha, thanks! Your videos have been really helpful.

Thanks for this video. This is still fuzzy, but I’m getting there. Thanks for the help. :)

thank you dear .. very nice

best and simple .thank you

Thank you!

Yes at last. Now I have past my real analasis course. Can you do for f(z) complex plane.

Thank you Mr.patrickJMT :)

oh. my. goodness. you are godsent.

This video is pretty old and pretty useful till nowadays 👍

thanks alot man . best explanation ever .

Please make a vid about the precise definition of a limit for series

Great videos...its very helpful for me

thanks

Your video is great! But I face some probrems on how to prove a limit exist，like limit x approach to 0 xcos(1/x)=0, using the epsilon-delta definition. Would you mind doing some examples like this to share with us?Thank you!

I got it in one go ! But that's probably only because I studied this concept at age 19 not long before taking my final degree examinations in Mathematics . I admit I had forgotten it - I never really had to use it afterwards - but it's amazing how quickly it all comes back .Your explanations are so precise and so clear I think it would probably be more difficult NOT to understand you than to understand you .

Great help buddy🖖🖖

Perfect! Thank you!

Thank you so much❤️

Really helpful !!! Thanks !!

Sir you are fantastic

In what part of the limit definition it´s said that the point can´t be L? or a ?

He is a genius!!!!!

great job.please I m stuck in the examples of fractional functions.

I have one doubt why was there a zero lesser than in the first inequality but not in the second.

Tnx

My question is , what is with epsilon being greater than zero for these? What I mean sorry is not why it’s greater than zero but why is it we need this arbitrary error? Why can’t we be pretty much exact especially in terms of limits, I still don’t see how in mathematical proofs , when we do analysis, if something is less than epsilon it somehow satisfies the proof? Can anyone explain this?

Thank you very much, now that makes sense ;)

Amazing

good job.

Awesome Video.

This content is profoundly engaging. A book I once explored with similar themes significantly altered my perspective. "A Life Unplugged: Reclaiming Reality in a Digital Age" by Theodore Blaze

Just imagine some smart-arse teacher in Mongolia decided that it's just enough that we only have formal definition of "Limit" in "Middle" grade textbooks with not much explanation provided. No wonder my country falls behind in science.

god bless ya

Thank you! Idk wtf my teacher was trying to teach...

I think I got it. Thx

So we must show that a is an accumulation point

“-wouldn’t you throw 3 pennies at ‘em everyday and... imagine how fun would that be.”

wow !!! seriously save me !!!

WOW

tysm omg QAQ

10/10 would reccomend

He's right it's not that hard, it's just you thinking it is hard, a litle advice: if you're studying mathematics you really need to focus on it, remember that the brain cannot focus on two or more things at a time, so say you're studying a concept while thinking it is hard at the same time, you won't get any progress my friend, just focus on the concept nothing more. This is from my own experience :)

This is literally a life saver. I had a 2 hour lecture that sounded like literal gibberish to me, and you beautifully explained it in a couple minutes.

For my Calculus kids watching this: a is the same thing as c.