I love the way you are so enthusiastic about teaching!! thank you so much for the video :)

My first time to appreciate someone on KZfaq

You are the best math teacher that exists!

9:18 I did the same expression and the meme appeared! Truly magnificient! YOU GOT ME! LOVE FROM INDIA

My professor prooved the same thing to us. He skiped all the (un)necessary comments what's coming from where so I was so lost looking back at my notes. Your videos are for sure saving me :D

Mathematics becomes easier for me because of how you explained it in such simple ways....Thank you very much

You're really making our life much simpler and thanks a lot. You simplified the proofs very well.

This is it. Two hours of working on the same delta-epsilon problem, and this is the video that made it click for me. Thank you.

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First I need to tell you that you have great videos with excellent explanations. These definitely make math learning interesting, enjoyable and easy to understand. The point of this comment is to let you know about a very important notation matter. When we right limit at the beginning without a parenthesis, the limit only belongs to the first term. So, the correct way to write it is to use a parenthesis around all three terms as lim{ x → 1} (x²+5x+6) = 12. Keep doing what you are doing. Thank you.

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This is the best I have ever heard this concept explained. I was struggling with understanding how the proof worked for the past 2 days, and I finally understand now. Thank you!

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Love❤ from India

Great video! Thanks. It would be nice to add some graphics to bring this concept to clarity.

Great!

Can someone please explain when 9:04 he writes x+6 as 8 in the inequality. Because he showed that x+6 is less than 8, but when he inserts 8 in the epsilon inequality, he technically increased the left hand side of the inequality without increasing the right hand side (epsilon). Which makes me a little suspect on whether the inequality will hold true. I am no professor and I respect everything he does, but I get delta=epsilon/6. Please feel free to enlighten me. Cheers from Denmark

Respect from Cameroon +237, 3:19 🎉🎉🎉

U're genius

Hello Sir, there is a mistake in this proof. You cannot replace |x+6| with 8 and be sure that 8|x-1|< E. We can take 6 instead of 8 but in that case in the last step you wont be able to replace |x+6| with 6, hence we get stuck. Could you please check for this.

why x-6 cannot be replaced with 7? it is smaller than 8 how we replaced that?

thank you so much sir, it really helps me a lot. And now, maybe I can answer our exam tomorrow hhahhaha

It is good. I am lucky if you add another example.

Bravissimo. Con te e con Robert Ghrist la matematica è un incanto. Grazie 😊😊

Nice❤

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The proof has fundamental error! The correct proof is as follows Let f(x)=x^2+5x+6 We want to show lim x->1 {(f(x))}=12 For all e>0 whenever |f(x)-12|

Sir which camera are you using

Thanks for video.... epsilon and delta greater than zero is true

That is easy and clear , do you do one to one tour ?

Countless hours of calculus and epsilon delta videos and I still have no clue what is going on

In your linear example, you had the process right, but you stated it as “for every delta, there exists epsilon.” It is an easy mistake to make. I actually had to read an epsilon-delta proof in my textbook to understand why it had to be “for every epsilon, there exists delta.” We first find the delta and then prove that it implies the given epsilon.

What if you are asked to proof lim X--2 2x² +3 =11 . How can I go about it?

Can you please try this problem Use Epsolon delta Def to show that Lim x-->-1.(2x+3)/(x+2)=1

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in the second part can we not substitute delta = epsilon/8 into |(x-1)|< delta for the proof to be satisfied.

this is the serious issue what am i going to tell you.... if 6 < x+6 < 8 and at the same time |x+6|.|x-1| 6 and now replace x+6 with 6 then it will be not contradict because the product of |x+6|.|x-1|

8:58 We substituted 8 because we |x-1

Every time I see these videos on delta-epsilon I come to the conclusion that the proof is always a tautology 🤷🏻

Nice dress sir

I speak portuguese but undertand very well

Wow

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Here I can't see the value of proving this as a limit , since one can just plug in the value 1 into this continuous function.

i think u should choose delta=min{ ep/8, 1 }, this is my idea

my mind asks me "why" I get what your doing but I do not get why this makes sense or how I can remember this because I do not understand its logic

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8:40 no i dont get that. Why does that work? Why does replacing |x+6| by 8 as a result of that inequality work?

lim(...............)=12 X->1sans parenthèses c est faux. .

Can’t you just input x = 1 into the function retrieve 12 and there is your proof?

With all due respect, i recommend you to learn about limits and all about what they are, before explaining them to unaware people on yb. Because this explanation is all wrong. It's wrongly stated from the start, it's wrongly stated what the goal is, it's wrong in its conclusion. Just as an example it's not true that with delta

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Plus the way u smile doing some cracks, while solving, its just fantastic, u wont be left with any qsn