How to Prove a Function is Continuous using Delta Epsilon

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The Math Sorcerer

Күн бұрын

Пікірлер: 104

@hunter-tm2kl 4 жыл бұрын

with all my classes online you're a god send man

@TheMathSorcerer 4 жыл бұрын

Happy to help👍

@oliverlinehan8701 2 жыл бұрын

How did an 8 minute video help me more than 3 hours of class on the topic!? Good stuff dude!

@bachi5373 3 жыл бұрын

Hearing an actual explanation instead of just an example helped me out a ton! Thanks

@TheMathSorcerer 3 жыл бұрын

You are welcome!

@masontdoyle 5 жыл бұрын

Real Analysis final is tomorrow. This brought a lot of clarity! Thank you.

@TheMathSorcerer 5 жыл бұрын

awesome!

@bebarshossny5766 5 жыл бұрын

I swear to god This is one of the best math channels on youtube Gold mine

@TheMathSorcerer 5 жыл бұрын

Thank you!!!

@steadystudying Жыл бұрын

I've got an ACalc test where we have to prove this in less than ten minutes and this made things so easy to understand. thanks so much

@WritersDigest-b8f Жыл бұрын

Your Calculus is specially suitable for those like me with continuing education spirit, because u don’t assume your audience already knows or remembers it. I did calculus in undergrad engineering and advanced calculus, tensor analysis, statistics in masters many years ago, and still enjoy it every bit of it. I am also looking for FFT videos on YT. Thank u so much for making it so interesting. Keep it up. Calculus is the best pastime for me. I love Calculus.

@이성원-i1r 4 жыл бұрын

finally i got it it makes so many things clear thx!!

@animeonfire1790 11 ай бұрын

Loved that video ❤. Straight foreward and on point. Thank you so much!

@isha9428 2 жыл бұрын

With the proof I also like the honesty.... 👍

@jessicasanchez134 4 жыл бұрын

This is the only thing that gives me hope 👍🏼

@SousouSousou-gp6vu 4 жыл бұрын

Hi I'm a math student and my math exams are really hard they ask us for demonstration and thus helped a lot thank you sir

@TheMathSorcerer 4 жыл бұрын

You are welcome!

@codingmania7958 Жыл бұрын

you're an excellent teacher!

@crastycy7207 5 жыл бұрын

Thank you sir, this was really helpful!

@TheMathSorcerer 5 жыл бұрын

awesome! very happy it helped!!

@e4zyphil 4 жыл бұрын

hey i guess that'd mean a lot to me: i'm from germany and your videos are helping me a lot to learn this stuff :) guess i'll just have to repeat it a lot now. how long did you take to get good at this to the point you can make a proof up on the spot?

@TheMathSorcerer 4 жыл бұрын

Ya it takes time, lots of time, you take classes, you do some proofs you learn, then repeat. It's a progression over time. It takes a while. Looking back even after I had my math degree I wasn't nearly as good as I am now. It just takes time. If you go to grad school you get even better.

@TheMathSorcerer 4 жыл бұрын

Practice and time obviously, wanted to emphasize the practice part. But time is key I think,it takes time to digest things.

@louisemessenger571 3 жыл бұрын

Thanks a lot lecture notes were useless on this!

@pritampadhan5977 3 жыл бұрын

Amazing explanation 😍😍😍🙏🙏🙏🙏

@jimothy221 5 жыл бұрын

how would you prove that x^n on R is continuous for all natural n?

@tabmax22 5 жыл бұрын

you can prove by induction

@morten_8086 4 жыл бұрын

Or just show that if f and g are continous functions then also fg is continious. Hence for f(x)=x we get that f*...*f (n times) = x^n is also continous.

@montexic5201 3 ай бұрын

does it matter that delta is defined with c, when the assumption defines delta through c? for some reason that sounds counterintuitive

@Adventurin_hobbit Жыл бұрын

Thanks sir , I was literally confused

@AAAAAA-kl7qm 3 жыл бұрын

Very epic video, helped me a lot with understanding this.

@ntvonline9480 4 жыл бұрын

I think I missed something. Why did you use c as your endpoint instead of infinity. Is that because c is more attainable?

@TheMathSorcerer 4 жыл бұрын

so in the definition it has to be a number, so we typically use c for that number, also... we had to show it's continuous on [0, inf), this means we have to show it's continuous at EVERY number in [0, inf), so we show the proof works for some arbitrary c, and that shows it must work for all values in that interval

@rizkaapriliani1630 3 жыл бұрын

@@TheMathSorcerer sir i was wondering about this too. but does that mean we don't need to actually use the first proof then?

@JMRG2992 3 жыл бұрын

In 2:47 how you actually assume that or want to choose that δ to be ε^2

@Chilliak10 2 жыл бұрын

how do you know what to choose for your epsilon / delta value, what about the function sin(1/x)? how would you prove that sin (1/x) is continuous? because it seems like you cant just slot in a sin like you did with square root in in this example (on the scratch work part)

@montexic5201 3 ай бұрын

i don't think sin 1/x is continuous....

@lm1890owpke 5 жыл бұрын

this is good stuff, thank you

@ekeebobs7520 3 жыл бұрын

Thanks very much for your awesome videos! Please when writing epsilon-N and epsilon delta proofs should I include the scratch work? I've got the exam coming up so I'm wondering.

@TheMathSorcerer 3 жыл бұрын

yeah do it on the side, and label it, so your teacher knows it's the scratch and not the proof, just make it super clear to the teacher,it will help

@victors8718 10 ай бұрын

You are the best

@adilenurtokmakco6508 5 жыл бұрын

tomorrow I have analysis exam and this video helped me a lot. thank you sir.

@TheMathSorcerer 5 жыл бұрын

excellent, good luck:)

@nullimits 3 жыл бұрын

I have a quick question: shouldn't you be proving that f is continuous at 0 using the left-hand ε-δ definition of a limit instead of the general definition?

@louismilone6812 Күн бұрын

Why did you drop the absolute value at 2:25 ?

@djgbwhat7434 4 жыл бұрын

amazing proof thank you !!

@AAAAAA-kl7qm 3 жыл бұрын

for the second proof, can delta be anything less than or equal to epsilon * sqrt(c)?

@tebellomokgomole772 4 жыл бұрын

I can use this method for Real Analysis? Or just for Calculus?

@TheMathSorcerer 4 жыл бұрын

definitely can use it for real analysis:)

@tebellomokgomole772 4 жыл бұрын

@@TheMathSorcerer it seems so simple, thank you

@Cookieinthehood 5 жыл бұрын

Insightful video! Any idea how I could use this method if I don't know what the function f does?

@douglasstrother6584 9 ай бұрын

Some Old School Math Sorcerer!

@daonedaonly942 3 жыл бұрын

Great video :0) But I was wondering why you have to split up 0 and the positive numbers. Is there a way you could prove true for all possibilities at once?

@daviddegenhardt5420 2 жыл бұрын

correct me if I'm wrong, but I think it's easier that way, because in the second proof he had to assume, that c ≠ 0. Otherwise he would've needed to find a value for δ such that the proof holds even if both x and c are 0 which is much more difficult.

@shankarkubal5259 3 жыл бұрын

Sir is that defination of continuety or Uniform continuity?

@collcds 5 жыл бұрын

Good stuff my friend

@TheMathSorcerer 5 жыл бұрын

glad it helped:)

@waynelau3256 3 жыл бұрын

what happens when c is given? such as needing to prove at x=2

@frka3176 4 жыл бұрын

I like your video, but I'm some what confused as to why you can just chose that delta equals "epsilon times the square root of c"?

@TheMathSorcerer 4 жыл бұрын

You are allowed to choose Delta, you have to in order to satisfy the definition

@tekaaable 5 жыл бұрын

Thank you!

@anshumanagrawal346 3 жыл бұрын

Is this definition the same as the one you learn in how school. (F is continuous at x=a iff lim_x->a [f(x)] = f(a)) where the limit exists and the fn is defined at 'a' (obv)

@anshumanagrawal346 3 жыл бұрын

I know the precise definition of a limit is similar to this and it looks like if just replace L with f(a), you get this. So it looks like it's the same thing

@Thanushan925 4 жыл бұрын

Thanks a lot, this helps! By any chance do you know how to do a question like this but with F(x) = x^-2

@diontulloch349 4 жыл бұрын

thank you sir

@TheMathSorcerer 4 жыл бұрын

You are welcome!

@mikejun609 3 жыл бұрын

why do you put 0

@johannesvaasalainen7075 3 жыл бұрын

Mike Jun I would guess that is because the definitions are different. A function can have a limit at point c even if it is not defined at point c but it cant be continuous at point c if it is not defined at point c so you cant rule it out.

@mikejun609 3 жыл бұрын

@@johannesvaasalainen7075 Ah yes, I see. I'm in my first semester of university and we're doing Real Analysis in Calc1. It's very different kind of maths to what I've seen in A levels. The only thing Ive covered remotely similar to the likes of proofing is Proof by Mathematical Induction. Please wish me luck that I wont flop this course! :))

@b.blokzijl1189 5 жыл бұрын

For the 2nd proof can you use the following: |√(x) - √(c)| ≤ | x - c | thus take ẟ = ε?

@jabbajavbab 4 жыл бұрын

I don't think you can. In the second prove we are looking at x>0 and for 0

@alirajpoot340 4 жыл бұрын

You can only choose that in case f(x) = x

@baifernv9754 4 жыл бұрын

Sir may I ask if a trigonometric equation with a sigma on the right-hand side while theta on the left-hand side will be True or False when verified? Example: Sin (sigma) = Sin (theta)

@comingsoon770 3 жыл бұрын

Sigma and theta should have periodic

@hhhhhhha954 2 жыл бұрын

hi sir， i wonder what if we know a function is continues how can we use this information ?

@aneeshsrinivas9088 2 жыл бұрын

eps^2 works to prove uniform continuity in general over [0,∞)

@ballingchampagne 4 жыл бұрын

Why did you start by choosing c=0 ?

@TheMathSorcerer 4 жыл бұрын

Simple case

@Gaelrenaultdu06 4 жыл бұрын

Hi. I really have issues finding a video or paper related to the proof of x^2 being continuous on R. It seems that the continuity of this function is obvious on R in every exemple i find, and it is proved for all x0 in R, but is it possible to prove it with the definition of continuity at a point, that x^2 is continuous on 0 ? I tried to use your method for the square root function on the x^2 one, but i can't seem to find a solution. Thanks in advance.

@TheMathSorcerer 4 жыл бұрын

hmm I thought I had something similar already, I found it, would this work? kzbin.info/www/bejne/b3yUgnWgfceWbdU& Just replace 2 with c and 4 with c^2. Try that? Obviously just modify the definition a bit it should work ok:)