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.
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?
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.
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.
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
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.
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)
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?
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.
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?
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)
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
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)
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.
@@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! :))
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.
hmm I thought I had something similar already, I found it, would this work? ua-cam.com/video/9K1QBjHbc7s/v-deo.html& Just replace 2 with c and 4 with c^2. Try that? Obviously just modify the definition a bit it should work ok:)
with all my classes online you're a god send man
Happy to help👍
How did an 8 minute video help me more than 3 hours of class on the topic!? Good stuff dude!
Hearing an actual explanation instead of just an example helped me out a ton!
Thanks
You are welcome!
Real Analysis final is tomorrow. This brought a lot of clarity! Thank you.
awesome!
I swear to god
This is one of the best math channels on youtube
Gold mine
Thank you!!!
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
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.
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
You are welcome!
finally i got it
it makes so many things clear thx!!
With the proof I also like the honesty.... 👍
This is the only thing that gives me hope 👍🏼
Loved that video ❤. Straight foreward and on point. Thank you so much!
you're an excellent teacher!
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?
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.
Practice and time obviously, wanted to emphasize the practice part. But time is key I think,it takes time to digest things.
Thanks sir , I was literally confused
Thank you sir, this was really helpful!
awesome! very happy it helped!!
Thanks a lot lecture notes were useless on this!
Amazing explanation 😍😍😍🙏🙏🙏🙏
tomorrow I have analysis exam and this video helped me a lot. thank you sir.
excellent, good luck:)
Some Old School Math Sorcerer!
how would you prove that x^n on R is continuous for all natural n?
you can prove by induction
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.
Very epic video, helped me a lot with understanding this.
I think I missed something. Why did you use c as your endpoint instead of infinity. Is that because c is more attainable?
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
@@TheMathSorcerer sir i was wondering about this too. but does that mean we don't need to actually use the first proof then?
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.
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
this is good stuff, thank you
In 2:47 how you actually assume that or want to choose that δ to be ε^2
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)
i don't think sin 1/x is continuous....
You are the best
amazing proof thank you !!
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?
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.
does it matter that delta is defined with c, when the assumption defines delta through c? for some reason that sounds counterintuitive
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?
Insightful video! Any idea how I could use this method if I don't know what the function f does?
for the second proof, can delta be anything less than or equal to epsilon * sqrt(c)?
I can use this method for Real Analysis? Or just for Calculus?
definitely can use it for real analysis:)
@@TheMathSorcerer it seems so simple, thank you
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"?
You are allowed to choose Delta, you have to in order to satisfy the definition
Good stuff my friend
glad it helped:)
Thanks a lot, this helps! By any chance do you know how to do a question like this but with F(x) = x^-2
what a beautiful proof
Sir is that defination of continuety or Uniform continuity?
For the 2nd proof can you use the following:
|√(x) - √(c)| ≤ | x - c | thus take ẟ = ε?
I don't think you can. In the second prove we are looking at x>0 and for 0
You can only choose that in case f(x) = x
eps^2 works to prove uniform continuity in general over [0,∞)
thank you sir
You are welcome!
Thank you!
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)
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
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)
Sigma and theta should have periodic
what happens when c is given? such as needing to prove at x=2
why do you put 0
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.
@@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! :))
thanks man
You are welcome!
My teacher gave to me an alternate definition to prove continuity, but I don't know how to use it properly, can u help me?
what is your definition?
hi sir， i wonder what if we know a function is continues how can we use this information ?
Why did you start by choosing c=0 ?
Simple case
Great thanks
You are welcome !
😍😍😍 wow
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.
hmm I thought I had something similar already, I found it, would this work? ua-cam.com/video/9K1QBjHbc7s/v-deo.html&
Just replace 2 with c and 4 with c^2. Try that? Obviously just modify the definition a bit it should work ok:)
Helpful
The goat
Amazing
thank you!
how do we know c=0. i didnt get it, if anyone knows?
It’s an assumption in order to prove continuity at 0, it’s just a step not a given condition
At least that’s what I think
Sir 1/0= infinity now 0× infinity =1 how it is happens please clear my doubt
1/0 is not infinity. Its not defined.
Sir
Eppadi c =0 sonningha
omg best
How f(c) =0?
Math warrior
EXAMS