I just spent a whole day to understand it but it was not clear. I was always getting off for delta and epsilon. But your video just made it easy and clear for me. Thank you so much!
love this channel but topics like this are why people hate math. at least derivatives are useful. this seems like nothing more than doing algebra for fun and then undoing it lol. but this will most likely be on my exam so thanks 👍
This topic is far from useless. With the epsilon-delta definition we prove limits in a very mathematical rigorous way. This is important as limits are a fundamental concept of calculus as a whole.
Good Job, Patrick! I enjoy watching your videos. You have definitely been one of my best Math tutor. My university lecturer also used a lot of your videos to assist us during pre-cal 2, and I continued to use your videos for all my calculus courses.
hey Patrick, could you please post a video to prove Precise Definition of a infinite two sided positive limit that prove ,for any positive number N there is a corresponding number delta>0,such that f(x)>N,whenever -delta
you can think of epsilon as being a measure of 'distance' or 'closeness'. since those only make sense conceptually if they are positive or zero, that is why we make that restriction.
It means 1st ....we take functional absolute value and proof points absolute value less than dell( which is related to e) 2nd ....we reverse method with absolute of points less than dell( related to e and also write it in terms of e) which implies absolute of function less rhan e
hello sir, if we do the long method of taking out the absolute value and there is negative (epsilon) e in the left side and positive e in the right side, will it be -sqrt e or sqrt -e? thank you in advance, sir! your video is really helpful i just need the complete solution of this 💗
This is essentially a proof of a limit by using its definition. When you are saying "if and only if" or "iff" for short, that means a statement is strictly true only if the conditions are met to make it true. Therefore, no, this is not an "if and only if" example because it can be proven false depending on the example that is given to you.
Awesome!! Thanks Patrick! But for Calc 3 students, i.e. Vector Calc, there is also some Epsilon-Delta Definition in 3-D.... Sounds frightening.. Could you make a video of Epsilon-Delta for 3D??? Thnx!!!
All your videos are extremely helpful! Do you think you could make any videos demonstrating how to use the precise definition of limits to/equal to infinity? Thank you!
Shouldn't there be some kind of criteria for the relationship between Delta and Epsilon? Or can you just have them whatever you like so long as they are proportional?
Nice example. However the example is very simplistic and this method won't help you prove for example that lim x->3 (x²-4x+5) = 2, since you end up with |x-3|
The critical thing is to get |f(x)-L| in terms of |x-a|. So, in your question, |(x^2 -4x+5)-2| = | x^2-4x+3| can be written as |(x^2-6x+9) + 2x-6| {adding and subtracting (-2x + 9)}. This can be written as |(x-3)^2 +2(x-3)| which is < |(x-3)|^2 +2|x-3|. Replace |x-3| with delta and continue as above. The final expression needs quadratic formula.
Hi Patrick, @patrickJMT Can you do that to delta? just let it be sqrt(e)? or you need to do two cases, one for +sqrt(e) and the other for - sqrt(e)? Have a good day, Great Video!
Of course (x-2)^2 is always positive...but I guess the absolute value sign is retained since it's part of the definition of the limit ...idk just my thoughts
This was a very convenient f(x), that happened to factor into the x-a statement he was looking for. I don't really think this was a good example. Maybe try proving lim as x approaches 3 of f(x) = 2
I loved the way he explains But choosing the ease topics where no need of explanation makes me not to follow his channel anymore. I’m sure 90% of people are looking for complicated examples not this.
I just spent a whole day to understand it but it was not clear. I was always getting off for delta and epsilon. But your video just made it easy and clear for me. Thank you so much!
Glad it helped!
love this channel but topics like this are why people hate math. at least derivatives are useful. this seems like nothing more than doing algebra for fun and then undoing it lol. but this will most likely be on my exam so thanks 👍
This is in a sense needed to prove derivatives
You just translated my toughts.
Doesn't it also refute the (impossible) possibility of infinitesimal "holes" in the number line?
@@OptiGE It definitely is! The derivative is defined using the limit of the difference quotient.
This topic is far from useless. With the epsilon-delta definition we prove limits in a very mathematical rigorous way. This is important as limits are a fundamental concept of calculus as a whole.
Good Job, Patrick! I enjoy watching your videos. You have definitely been one of my best Math tutor. My university lecturer also used a lot of your videos to assist us during pre-cal 2, and I continued to use your videos for all my calculus courses.
I also bought your Calculus book "1001 Calculus Problems for Dummies". It's awesome! Highly recommended
men your explanation is just get in straight forward, great thanks
Thank you for this series! Great initial explanation video and the 2 examples are really clear
Can you please do more complicated quadratic delta-epsilon’s proofs.
Yeah, I thought he was going to do the "delta = min {a, b}" method.
hey Patrick, could you please post a video to prove Precise Definition of a infinite two sided positive limit that prove ,for any positive number N there is a corresponding number delta>0,such that f(x)>N,whenever -delta
Thank u so much Patrick 🙏🏻
Could u please tell me why we always take "epsilon>0"??
you can think of epsilon as being a measure of 'distance' or 'closeness'. since those only make sense conceptually if they are positive or zero, that is why we make that restriction.
@@patrickjmt yeah!
thanks a lot for ur help
I appreciate it so much 🙏🏻
It means
1st ....we take functional absolute value and proof points absolute value less than dell( which is related to e)
2nd ....we reverse method with absolute of points less than dell( related to e and also write it in terms of e) which implies absolute of function less rhan e
hello sir, if we do the long method of taking out the absolute value and there is negative (epsilon) e in the left side and positive e in the right side, will it be -sqrt e or sqrt -e? thank you in advance, sir! your video is really helpful i just need the complete solution of this 💗
the best explanation saw at youtube yet!!
Is it mathematically wrong if i made delta to be equal to E/x-2? instead of the square root of epsilon?
Is the concept here to show that it is an If and Only If statement?
This is essentially a proof of a limit by using its definition. When you are saying "if and only if" or "iff" for short, that means a statement is strictly true only if the conditions are met to make it true. Therefore, no, this is not an "if and only if" example because it can be proven false depending on the example that is given to you.
***** I ask this because untracing the steps kind of seems like proving the converse.
Can we disprove a limit using the definition?
Yes
Yes! Simply negate the limit definition.
Yes but using Divergence Criteria is easier.
@@chaoticoli09 I see you have your own channel for math. I subscribed. Keep up the good work.
@@CaribbeanMathGem Thanks!!! I subbed to you as well :).
What would happen if you do an example where you're required to prove that the limit of a function approaching some a equals an L that's wrong?
What should I do when a limit is defined on not to be x equal the a and just exists a limit for fx when x approaches a.
Awesome!! Thanks Patrick!
But for Calc 3 students, i.e. Vector Calc, there is also some Epsilon-Delta Definition in 3-D....
Sounds frightening..
Could you make a video of Epsilon-Delta for 3D??? Thnx!!!
All your videos are extremely helpful! Do you think you could make any videos demonstrating how to use the precise definition of limits to/equal to infinity? Thank you!
yes please
Shouldn't there be some kind of criteria for the relationship between Delta and Epsilon? Or can you just have them whatever you like so long as they are proportional?
Why no one answered u🥲
If u know the answer pls tell me
I know i came late but i need the answer 🙂
The original BlackPenRedPen 😂😂
awesome trick....thank you
its not a trick
Thank you so much! I finally got this!
what is a is infinity? I can't get it
please comment as to whether this technique can be used for any function, not just polynomials.
Nice example. However the example is very simplistic and this method won't help you prove for example that lim x->3 (x²-4x+5) = 2, since you end up with |x-3|
The critical thing is to get |f(x)-L| in terms of |x-a|. So, in your question, |(x^2 -4x+5)-2| = | x^2-4x+3| can be written as |(x^2-6x+9) + 2x-6| {adding and subtracting (-2x + 9)}. This can be written as |(x-3)^2 +2(x-3)| which is < |(x-3)|^2 +2|x-3|. Replace |x-3| with delta and continue as above. The final expression needs quadratic formula.
great job..understandable
Oj Thank you soooooo much
Hi Patrick, @patrickJMT
Can you do that to delta? just let it be sqrt(e)?
or you need to do two cases, one for +sqrt(e) and the other for - sqrt(e)?
Have a good day,
Great Video!
never mind, I thought about it and delta must be positive
so you cannot use -sqrt(e). Great video
Thank you so much SIR
oh yes, what if the limit is infinity?It seems we can not apply this definition. Can someone help me?
Infinity can't be a limit. We just use infinity to describe graphs that follows those trends. Infinity isn't a definitive number.
Not true, you use a different definition involving M and if N>M then blah blah lim proven.
Thank you
Thank you!
amen to this God bless you
it was awesome
I LOVE YOU
thank you :)
Why do you have to keep the absolute value sign on the equation? Isn't (X-2)^2 always positive. Also thanks for the video:) Really helped!
Of course (x-2)^2 is always positive...but I guess the absolute value sign is retained since it's part of the definition of the limit ...idk just my thoughts
@@silversharky3258 you're probs right
U keep restating and rewriting and expand and simplify the function, seems overkill and redundant?
Thanks Sir
thanks
why is your voice so high sometimes like you inhaled helium and sometimes its so low. great vids btw thank you
Inhaling Helium is known to increase your math skills.
Similarly, inhaling methane is known to give you superpowers.
Ah I see, a delicate balance must be found.
I think I got it now
This was a very convenient f(x), that happened to factor into the x-a statement he was looking for. I don't really think this was a good example. Maybe try proving lim as x approaches 3 of f(x) = 2
try to do exactly what you said (if you did not) and see what happens. you might just be surprised.
awesome
🍅
I loved the way he explains
But choosing the ease topics where no need of explanation makes me not to follow his channel anymore.
I’m sure 90% of people are looking for complicated examples not this.
smell ya later
thank you