UA-cam is the new classroom. The educational revolution is coming, just look at how much more efficient it would be if everybody learned calculus from patrickJMT. Thank you Patrick!
you have no idea how great is to watch your vids.... One of the many things I like about your vids, is that you put your things in perspective... i mean, you show how everything in calculus in related to everything in calculus, and show us there us no reason to learn things like a robot... but knowing where things have its origin Cheers from Venezuela (Sorry if it sounds funny, my english is not that well)
You are my hero. I figured this out a few days ago but I couldn't find a video with the squeeze theorem type problem. This confirmed that I was doing it right. So HUGE thanks.
Thank you for posting this video! I don't remember factorials and this problem came up on my homework today. I got through it, but I didn't really understand until I .watched this. And the cos^2 problem came up too! The person that assisted me was very smart, but not as clear as you. I've been subscribing to your website for a few years now and I am never disappointed. You go further than any other ones I've checked out. Once I hit calc II, helpful videos became harder and harder to find.
Just wanted to say thank you for all your videos in Cal I&II. I had all A's in both class by constant practice and your helpful video, and I even got your Itunes app for all the classes in Cal II. I have always and would always share your video series. I am glad I had You (Patrick), Krista and this other MIT lady (Christine's) videos. Thanks once again and happy holidays.
@bmdoubleuu well, you are trying to write things generically. for a large n, the value of n! will get multiplied down until at the end you have 3 x 2 x 1. So 100! = 100 x 99 x 98 x .... x 3 x 2 x 1 cause people do not want to write out all 100 factors.
hey patrickJMT i notice how your videos in general are so helpful and useful than any of my professors' lectures. Quite impressive. What are you? teacher? graduate student? or just a normal guy who loves studying?
thanks! theres such a big difference between teachers (especially in maths) who simply show of their knowledge compared to teacher who actually want to teach their knowledge ....thanks for the vid :)
Killer video! Nice handwriting, nicely spoken, well done. I could not, however, avoid getting goosebumps as I imagined the sound of that sharpie hitting the paper! *squeak* *squeak* lol, details!
When you said "mkay" it reminded me of my maths teacher who died few months ago because of cancer. He was really good. Too bad now I got a 60 year old teacher who can't really teach and is just dead boring. Oh well I better get that geometric sequence quetions done for tomorrow. Keep it up man!
The only downside to watching your videos is that I need to soon buy another math notebook b/c of what I write in class combined with the sheer volume of notes that you give. Thank you many times over. :D
@mikeetg As n goes to infinity, 2^n gets larger and larger and gets to a point where you can call it infinity. Now any constant number over infinity is 0. Think of it as 1/20000000000000000000000000000 its basically 0 You can find out by plugging 1/2^n into Y1 in your calculator, go to TBLSET and for INDEPNT. Go to the Table , and plug in 1, 2, 3, 10, 100. At 100, 1/2^100 = .000000000000000000000000000008, and anything much bigger than that comes up as an error.
I know @AdamFidler1 already kind of explained it, but I thought it might be a bit unclear. Look at the y and x values of a sin and cos graph. it is a wave that goes from -∞ to +∞ in the x direction, but can only go up to 1 and down to -1 because it is alternating. cos is exactly the same scenario but cos is shifted over by a factor of π/2. tan on the other hand (look at the graphs for these, it will help a lot) has vertical asymptotes at the factors of 2π=x but includes all y values.
For the second problem, we could have also reasoned that cos(x) will have a max value of 1 for any x and so the highest value we can get for the numerator is 1 while the highest value we can get for the denominator is infinity, therefore we will have the limit evaluate to 1/infinity and it leads to the same answer.
Mariz Galo Though this might be too late. I do believe the (3)(2)(1) comes from the (2n-1)! Think of it this way if it was 10! which is (10)(9)(8)(7)(6)(5)(4)(3)(2)(1) until 1 and only 1 the numbers (3)(2)(1) can be seen multiplied together. The same concept can be applied here eventually (2n-1)! must reach the point of multiplying (3)(2)(1).
@patrickJMT In the first example, when you subtract from the n because of the factorial shouldn't you get (2(n-1)-1), (2(n-2)-1), etc... I think the end result is the same im just asking in case it matters in some example somewhere
ooo ok thanks thanks again for doing these videos, they have helped me a lot throughout my highschool and university when I start earning money I'll send you a check : D
Patrick, I love the videos. You helped me get through a lot of my math classes. However, I was wondering if you could show write a proof correctly? I'm struggling with proof writing.
Hey Patrick! I'm just wandering that for the first example in this video, if 1/(2n+1)(2n) limit is zero, which means the denominator would be zero. If that fine for this problem to let the denominator to be zero? Sorry if I asked a stupid question:)
hey patrick, for your first example, lim n>infinity of An goes to 0. Doesn't that mean it can converge or diverge? because u saw your video about test ofr divergence and geometric series. O.O
thanks for the awesome vid. just wish i found this at the beginning of the semester :D i still have the final left so :) thanks a lot for this and all the other vids.
Hello! Thank you so much for all your videos! i had a question tho.. in a sequence, if the limit of something is neither 0 nor infinity, does it converge or diverge?
Patrick, could you explain why you ended the sequence with 3*2*1? Is this just the very last part of the factorial already expanded for the very last term of "infinity?" Apparently I'm not the only one who got a little lost by that. Thanks bunches.
hey patrick, did you ever make videos for the website webassign? (calc related) some of the problems have tip videos with handwriting and voice eerily similar to yours...
Dumb question, how do you get to the (1)(2)(3) when doing the factorials on the first example. PS: I'm on chapter 11 of Stewart's Calculus and your videos are a godsend! I thought Calculus 2 was easy and totally made sense, that is until this chapter hit, now up is down, down is up, cats and dogs living together, mass hysteria!
How would you go about solving Σ((cos^2n)/(√(n^3))), n=1 to ∞ when the textbook is telling you to use the comparison test to see if it converges or diverges
Whenever I think of sequences as they relate to convergences/divergences, I find myself becoming confused by concepts of absolute axes. One theory that soothes my mind is the elongation simplification theory: imagine in a parallel universe, everything is simply twice the size and no more. This helps me coordinate ideas about convergence/divergence 'control' with ideas about 'macro-congruence' (i.e., mirror plane motion or quantization).
10 years later and this dude still saving calculus lives
He is a Maths Hero 😍
*11 years now
Straight up my exam is this Thursday
12 years now*
2022
UA-cam is the new classroom. The educational revolution is coming, just look at how much more efficient it would be if everybody learned calculus from patrickJMT. Thank you Patrick!
2020 and you're still saving people's asses.
people's asses are my calling in life
I'm in a college weed-out calculus course and your videos save my ass on a regular basis. Thanks for posting all of these.
Agreed. Sect of JMT converges today
Lol they are weeder courses. Having you learn 3 topics in a week really fast
@chemkokolette then it would converge to 4. if you are unsure of these things, look up the definitions.
@ruttatata been out of school for a long time. taught for a bit. now i am just a guy that makes math videos on youtube cause people seem to like them
you have no idea how great is to watch your vids....
One of the many things I like about your vids, is that you put your things in perspective... i mean, you show how everything in calculus in related to everything in calculus, and show us there us no reason to learn things like a robot... but knowing where things have its origin
Cheers from Venezuela
(Sorry if it sounds funny, my english is not that well)
Thank you for this video, Patrick. This really is a new paradigm for learning at your own pace.
You are my hero. I figured this out a few days ago but I couldn't find a video with the squeeze theorem type problem. This confirmed that I was doing it right. So HUGE thanks.
Thank you for posting this video! I don't remember factorials and this problem came up on my homework today. I got through it, but I didn't really understand until I .watched this. And the cos^2 problem came up too! The person that assisted me was very smart, but not as clear as you. I've been subscribing to your website for a few years now and I am never disappointed. You go further than any other ones I've checked out. Once I hit calc II, helpful videos became harder and harder to find.
Clear concise examples! 😊
I'm left-handed too, but I smudge the page a WHOLE lot more when I write. You're an inspiration!
@othepangel if the limit of the corresponding sequence is zero, it may or may not converge; you still do not know for sure at this point.
Just wanted to say thank you for all your videos in Cal I&II. I had all A's in both class by constant practice and your helpful video, and I even got your Itunes app for all the classes in Cal II. I have always and would always share your video series. I am glad I had You (Patrick), Krista and this other MIT lady (Christine's) videos. Thanks once again and happy holidays.
@bmdoubleuu well, you are trying to write things generically. for a large n, the value of n! will get multiplied down until at the end you have 3 x 2 x 1. So 100! = 100 x 99 x 98 x .... x 3 x 2 x 1 cause people do not want to write out all 100 factors.
@nathanialmunir yes, they are the same.
You are awesome for getting examples out from the textbook that I'm using man (The James Stewart one) Helps a lot! God bless!
my pleasure my friend! i hope the videos help!
thanks friend, i am glad that i have been able to help you
hey patrickJMT i notice how your videos in general are so helpful and useful than any of my professors' lectures. Quite impressive. What are you? teacher? graduate student? or just a normal guy who loves studying?
happy holidays to you too :) congrats on the good grades
You are the only reason why I have an A in Calc II. Bravo. You are fantastic.
@Canada9318 yes they should :)
yes, i always end with ....*3*2*1 as the end of a 'generic' factorial expanded out.
that is the trick with factorials: expand and cancel
thanks! theres such a big difference between teachers (especially in maths) who simply show of their knowledge compared to teacher who actually want to teach their knowledge ....thanks for the vid :)
Why are you not my professor??!!!! 😭😭😭 you make everything sounds so simple and easy. And eventually so easy to solve!
Killer video! Nice handwriting, nicely spoken, well done. I could not, however, avoid getting goosebumps as I imagined the sound of that sharpie hitting the paper! *squeak* *squeak* lol, details!
this dude is awesome. I'm learning more from these videos than my teacher
Thanks so much for these videos, my textbook is terrible at explaining series and sequences and these are helping a lot...
I should just give you my tuition... I learn more from you than any of my professors.
@consumev i have one on my website. click any video and on appears. you should go visit now
i have never seen this topic explained so clearly thanks!
@engineerrob1 happy to help!
Patrick can you please link related/concurrent videos together in the description?
When you said "mkay" it reminded me of my maths teacher who died few months ago because of cancer. He was really good. Too bad now I got a 60 year old teacher who can't really teach and is just dead boring. Oh well I better get that geometric sequence quetions done for tomorrow. Keep it up man!
i agree...you explain much clearer than even my class teacher...
no problem!
The only downside to watching your videos is that I need to soon buy another math notebook b/c of what I write in class combined with the sheer volume of notes that you give. Thank you many times over. :D
@mikeetg
As n goes to infinity, 2^n gets larger and larger and gets to a point where you can call it infinity. Now any constant number over infinity is 0.
Think of it as 1/20000000000000000000000000000
its basically 0
You can find out by plugging 1/2^n into Y1 in your calculator, go to TBLSET and for INDEPNT. Go to the Table , and plug in 1, 2, 3, 10, 100. At 100, 1/2^100 = .000000000000000000000000000008, and anything much bigger than that comes up as an error.
I know @AdamFidler1 already kind of explained it, but I thought it might be a bit unclear. Look at the y and x values of a sin and cos graph. it is a wave that goes from -∞ to +∞ in the x direction, but can only go up to 1 and down to -1 because it is alternating. cos is exactly the same scenario but cos is shifted over by a factor of π/2. tan on the other hand (look at the graphs for these, it will help a lot) has vertical asymptotes at the factors of 2π=x but includes all y values.
11 years later still helping!
sup dog
glad i could help you out :)
but there is a (2n-3) in the denominator... i just do not write out all the factors
@nelmsters this is a sequence, not a series.
THANK YOU SO MUCH! Please keep these videos coming. They are really helpful!
i have a bit of it up there... but i could do more!
thanks! glad they are helping
Thank you ! (factorial).....
I promised once I graduated and I got a job I'll donate to your website..
For the second problem, we could have also reasoned that cos(x) will have a max value of 1 for any x and so the highest value we can get for the numerator is 1 while the highest value we can get for the denominator is infinity, therefore we will have the limit evaluate to 1/infinity and it leads to the same answer.
I gotta say, that squeeze example was pretty neat :3.
in the first example, where do you get the (2n-1)(2n-2)....(3)(2) (1)..... where does the (3)(2)(1) part come from??
I ask the same question too
Mariz Galo Though this might be too late. I do believe the (3)(2)(1) comes from the (2n-1)! Think of it this way if it was 10! which is (10)(9)(8)(7)(6)(5)(4)(3)(2)(1) until 1 and only 1 the numbers (3)(2)(1) can be seen multiplied together. The same concept can be applied here eventually (2n-1)! must reach the point of multiplying (3)(2)(1).
aaqamar lol and printer paper
Thanks Tommy. Ur a math G.
put the value of n and check the pattern...
Dude, you more useful than my lecturers
You are a fucking saviour. Become a professor, the industry is saturated with BAD teachers but GENUIS mathematicians
Patrick, your very helpful to many.
@patrickJMT In the first example, when you subtract from the n because of the factorial shouldn't you get (2(n-1)-1), (2(n-2)-1), etc... I think the end result is the same im just asking in case it matters in some example somewhere
Great example with the squeeze theorem! :)
Thanks Patric MJ you are great.
best Channel ever
happy to help : )
Finally a legit application of the squeeze theorem! :')
yep! most of my problems come from james stewarts calculus text book! 5th edition i think
ooo ok thanks
thanks again for doing these videos, they have helped me a lot throughout my highschool and university
when I start earning money I'll send you a check : D
Patrick, I love the videos. You helped me get through a lot of my math classes. However, I was wondering if you could show write a proof correctly? I'm struggling with proof writing.
love this man
Thanks Patrick , your videos really helped me out :)
At 5:21, why does 1/2n = 0?
Thanks, and thanks for all the great videos!
Should you always use the squeeze theorem for trig stuff?
So do we usually use the squeeze theorem and write the boundaries when dealing with trig functions?
Where was this vid. when i needed math? :| GJ
thanks!!
@alleverrr make cake, not war
the limit of cos^2n/2^n was on my last test. Patrick ftw
You are a great teacher :)
Hey Patrick! I'm just wandering that for the first example in this video, if 1/(2n+1)(2n) limit is zero, which means the denominator would be zero. If that fine for this problem to let the denominator to be zero? Sorry if I asked a stupid question:)
You're a Wizard! A math wizard that is
Patrick have u thought of making some multivariable calculus stuff ???
hey patrick, for your first example, lim n>infinity of An goes to 0. Doesn't that mean it can converge or diverge? because u saw your video about test ofr divergence and geometric series. O.O
Extremely clear, thanks much!
thanks for the awesome vid.
just wish i found this at the beginning of the semester :D
i still have the final left so :) thanks a lot for this and all the other vids.
So in the example with an = cos^2n/2^n, you are using the squeeze theorem ?
@FaiththeHairstylist naaah, it is not bad : )
@Goldfishhhhhhhhhh 5n^2 / (10n^2 + 3n + 4)
Hello! Thank you so much for all your videos!
i had a question tho.. in a sequence, if the limit of something is neither 0 nor infinity, does it converge or diverge?
Patrick, could you explain why you ended the sequence with 3*2*1? Is this just the very last part of the factorial already expanded for the very last term of "infinity?" Apparently I'm not the only one who got a little lost by that. Thanks bunches.
In the 2nd example, why is (cos(x))^2 / n^2 less than or equal to 1/n^2 on the right hand side?
great job, keep it up dude.
i try!! : )
hey patrick, did you ever make videos for the website webassign? (calc related) some of the problems have tip videos with handwriting and voice eerily similar to yours...
Thank you very much .. your videos very useful
Dumb question, how do you get to the (1)(2)(3) when doing the factorials on the first example.
PS: I'm on chapter 11 of Stewart's Calculus and your videos are a godsend! I thought Calculus 2 was easy and totally made sense, that is until this chapter hit, now up is down, down is up, cats and dogs living together, mass hysteria!
yep, popular book... his and larsons
How would you go about solving Σ((cos^2n)/(√(n^3))), n=1 to ∞ when the textbook is telling you to use the comparison test to see if it converges or diverges
thanks @Patrick
@fatqwert200 dave chappelle is great
thanks a lot patrick... a big help.
how do we know when we are supposed to go to the negatives with the factorials?
Is the squeeze theorem same as the comparison test?
Whenever I think of sequences as they relate to convergences/divergences, I find myself becoming confused by concepts of absolute axes. One theory that soothes my mind is the elongation simplification theory: imagine in a parallel universe, everything is simply twice the size and no more. This helps me coordinate ideas about convergence/divergence 'control' with ideas about 'macro-congruence' (i.e., mirror plane motion or quantization).
at 1:28, how could that factorial have 2 as a term? since its 2n-3, n would need to be 2.5 ... right?
Thank you! Very clear!