Graph of r = 1 + cos(theta/2) | MIT 18.01SC Single Variable Calculus, Fall 2010
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- เผยแพร่เมื่อ 6 ม.ค. 2011
- Graph of r = 1 + cos(theta/2)
Instructor: Christine Breiner
View the complete course: ocw.mit.edu/18-01SCF10
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
omg, this is like the best maths explanation I have ever seen! Well done!
Absolutely
Wow... so much clarity and depth. I cant explain how much this has cleared up my confusion.
My Cal3 teacher from Ecuador is incompetent and we had to correct a dozen of mistakes for him in one single lecture. Thanks Christine, I have learned something from you finally!
everybody from that country is incompetent hahahaha
@@JJOSEMORALES perhaps like your parents were, at raising you.
Thank you so much.
This world is a good place to be alive and educated.
I am grateful that I am a part of this good world :)
when I become an engineer coz of your teachings, I will never ever forget you ever
thank you so much. if the courses from mit opencourseware are like this, i wish i could just take that for credit. these videos are sooooo much better than what i am getting right now. our teacher didn't even bother to teach us how to graph these equations by hand in precalc or now in calc 2, so it's nice to get an intuitive sense as to why limacons look like this.
I like your videos. Thanks for posting them !
Watching in 2k24
Amazing class
Excellent presentation of a concept that often confuses my students. Well done! ;-)
Very excellent presentation Madam. All students are blessed to sit in your Classes. One time listening is sufficient for ever to remember.
Thank you for this. So helpful😭
Thank you for your help.
Great, Christine.
thank you. the video was very helpful.
Excellent explanation.
great explanation
love your delivery method, I am 43 now, and haven't heard chalk on a blackboard in a while, it was in high school (1995) that they started the transfer from black to white boards, and now they don't even use over head transparencies any more, a real shame, as you and your chalk is so asmr with a soft voice, a great companion, you would make an excelent teacher in your own right, not just a tutor.
PS: I have Autism, so that it is not so weird, just like the tone, and the pace, I dropped maths in year 10, as they just got to algebra, had a horendous teacher, the staff there didn't know about autism, learning disabilities, even bullying!; so I can't understand half of this, but the formula re-arrangements I can, just, but would be nice for you to show HOW one uses these skills, as it looks all a lot of physics, lasers, etc. that would use this stuff, no wonder you need a high grade before you get taught this stuff.
It really helps me!!
Isso foi lindo!
From Brazil.
thankyou, i'm insomnia, and i can deep sleep after watch this video.
Thx!! It's very useful!
Thank you very much!!! Ah pretty graph! (=
The graph of r equals one plus cos(theta/2) and setting up the problem is beautiful, however placing the upper and lower limits on the integration continue to give me problems in Calculus. Thank you for the lecture.
Is that a gigant chalk???? Nice explanation!!!
Fabulous.
You will obtain the same graph. If you graphed up to 8pi, you would essentially plot a bunch of points that you had already plotted in the first 4pi radians. If any of that was confusing please tell me and I will try to clarify!
Fabulous!
This is an MIT class and I am not saying that there won't be any mistakes done by tutors. However, you should have to be much careful and/or think twice when criticizing and saying that there is something wrong with graphing and her solution. Anything she did in this video is absolutely correct. You should have to be aware of the importance of the period of a trigonometric function while graphing in polar coordinates.
DMENC I almost had a stroke reading this
good explanation
Cool stuff. The basics!!
The blue stuff or the pink stuff? 😜
useful. thanks
How did she get to 2pi to 3 pi
My professor made the graph of r=1+Cos Theta . Which was basically the same on the outside with no inner curves i.e. A heart on its side with no curved line inside. I don't under stand why theta over two made the difference of an inner curve. I would think only the width would be affected. Can you draw a graph of
r=1+Cos Theta? No need to fined the area. Thank you.
Ask you a question where is the x-y plane related to r-theta??
She's amazing!
When calculating the area of the blue, wouldn't you have to subtract 2 * the pink part? (integral of (1 + cos theta/2 )^2 from pi to 2pi)
Thanks 🤩 😌👍
I have NO idea f what I just saw, but it looks interesting no doubt!
Nice.
Also theta is a real number - a very important assumption
If we integrate the area from A π to 3π, won't negative and positive area make zero as sum?
Can anyone clear my doubt?
Good question. The issue in your understanding lies in that you're treating the bottom picture as if it were IN cartesian space, when in fact it's just a projection of polar space onto a cartesian frame of reference. The area accrued is positive.
@@vivekpatel6530 thank you
She doesn't read these comments. This is MIT's youtube page
Good
My head!
There was no reason to change the limits on the second integral to obtain the blue area. Not sure why she chose to do that, probably created confusion even though it gave the correct area. Otherwise a good lecture.
my head!!!
i dont think if she graphed it right.. :(
she can't read the comments but at least anyone see this comment must try to do it on your own to know my point... there's given value of theta and just plug it in there...graph is different..correct me if im wrong
Graph was correct, I think you might be mistaking polar with rectangular coordinates
Theta 4 pi not pi over 4 1:07
y is everyone applauding her tuition. I kno she's smart n all...but i got a brain freeze as soon as question appeared! where's my dummy?!
12:34 , explain that bit to me please
Thanks for the tutorials, but now i'm more confused. :(
what's a beautiful shape of this graph :)
Great explanation. I think there is a little mistake from 17:25. She forgot to multiply the second integral with a factor two (to subtract the 2 smaller pink areas).
the integral she subtracts is equal to the entire pink area, she multiplied it by two a little before 17:25 :)
yes, 4 pi, as many people can eat 1 meat pie, but not many can eat four!!
Which equations governed mechanical barometer so we easily calculate energy sources by atmospheric pressure which is enough to cook food for 1000000 peoples 👅👅👅😃
so big chalks used in MIT, that is what makes them different
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MARGELLAN
I know all these kind of of problem because I am from India.
I am in 1st year of my college
i got a raspberry pi...python:)
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Who the hell writes the dialogues? Cosine time function? Whoever is writing the commentary needs to do some math themselves. I've seen a number of mistakes on these videos.
Ok, is it normal I tottaly understand anything from all of this ahah wtf
Too easy.