Taylor's Remainder Theorem
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- Опубликовано: 12 дек 2024
- This calculus 2 video tutorial provides a basic introduction into taylor's remainder theorem also known as taylor's inequality or simply taylor's theorem.
Series Tests - Practice Problems: • Calculus 2 - Geometric...
Taylor & Maclaurin Polynomials:
• Taylor Polynomials & M...
Taylor's Remainder Theorem:
• Taylor's Remainder The...
Power Series - Interval Convergence:
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Power Series - Derivatives & Integrals:
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Power Series - Function Representation:
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Finding The Power Series:
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Power Series - Representation By Integration:
• Power Series Represent...
Power Series - Representation By Natural Logs:
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Taylor & Maclaurin Series:
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Binomial Series:
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Parametric Equations:
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my final is tmrw and im literally inhaling all of organic chemistry tutor's videos
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I've watched hours worth of videos from both Calculus teachers at my school and retained nothing, yet you made it possible for me to understand Lagrange Errors in 14 freaking minutes! I would Die for you, sir
die? is crazy... getting down this concept isn't worth dying lol
@@aarondominguezruiz1596 bro chill it’s a hyperbole
@@anjanathreya8306 with how frustrating it could to try to grasp a difficult concept through a teacher, this tutor is worth founding a religion for at this point.
My calc professor cannot seem to teach me anything about Taylor series over the course of 2 weeks, but you somehow managed to teach me an entire theorem on one of the objectively hardest subjects of calculus in 14 MINUTES. You sir are my lord and savior. I hope your pillow is always cold on both sides.
frfr this man is the GOAT
Dude, that is one of best wishes I've ever heard..xD Nice of you!. Though, I hope for the Tutor, same!
your teacher at least tried to teach you. Our teacher just came with some slides. read it aloud, told us to get the theory ourselves and then proceeded to read through the problems and then told us to read these for our next week's test XD
This man has no idea how much of a god he is
How are you so versed in such a wide plethora of subjects?
Miruz Zz what is all the world,s land worth?
El Mahdi Ettaleb you learned this in highschool?
I’m learning this right now in highschool. My class is all seniors and 3 or 4 juniors.
@@TheHmmer4 huh? It's AP calculus BC
@@megaduckwen Fuck my bad, I thought I replied to El Mahdi Ettaleb. Definitely not freshman maths. AP calc BC is equivalent to college-level calc.
When text books and other youtubers gloss over this core details. Its leaves you super confused
What core details? This is "plug and chug".
what textbooks? this shit is free dawg
Professor Organic Chemistry Tutor, thank you for a powerful analysis of Taylor's Remainder Theorem in Calculus Two. In order to understand this topic, I will rewatch this video. I found this topic problematic from start to finish. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
I desire you carnally. I literally could not wrap my head around this for the longest time (like a week lol) and this video has saved me.
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I love you. Not even Khan Academy could help me like you just did.
this video is an absolute lifesaver omg
Definitely the hardest concept to apply in Calc II imo
thank you my brother , you are the teacher i never had and you are for sure far superior from my eggheaded professor who does nothing but copy the book
thanks for carrying me through highschool and my entrance exams
A tangible approximation of the theorem, thank you
You are currently my favorite human!
Thanks so much! Sometimes a textbook just doesn't cut it.
Is a version of Taylor’s Theorem for complex functions
Thanks for making it so easy !!
I can bet on one thing, an engineering student from Mulungushi university is watching this 😂😂 we'll be writing a test 🤣😂
Omg, you can help me more than my teacher. Thx for all these good contents.
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Thank you. I love your teaching. Such beautiful minds like you are much much appreciated.
is this also called a relative error ?
because in exam i got a question like estimate the relative true error of the given function
fun fact: the organic chemistry tutor sold his soul to the devil in 1950 to become the best tutor in the history of mankind
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My final is in 15 min.😭
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Wow you actually helped me so much in the first 4 minutes LMAO
you saved my life
So the 4th degree approximation is accurate to at least 5 decimal places
For the first problem(0:45), how does he know that the n starts at 1? Normally, for taylor series n starts at 0, but how come here the first term is n=1 ?
No doesn’t matter it depends on your original function and what first value you get when you differentiate it and depends also on value of x that you are calculating Taylor series at
@@reamabdulsalam524 I’ve not a clue what my comment was about but if I get the chance I will revisit this, thanks
Thank you so much, so clear!!
organic chemistry tutor > everyone else
Is this the same as lagrange error ?
Lol, I thought it was so hard 🙈
same lol
Quick thing but is this the same as Lagrange Error Bound?
What if you get a negative value for the f(n+1)(z) because of the nature of the derivative? Negative error?
my help every time i have an assignment i dont quite understand
Can someone help me?
When i looked at the remainder formula, if you replace the z with an x, its basically just giving the value for n+1th power. Given we apply Z to find the 'max' error, why dont we also include the same formula added but instead with n+2 as n and then n+3 then n+4 and so on. because surely the error we have found is just the missing approximate error of the term for a power of n+2, not including the errors for all the next terms as well. Hopefully someone understood what i just said ;)
I understand what you said! I thought about the same thing. I think the trick here is that we are taking the maximum possible error, rather than trying to compute the polynomial for any particular point. Since it's the maximum error for anything in between our center point and our "desired" point, the desired point can't be off by more than what our remainder term gives us. And this can't just keep increasing all the time, because the whole point is that we are getting closer and closer. So the (n+1)th error term includes any possible errors for (n+2) or (n+3)... and so on.
@@vez3834 haha thanks for the reply, i do get this stuff now anyway but not even i could understand what i asked back then so good job!
@@adam-jm1gq Thanks for the nice reply! I enjoy answering such questions, because explaining something to someone else gives me a reason to think about it for myself as well. And even if you already know it, someone else could find the discussion useful or interesting or inspiring.
Take care! :)
@@vez3834 I 100% agree, have a good one!
how do you use the remainder estimation theorem if you are only given x, f x and p x ?
We are all watching this video on May 8th and we all know why
yall please pray for me I'm cramming on the day before my AP exam
how did it go
is the value he's putting in the parenthese in the polynomial 0.1 because it's centered at that?
it's the c value meaning the distance from x, which in this case is 1.
in the second example it's 0.2 but the same rule applies
thanks for this video my book just says like 2 words about this
In the first question, f(x) is ln(x) or ln(1+x)
why does the lagrange remainder use Z instead of X itself?
Why is it over 3 and 4 not 3! and 4!
How do you find the value of n when you are asked to estimate to a certain value?
Trial and error with n
Hi sir,can u plz upload video on how to find the n term in the Taylor remainder when we are given a certain level of accuracy,since two days em working on it but failed ... kindly help...love from India
Thank you so much!
Legend fam.
God job bro 💪
way better than khan academy
my confused dumb ahh really thought 1^5 was 5 💀
شكرا يغالي ❤
Thank You sir
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When would the max error occur?
RuskiSrpskiBros max error occurs when you do not round the decimals for (in first example) ln (1.1) and Tn(1.1). It also occurs when you choose a z value such that the derivative of the next term in the series is the largest it can be. Z ranges between c and x so z can be an infinite number of values. In example 1 in this video, he chose the smallest z since it yielded the largest derivative. The larger the derivative, the larger the error
can someone tell me why we choose z = 1
x was in the denominator so between 1.1(aka x) and 1(aka c), the number that would create the largest value would be 1
God bless u bro
"Taylor's remainder"
Me: Please don't, I wanna concentrate...
Brain : *tAyLoR sWiFt*
Taylor did you write this? Lol.....Praise Jesus Christ forever ❤SE7EN
My final is JCTC W I N S rut ro raggedy rag lol 😂 SE7E7N AND EI8HT
I don’t think the first Taylor polynomial is correct, I would look up Taylor polynomial of ln(x) before you watch the video
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First video of his where I came out more confused than going in - strange causes he's usually pretty good
Yes I do agree this time he was too fast
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Life saving vedio
الله يرحم والديك
한국사람
How to choose the z value
You skipped it
You are not supposed to find z;
you know that it is between x and c,
so you can plug a value for z that maximes Rn(x)
this will give you an upper bound for the error,
Even if it's a tad larger then the actual error
You do choose z. If you want an upper bound, you choose z that will yield the largest derivative and thus the max error. If you want a lower bound, choose z that will yield the smallest derivative and thus min error. Z can be any number between c and x. You choose z based on what error you’re looking for
Hello the lesson is not bad but you was very fast and for the first time I can’t understand the topic from you ! Please try to slow down explaining the reminder term as until now I could not understand it please when you reach the calculations show us what are you doing and how are you calculating and why you have choose 1.1or 1! Thanks please repost this video I have exam tomorrow and I am sure this will be a question which I still don’t understand
بالعربي اكو واحد يشرحه
merci copain !
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You're definitely a high degree Mason
This doesn't work if you're given a range for x, instead of a specific value. It's not that easy.
ગુજરાતી IndiaGujarati it does work, you just have to rearrange the inequality differently. If 1
This was extremely helpful. Thank you