Taylor Polynomials & Maclaurin Polynomials With Approximations
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- เผยแพร่เมื่อ 30 มี.ค. 2018
- This calculus 2 video tutorial provides a basic introduction into taylor polynomials and maclaurin polynomials. It explains how to find the 4th degree polynomial approximation of lnx and e^x. A maclaurin polynomial approximation can be found using a taylor polynomial approximation centered at 0. This video contains a few examples and practice problems.
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:
• Power Series - Finding...
Power Series - Derivatives & Integrals:
• Power Series - Differe...
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Power Series - Function Representation:
• Power Series - Represe...
Finding The Power Series:
• Finding Power Series B...
Power Series - Representation By Integration:
• Power Series Represent...
Power Series - Representation By Natural Logs:
• Power Series Represent...
Taylor & Maclaurin Series:
• Taylor Series and Macl...
Binomial Series:
• Binomial Series
____________________________________
Parametric Equations:
• Parametric Equations I...
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0 - 6:28 Taylor
6:29 Maclaurin
LOVED ❤
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thank you
does the value of the degree represent the number of accurate decimals ?
Our professor gave us an assignment. And it doesn't have any polynomials on it. Just the approximate value. But we have to find its estimate value? I'm confused, is that possible.
what does the center mean conceptually?
If its not stated in the problem, how so you know where is the function centered?
Interesting Fact: This video gets on average 1 like per day, since it was created 997 days ago and i just put 997 th like
There are 5.2k likes right now!
Thank you for this great explains but I hope you can raise the voice of videos Because its hard to listen to it 🥲💔
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when we increase the terms, why do we need to add (x-a)^n (where n is equal to the number of derivatives)? I get that we need to substitute x and a to find approximation, but why do the exponents increase?
As he said, the number of terms indicates more accuracy. If you have a function and take more derivatives into account, you'll end up with a better approximation. It might be difficult to put it into words. Check out 3Blue1Brown's Taylor polynomials video. His animations were really helpful.
2:35 I thought a negative value cannot be evaluated inside a natural log function. How did he get ln(-1) = -1 when negative number are outside the domain of ln ?
he is evaluating c = 1 at the second derivative of f(x) which is -1/x^2 , not at f(x) = ln(x). when we plug c=1 into that second derivative we get -1 as the answer. he did not take ln (-1), because as you said that would be undefined!
Im watching the calculus 2 playlist and im a bit confused to be honest. How did we come to this from divergent tests :d
Professor Organic Chemistry Tutor, thank you for a detail analysis of the Taylor and Maclurin Polynomials with Approximations in Calculus Two. Taylor/Maclurin Polynomials are common/well known topics in Science and Engineering. Professor Organic Chemistry Tutor, you made a typing error at the 1:04 minute mark in the video. For the nth term in the Tayor Polynomial, you have f raised to the n (x - c) raised to the fourth divided by four factorial, instead of f raised to the n (x - c) raised to the n divided by n factorial. Professor, please correct this small error in the video.
struggling in calc bc ;-; thx for the help
Why didn't you subtract 1 when subbing for x=1.1 in the P(4) equation?
he did, it became .1 where the (x-1) things were
Derivatives of 2/x^3 is not 6/x^4?
the video put -6/x^4 because 2/x^3 is basically 2x^(-3). and so by doing simple exponential differentiation...
(-3)*2x^(-3-1) = -6x^(-4)
which is = -6/x^4
you're right, its negative
He said -6/x^4
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Wish I had watched this *before* the exam
:(
thank you! T-T
wow, wish my teacher will explain it like this instead of skipping most of the steps.
For ln(1.1), why put 0.1 instead of 1.1?
1.1 - 1 = 0.1. He just didn't show the work for it because it wasn't needed
@@babygravy7 Is 1 the center?
Take my whole degree
if 3! = 3 x 2 x 1 why don't we just write 6? Same with 4! why isn't just written as 24
You could. He just didn't. They are the same thing though
It's for making the general formula easier to write. So rather than listing all factorials 1, 2, 6, 24, 120... we write n! where n is the degree of our polynomial. So then when plugging something into the equation, it's nice to see where it came from.
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wrong, you must use the Landau's symbols
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I am an idiot. 1.1-1=0.1
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lol it's not like Khan Academy and Organic Chemist have an oligopoly on FREE math and science help videos. And there are plenty of videos from a wide range of YTers on these very topics. If you're tired of their voices, stop clicking on the first/second search result.
Then why tf are you here?
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philosophy of the method
you can make a video about it then
can you share a link?
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