Taylor Polynomials & Maclaurin Polynomials With Approximations

[@TheOrganicChemistryTutor]

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[@lazarnikolic65]

0 - 6:28 Taylor 6:29 Maclaurin

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Yes the videos from 2006 are working on if you walk with organic tutor

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[@jaydenrussell7491]

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 ?

[@someone1459]

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!

[@bexruzkarimov6783]

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

[@Susu16243]

There are 5.2k likes right now!

[@curtain1810]

If its not stated in the problem, how so you know where is the function centered?

[@BenzeneBird]

struggling in calc bc ;-; thx for the help

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LOVED ❤

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Thank you, I really got it

[@RandomGuy0400]

Wish I had watched this *before* the exam :(

[@georgesadler7830]

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.

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study pug needs to chill

[@MinaHussainArt]

wow, wish my teacher will explain it like this instead of skipping most of the steps.

[@destinyobamwonyi]

I think the first formular is supposed to end with f^n(c)(x-c)^n ÷ n!

[@sfcxwedsx]

does the value of the degree represent the number of accurate decimals ?

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Im watching the calculus 2 playlist and im a bit confused to be honest. How did we come to this from divergent tests :d

[@meep7895]

what does the center mean conceptually?

[@ma.jenelynfernandez1860]

THANK YOU!😘

[@kuroshitsuji2580]

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.

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[@krislegends]

For ln(1.1), why put 0.1 instead of 1.1?

[@babygravy7]

1.1 - 1 = 0.1. He just didn't show the work for it because it wasn't needed

[@krislegends]

@@babygravy7 Is 1 the center?

[@ShadowReaper-pu2hx]

Yes, one is the center (the problem says it’s centered at one).

[@nraishanzr3333]

if 3! = 3 x 2 x 1 why don't we just write 6? Same with 4! why isn't just written as 24

[@g.molina10]

You could. He just didn't. They are the same thing though

[@vez3834]

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.

[@katrinawalker1702]

Why didn't you subtract 1 when subbing for x=1.1 in the P(4) equation?

[@queenpenguin5685]

he did, it became .1 where the (x-1) things were

[@internetsurfermr80]

Derivatives of 2/x^3 is not 6/x^4?

[@xkilla911]

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

[@Iron_Age]

you're right, its negative

[@zacharysantana3861]

He said -6/x^4

[@janieli]

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?

[@adnanmohammed4354]

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.

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[@martinhazard2025]

wrong, you must use the Landau's symbols

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just another cook book demonstration in a quiet no nonsense manner sadly no discussion of the beautiful underlying philosophy of the method

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can you share a link?

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I am an idiot. 1.1-1=0.1

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