Taylor Series and Maclaurin Series - Calculus 2

This calculus 2 video tutorial explains how to find the Taylor series and the Maclaurin series of a function using a simple formula. It explains how to derive the power series of composite functions using known Maclaurin series of elementary functions.
Full-Length Math & Science Videos:
/ collections
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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...
Calculus Final Exam and Video Playlists:
www.video-tuto...

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzbin.info/www/bejne/jGKkfHShfK-fhJo

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part of being a good student is also learning for yourself by looking for proper sources, such as this one, but be certain that a true understanding of the matter is not achieved by watching this video alone, although it does bring us a long long way ahead of just the school lectures. Also, exposure in class combined with these videos is much more effective than just the videos. Make no mistake this guy also maybe saved my finals

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[@kxngmar2748]

0:00 Taylor series for function f(x)=ln(x) centered at a=1 7:14 Taylor series for function f(x)=e^x centered at a=3 10:49 Maclaurin series for function f(x)=sin(x) 17:05 Maclaurin series for cos(x) using Maclaurin series for sin(x) 23:02 Maclaurin series for cos(x^2) 24:28 Maclaurin series for xcos(x) 25:30 Maclaurin series for function f(x)=x^2 e^(-x) 27:31 Maclaurin series for function f(x)=cos^2x

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[@tyscott4949]

I find it funny that I come across " The Organic Chemistry Tutor" -- and listen to a "tutor" run circles around calculus instructors on KZbin and in the classroom teaching calculus II. I have spent about an two hours or so taking notes reading reference calculus books and digesting the Taylor Series and at the same time find it soothing that things are becoming clear, what once was amiss, in the midst of the fog. Thank you, I will join the page when I start my calculus class this summer of 2022.

[@lesegomokgabudi5798]

i had no idea on how to solve Taylor series and its younger brother Maclaurin series....but now i have an idea. Thanks a lot my brother

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[@connectingspyyo8159]

i took calc 2 almost 2 years ago and I am super worried about calc 3! Thank you so much for this, as it is a great refresher. I feel like you taught this better than my professor did at the time

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[@V.Z.69]

I remember learning this. I got an 'A' in the class. An 'A' in Calc I, II, and III. Now, I just can't remember why I learned it and I never used it since I graduated.

[@sooners2037]

That happened to me when I was a undergrad barely used calculus until Atmospheric Dynamics decided to retake Calculus1-3 when I went to grad school occasionally I use Calculus but the computers do the calculations it’s good to know depending on the profession

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[@iqrakhanamansari8670]

Hey...is this 'TAYLOR SERIES' taught in clge or high schl??

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[@42laar]

wow, i've been taught taylor's series in class, review sessions, recitations, and youtube videos. this explanation is by far the best one at helping me understand it. i feel much more confident about taylor's series now. thanks a lot!

[@danielcash1037]

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I want to thank you so so much! my professor and IA made this series so hard to understand during lecture/discussion, but you made it so easy to understand!

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I like how you always bring it back to that larger formula =, and you parse out what the series will be from there. It makes it very repeatable.

[@EnjoimentProductions]

Thank you! The part that helped me most is when you are making the summation notation of the function. Your red notes show what part of the expression is n = 0, n = 1, n = 2, n = 3, n = 4 @ 10:04 . This was so helpful. I could not find any visual in my textbook that showed what part of the expression relates to which n. But you laid it out in red and that helped me make sense of it all. Thank you again!

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[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for explaining the difference between Taylor and Maclaurin Series in Calculus Two. The two names that are most commonly associated with Power Series are Brook Taylor and Colin Maclaurin. Elementary and Transcendental Functions can be represented as Taylor/Maclaurin Series. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

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It took me only 7 minutes to understand taylor and maclaurin series after watching 1 of your examples. Before that, I was scratching my head for 1 hour in class wondering what my professor was doing to get the taylor/maclaurin series.

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Thank you so much! Your videos really help me fill in the holes I missed in calculus originally.

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studying an hour and 14 minutes before my final calculus exam wish me luck

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Thank you so much! Didn't expect to understand Taylor and Maclaurin series this easily...

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I have an exam in 30minutes and I just learnt this for the first time..

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Passed my calculus thanks to this man.

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your way of teaching is really understandable sir. Thank you very much.

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That was awesome, it has just cleared all the doubts I had regarding to single variable. I just want to ask that what if there will be two variables in the function

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I literally watched this entire playlist from start to finish.

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this is perfect. watching your videos has helped me so much in university calculus!!!!!

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I HAVE A CALCLUS FINAL IN ABOUT 3 HOURS, I HOPE I PASS THIS COURSE. THANKYOUUU FOR THE EXPLANATION

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If I could pay you i would...your methods are simple and easy to understand

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Watching this on my train ride to school before a quiz, thank you thank you thank you

[@Backflipmarine]

This is the kind of thing you learn, execute, get graded on, forget, and never knew what it actually did. When would you actually use this for building/designing?

[@velcro8299]

For the Maclaurin series of cos x, I found out that ((-1)^n-1.(x)^2n-2)/ (2n-2)! works as well. the interval is n=1 to infinity.

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do this channel deserve the name organic chemistry tutor?

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I understand Taylor and Maclaurin series thanks to you

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19:12 ayo you need chill bruh xD dead

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that taylor thing pisses him off

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passive aggressive XD

[@danraacademy6233]

Maclaurin series starts at 11:01 =)

[@dequanthompson6658]

I'm not sure how much it really says about me or my calc 2 class when I have an easier time understanding this 30 minute video then I do nearly half a semester's worth of Taylor/Maclaurian series work.