❖ Taylor and Maclaurin Series - Example 1 ❖
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- Опубликовано: 31 янв 2025
- 📚 Taylor and Maclaurin Series Explained - Step-by-Step Example 📚
In this video, I walk through an example of finding the Maclaurin series for a function, specifically showing how to determine the series expansion for e^(5x) (assuming the series expansion is valid).
🚀 What’s covered:
Understanding the Taylor series: A function's series expansion centered at x = a.
Maclaurin series: A special case of the Taylor series where a = 0.
How to find the series expansion by calculating the values of the derivatives at x = a.
By the end of this video, you’ll have a solid understanding of how to compute both Taylor and Maclaurin series and how they relate to each other. This is a key concept in calculus, helping you understand how to approximate functions using infinite series.
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Hashtags:
#TaylorSeries #MaclaurinSeries #Calculus #SeriesExpansion #MathTutorial #LearningCalculus #MathHelp #Derivatives #ExponentialFunctions #STEM #Mathematics #MathConcepts #SeriesMath
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This was made on my birthday exactly.
to find the radius of convergence:
1) find the length of the interval of convergence (note that you do not have to worry whether the series converges at the endpoints of an interval)
2) Divide the length by 2.
That number is the radius of convergence
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Very good explanation! Not overcomplicated and not too brief. Teachers always have a habit of trying to instill the entire complicated concept into a student when he/she is just learning the basics, but that comes later. This is a good introduction which can help a student begin to understand the concept of Taylor series.
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glad it helped! i have a playlist on sequences and series as well if you would like to check it out. it is missing a few videos though, so you will probably want to do an individual search for any specific topics. good luck on the next calculus course!
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ha! well, i am sure your teacher was answering questions, doing more examples, and going into much greater detail : ) - thanks though! i am glad my 10 minute explanation helps!
Wow this video really helped me understand Taylor and Maclaurin series for the first time. I had trouble learning from the book and from my teacher but this really did it. Thank you so much! You did an extremely spectacular job at being clear.
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glad it helped : )
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Thanks for this video, it really clarified the Taylor series stuff for me..and leaving the terms as 5^2, 5^3, ...5^n is a really smart thing that I hadn't been doing...it makes coming up with the summation notation allot easier in harder problems.
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