Review Question 11: Table of Maclaurin Series

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    mes

    Published on Dec 01, 2023
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    In this video I quickly go over a list of common Maclaurin series and their radius of convergence. The first series is for the function 1/(1-x), then ex, sin x, cos x, arctan x, and finally ln(1+x). Note that in my earlier video I had used an earlier version of my Stewart calculus textbook, which went over the Maclaurin series for ln(1-x) instead of ln(1+x). I quickly recap on that derivation and show that we can simply input -x into ln(1-x) to obtain the Maclaurin series for ln(1+x).

    The timestamps of key parts of the video are listed below:

    • Question 11: 0:00
    • Solution: Recap on Taylor and Maclaurin series: 0:53
    • (a) to (f) Table of Maclaurin series: 1:33
    • Note on the Maclaurin series for ln(1+x): 5:00
    • Maclaurin series for ln(1-x): 5:18
    • Replacing x with -x to get ln(1+x): 6:00
    • Maclaurin series for ln(1+x): 8:08

    This video was taken from my earlier video listed below:

    Related Videos:

    Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .


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