Name: Review Question 11: Table of Maclaurin Series
Uploaded: 2023-12-02T04:50:58+00:00
Duration: 9 min 29 s
Description: 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 e^x, sin x, cos x, arctan x, and finally ln(1+x).

1 year ago

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Health & Science Education math calculus science stewart calculus table of power series interval of convergence radius of convergence

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 e^x, 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:

- Infinite Sequences and Series: Review and True-False Quiz: https://youtu.be/F0dsQLdXXpI
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-review-and-true-false-quiz
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FCqXVJv1r7eJvrvphfkr6L