Name: Problems Plus 21: Finding the Solutions of a Maclaurin Cosine Series
Uploaded: 2023-10-07T04:12:26+00:00
Duration: 11 min 10 s
Description: In this video I find the solutions of an infinite Maclaurin cosine series when it equals to zero. Although we aren't given that the series is a Maclaurin cosine series, we can see this to be the case

2 years ago

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Health & Science Education maclaurin series infinite sequences and series sequences trigonometry math calculus science stem education

In this video I find the solutions of an infinite Maclaurin cosine series when it equals to zero. Although we aren't given that the series is a Maclaurin cosine series, we can see this to be the case by looking at our table of common Maclaurin series and replacing the x terms with -x^2. Given the periodic nature of the cosine function, we get an infinite number of solutions as a function of any given integer. I also include an important note at the end of the video about keeping track of the negative signs when transforming functions, something that my Calculus book solutions manual forgot to do!

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

- Problem 21: 0:00
- Solution: Case where x ≥ 0 is not a solution: 0:31
- Maclaurin series for cos x : 1:24
- Solutions for cos x = 0: 4:54
- Solutions for f(x) = 0: 7:38
- Note on the Solutions Manual: 9:32

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P