Name: Problems Plus 2: Where is the Function Continuous?
Uploaded: 2023-08-30T03:38:33+00:00
Duration: 11 min 29 s
Description: In this video I go over determining where a function, that is given in the form of a limit as n approaches infinity, is continuous. I solve this by using the problem-solving strategy of taking cases,

2 years ago

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math calculus infinite sequences and series sequences and series stem mathematics science education limits infinite limits limits at infinity

In this video I go over determining where a function, that is given in the form of a limit as n approaches infinity, is continuous. I solve this by using the problem-solving strategy of taking cases, in this case where the absolute value of x is less than 1, equal to 1, and greater than 1. Using our limit laws, as well as our previous r^n series, I show that the function is continuous for all values of x except at +/- 1.

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

- Problem 2: Where is f continuous?: 0:00
- Case (i): |x| is less than 1: 0:32
- Case (ii): |x| = 1: 4:27
- Case (iii): |x| is greater than 1: 6:21
- Putting it all together: 8:42

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