Problems Plus 2: Where is the Function Continuous?

Math Easy Solutions

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, 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