Continuity | Calculus Lesson 5 – JK Math

Continuity of Functions (Calculus Lesson 5)

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In this lesson we discuss continuity and what it means for a function to be continuous from a calculus perspective. We use limits to help us determine if points on a function are continuous or are a discontinuity. We also classify the two different kinds of discontinuities: removable and nonremovable.

This course is designed to help students understand the concepts of calculus at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with each lesson under 20 minutes!

Calculus requires a solid understanding of precalculus and algebra concepts and techniques including factoring, equation manipulation, trigonometric equations, logarithms, finding slope, graphing, and many more. If you are not familiar with these prerequisite topics, be sure to learn them first!

Video Chapters:
0:00 What is Continuity?
0:24 A Continuous Function on an Interval
1:20 A Jump Discontinuity on an Interval
2:51 A Hole in a Function on an Interval
6:04 Calculus Definition of Continuity
7:51 Removable Discontinuities
9:35 Non-removable Discontinuities
10:30 Example 1 – Everywhere Continuous
11:30 Example 2 – Non-removable Discontinuity (Vertical Asymptote)
12:40 Example 3 – Removable Discontinuity (Hole)

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#calculus #limits

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