3 Step Continuity Test, Discontinuity, Piecewise Functions & Limits | Calculus Video
This calculus video tutorial explains how to identify points of discontinuity or to prove a function is continuous / discontinuous at a point by using the 3 step continuity test. This involves evaluating piecewise functions using one sided limits. The first step is to determine if the function is defined at the given point. The second step is to prove that the limit exists by showing that the right side equals the left side. If the limit does not exist, it could be a jump discontinuity or an infinite discontinuity which are nonremovable. The 3rd step is to show that the limit equals the function at the given point. If the limit exists but does not equal the function, then it's a point discontinuity also known as a hole which is removable.
Introduction to Limits:
https://www.youtube.com/watch?v=YNstP0ESndU
How To Evaluate Limits From a Graph:
https://www.youtube.com/watch?v=7Q2HwTHcxA0
Evaluating Limits By Factoring:
https://www.youtube.com/watch?v=fOrOeZA-vdY
Limits of Rational Functions :
https://www.youtube.com/watch?v=M2BgBG2Su94
Limits of Radical Functions:
https://www.youtube.com/watch?v=qay5HvT1UK8
Limits of Trigonometric Functions:
https://www.youtube.com/watch?v=HbtuSC_WOW0
___________________________________
How To Find The Limit at Infinity:
https://www.youtube.com/watch?v=NmLljBAg82o
Infinite Limits + Vertical Asymptotes:
https://www.youtube.com/watch?v=xvFqomOpLrs
Limits at Infinity With Radicals:
https://www.youtube.com/watch?v=1hyoTeWg6Bs
Limits of Absolute Value Functions:
https://www.youtube.com/watch?v=wFeh4ByT0xs
Limits of Composite Functions:
https://www.youtube.com/watch?v=KjL9cWHzeIc
The Squeeze Theorem:
https://www.youtube.com/watch?v=lVIb9iJ-rRI
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Limits and Logarithms:
https://www.youtube.com/watch?v=fHzmQmcvheI
Limits of Exponential Functions:
https://www.youtube.com/watch?v=pcUXo7XbRaM
Piecewise Functions - Limits:
https://www.youtube.com/watch?v=JrYmEo6hoiU
3 Step Continuity Test:
https://www.youtube.com/watch?v=WT7oxiiFYt8
Continuity and Differentiability:
https://www.youtube.com/watch?v=fml0-ELYLaE
Limits - Test Review:
https://www.youtube.com/watch?v=6e4Wtgc43KQ
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Final Exams and Video Playlists:
https://www.video-tutor.net/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathScienceTutor/collections
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