3 Step Continuity Test (Patreon)

3 Step Continuity Test, Discontinuity, Piecewise Functions & Limits | Calculus

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 Properties of Limits: https://www.youtube.com/watch?v=P7G7F3NzPw0 Limits of Polynomial Functions: https://www.youtube.com/watch?v=NswmsBaFkOM Evaluating Limits By Factoring: https://www.youtube.com/watch?v=fOrOeZA-vdY How To Tell If The Limit Exists: https://www.youtube.com/watch?v=5VPYZIaG4Eg 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 Inverse Trigonometric Functions: https://www.youtube.com/watch?v=UPUzKShJPuk _________________________________________________________________________________________ Limits of Hyperbolic Functions: https://www.youtube.com/watch?v=bVhcT2-QMEc How To Find The Limit at Infinity: https://www.youtube.com/watch?v=NmLljBAg82o Limits at Infinity + H. Asymptotes: https://www.youtube.com/watch?v=sjLFl7Z8W_I 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 Limits Composite Functions -2 Graphs: https://www.youtube.com/watch?v=yq3eri878II The Squeeze Theorem: https://www.youtube.com/watch?v=lVIb9iJ-rRI Limits of Logarithmic Functions: https://www.youtube.com/watch?v=6A4pbsXcI84 _________________________________________________________________________________________ Limits and Logarithms: https://www.youtube.com/watch?v=fHzmQmcvheI Limits of Exponential Functions: https://www.youtube.com/watch?v=pcUXo7XbRaM Greatest Integer Function With Limits: https://www.youtube.com/watch?v=teaD5isBTfk Piecewise Functions - Limits: https://www.youtube.com/watch?v=JrYmEo6hoiU Limits and Continuity: https://www.youtube.com/watch?v=9brk313DjV8 3 Step Continuity Test: https://www.youtube.com/watch?v=WT7oxiiFYt8 Continuity and Differentiability: https://www.youtube.com/watch?v=fml0-ELYLaE Limit Definition of The Derivative: https://www.youtube.com/watch?v=-aTLjoDT1GQ Alternate Form - Limit Derivative: https://www.youtube.com/watch?v=6yzaEpacZkg Limits - Test Review: https://www.youtube.com/watch?v=6e4Wtgc43KQ ____________________________________________________________________________________________ The Power Rule of Derivatives: https://www.youtube.com/watch?v=9Yz-RCdS2Tg Limits and Derivatives: https://www.youtube.com/watch?v=xGibYZiT5-U Product Rule For Derivatives: https://www.youtube.com/watch?v=17X5g9QArTc Quotient Rule For Derivatives: https://www.youtube.com/watch?v=8jVDEcQ0wXk Introduction to Related Rates: https://www.youtube.com/watch?v=I9mVUo-bhM8 Finding Critical Points: https://www.youtube.com/watch?v=Bp9EbV3COVA Local Maximum & Minimum: https://www.youtube.com/watch?v=WCq3sRzsJfs Optimization Problems: https://www.youtube.com/watch?v=lx8RcYcYVuU Antiderivatives: https://www.youtube.com/watch?v=xaCPDMEkbig ___________________________________________________________________________________________ Calculus 1 Final Exam Review: https://www.youtube.com/watch?v=WmBzmHru78w Full-Length Exams and Worksheets: https://bit.ly/4990rzU