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:
   • Calculus 1 - Introduction to Limits  

How To Evaluate Limits From a Graph:
   • How To Evaluate Limits From a Graph  

Evaluating Limits By Factoring:
   • Evaluating Limits By Factoring  

Limits of Rational Functions :
   • Limits of Rational Functions - Fracti...  

Limits of Radical Functions:
   • How To Evaluate Limits of Radical Fun...  

Limits of Trigonometric Functions:
   • Limits of Trigonometric Functions  

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How To Find The Limit at Infinity:
   • How To Find The Limit At Infinity  

Infinite Limits + Vertical Asymptotes:
   • Infinite Limits and Vertical Asymptotes  

Limits at Infinity With Radicals:
   • Limits at Infinity With Radicals & Fr...  

Limits of Absolute Value Functions:
   • Limits and Absolute Value  

Limits of Composite Functions:
   • How To Find The Limit of a Composite ...  

The Squeeze Theorem:
   • Squeeze Theorem  

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Limits and Logarithms:
   • Limits and Logarithms  

Limits of Exponential Functions:
   • Limits of Exponential Functions | Cal...  

Piecewise Functions - Limits:
   • Piecewise Functions - Limits and Cont...  

3 Step Continuity Test:
   • 3 Step Continuity Test, Discontinuity...  

Continuity and Differentiability:
   • Continuity and Differentiability  

Limits - Test Review:
   • One Sided Limits, Graphs, Continuity,...  

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