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3 Step Continuity Test, Discontinuity, Piecewise Functions & Limits | Calculus
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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:
How To Evaluate Limits From a Graph:
Evaluating Limits By Factoring:
Limits of Rational Functions :
Limits of Radical Functions:
Limits of Trigonometric Functions:
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How To Find The Limit at Infinity:
Infinite Limits + Vertical Asymptotes:
Limits at Infinity With Radicals:
Limits of Absolute Value Functions:
Limits of Composite Functions:
The Squeeze Theorem:
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Limits and Logarithms:
Limits of Exponential Functions:
Piecewise Functions - Limits:
3 Step Continuity Test:
Continuity and Differentiability:
Limits - Test Review:
_____________________________________
Final Exams and Video Playlists:
Full-Length Videos and Worksheets:
Introduction to Limits:
How To Evaluate Limits From a Graph:
Evaluating Limits By Factoring:
Limits of Rational Functions :
Limits of Radical Functions:
Limits of Trigonometric Functions:
___________________________________
How To Find The Limit at Infinity:
Infinite Limits + Vertical Asymptotes:
Limits at Infinity With Radicals:
Limits of Absolute Value Functions:
Limits of Composite Functions:
The Squeeze Theorem:
____________________________________
Limits and Logarithms:
Limits of Exponential Functions:
Piecewise Functions - Limits:
3 Step Continuity Test:
Continuity and Differentiability:
Limits - Test Review:
_____________________________________
Final Exams and Video Playlists:
Full-Length Videos and Worksheets:
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