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:
• Calculus 1 - Introduct...
How To Evaluate Limits From a Graph:
• How To Evaluate Limits...
Evaluating Limits By Factoring:
• Evaluating Limits By F...
Limits of Rational Functions :
• Limits of Rational Fun...
Limits of Radical Functions:
• How To Evaluate Limits...
Limits of Trigonometric Functions:
• Limits of Trigonometri...
___________________________________
How To Find The Limit at Infinity:
• How To Find The Limit ...
Infinite Limits + Vertical Asymptotes:
• Infinite Limits and Ve...
Limits at Infinity With Radicals:
• Limits at Infinity Wit...
Limits of Absolute Value Functions:
• Limits and Absolute Value
Limits of Composite Functions:
• How To Find The Limit ...
The Squeeze Theorem:
• Squeeze Theorem
____________________________________
Limits and Logarithms:
• Limits and Logarithms
Limits of Exponential Functions:
• Limits of Exponential ...
Piecewise Functions - Limits:
• Piecewise Functions - ...
3 Step Continuity Test:
• 3 Step Continuity Test...
Continuity and Differentiability:
• Continuity and Differe...
Limits - Test Review:
• One Sided Limits, Grap...
_____________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections
Limits - Free Formula Sheet:
bit.ly/3T3dD2X

Опубликовано:

24 сен 2024

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Комментарии : 617

@TheOrganicChemistryTutor Год назад

Limits - Free Formula Sheet: bit.ly/3T3dD2X Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-9brk313DjV8.html

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@lonevoyager6026 2 года назад

whats the differnece between a closed endpoint and a hole?

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@lonevoyager6026 2 года назад

whats the differnece between a closed endpoint and a hole?

@krishshah3974 Год назад

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when ur crying while working out these problems cause ur test is in a few hours

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Did you pass?

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@georgesadler7830 Год назад

Professor Organic Chemistry Tutor, thank you for an awesome video/lecture on the Three Step Continuity Test, Discontinuity, Piecewise Functions and Limits in Calculus. This is an error free video/lecture on RU-vid.

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@simoncheung2427 4 года назад

i got the idea clearly . similar to this topic . if a composite1 of function g(x) that x is smaller and equal to 2 , then put x= 2 into composite 1 of g(x) is equal to constant K and if composite 2 of function g(x) that x is greater and equal to 2, put x =2 into composite 2 is equal to a hole. secondly, the left hand limit of composite 1 is equal to constant K and the right hand limit of composite 2 is equal to constant K . then it is continuous too even composite 2 has a hole at x=2. if you know what i say, you probably understand it very much.

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@arway4766 3 года назад

Jump discontinuity if the limit from the left side and the right side aren't equal (limit DNE) Removable discontinuity: if the limit exists(lim left = lim right) but isn't equal to the value of the function. (hole) Infinite discontinuity: if the limit is equal to infinity (from the left and right)

@tonysparks5531 3 года назад

Can anyone answer me🥺 My lim x > 16 negative = 1/16 and my lim x > 6 psotive = 0, is that discontinues or continuous?? Pls help, really need dis for my performance task that is due in 7 hours😭 Also, my first step is f(x)=1