Piecewise Functions - Limits and Continuity | Calculus

This calculus review video tutorial explains how to evaluate limits using piecewise functions and how to make a piecewise function continuous by finding the constant c to make the two parts equal. This video on limits and continuity contains plenty of examples and practice problems for you to work. It discusses how to find if the limit exist by analyzing the one sided limits such as finding the limit as x approaches a number from the left and from the right.
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

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/
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Respected sir, If the limit approaching From the Right side , then why didn't you apply it on (x³-5x+3).. while the condition was(x>=4)??

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So I understand how you would find limits for a piecewise function when it’s for x->1+ or x->1- but how solve it if it was just x->1

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Now what can you do in an instance where the limit of x as it approaches 5

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How do i find value k when i was given a piecewise function of kx square, where x less than or equal to 2 and when x is more than 2. So that the function continuous?

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If the limits are very close like 13 and 14 is it still considered DNE?

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i have a question please
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why should i use the second equation?
the first equation says x

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Because x is also equal to 4 at the second equation nd we have to take the nearest polynomial to 4

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Why is f(2) defined, is it because it is equal to the limit?

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It’s defined because it’s defined by the function. ( the important part is that it’s only defined once btw. Otherwise there is a jump discontinuity and neither f(2) is defined or the limit as it approaches that value unless it’s from one side or another )