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-tutor.net/
Full-Length Videos and Worksheets:
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[@TheOrganicChemistryTutor]

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OMG FINALLY! THANK YOU ORGANIC CHEMISTRY TUTOR! I don't get why no one cared to explain that we are reading the limit for these piece-wise evaluations as less than or greater to the value of x that is being approached depending on the superscript sign. I was having trouble with the likes of lim x--> - a ^ + or - . Now I get how to read that, thanks organic chem tutor, you're the best!

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

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

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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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[@rahman_solo]

But then what if we're asked to find the coefficients of x, take for example all coefficients are represented with a letter, say k... I mean instead of 5x-2 we were given kx-2 instead, where the value of k is not given and neither is the limit of x, how are we supposed to find the value of k that makes the right and the left side limits? I need this pls.

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i have a question please
if "X" tends to 4 from the left side
why should i use the second equation?
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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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there's an issue at 3.10, if x should approach from the left side of 4, then x shouldn't equal 4

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6:30

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I completely dont get it 1:30, in the first one it clearly says that x

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[@kekeletsoletsoara48]

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

[@ms-dosguy6630]

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 )

[@chuckmoment]

how come he uses 2 even though he said he needs a number less than two in the beginning?? 1:13

[@novadark9607]

Because the limit you are looking for is x which is 2. What he was explaining is that when looking for the limit you look what the y is approaching the given x. The explanation given in the begin is meant for things such as what is f(2) not whats the limit of f(x) approaching 2

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@@novadark9607 oh okay i see now thank you

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[@Unknown-ni2ko]

So these are not continuous?