Limits & Continuity Please Read the Description
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- čas přidán 2. 08. 2024
- I explain how to test for Continuity at a given point and find Discontinuities in functions. I finish by working through a couple of examples. EXAMPLES 4:57 10:57. Though I say smooth and continuous a few times in this video, a function does not have to be smooth to be continuous.
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Thank you. I made this video while teaching out of my PreCalculus book. I am glad the definition is on the board when I said smooth and continuous, and I included a piecewise function which was not smooth. So many problems in the PreCalc book where polynomials, that just got stuck in my head:) I added an annotation in the video to clarify that smooth is not a requirement. I made a new video that is better for Calculus including open and closed intervals and with more examples.
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Professor RobBob, thank you for another amazing video/lecture on Limits and Continuity in Precalculus/Calculus One AB. The definition of Continuity and Limits are very important in Calculus and students should be well aware of these terms in Applied and advanced Mathematics. Problems solving will only help students to fully understand these terms.
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In the first example I have a rational function where the numerator and denominator are Polynomials. So, if the function is undefined there is either a hole or an asymptote and this will occur where the denominator is zero. With this knowledge I do not need to find the existence of the limit by finding the left and right limits separately like I always do for piecewise functions.
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For a limit to exist at a particular value of x the left and right limits must be equal. Polynomials are smooths and continuous graphs. Since we know this, and the numerator and denominator are both have polynomials, we can find those limits in one step as I have shown. For say a piecewise function, you will have to show the work where you are finding both the left sided limit and then the right limit and then checking if they are equal for the limit to exist at that value of x.
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If a function has a hole in the graph then this is called a removable discontinuity and the left and right limits would be equal.
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wonderful class, thank you !
The second example was my problem ..
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สวัสดีครับ It's the same hello.I'm from Thailand. I thought you teach better than prof in my university. I studied at my class 3-4 Hours, I didn't understand but You teached me a little bit time. I understand about limit and continuity and I saw a chain rule.Finally I'm sorry .I write not good grammar .I hope you understand me. Thanks a lot prof.
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Are you talking about when the graph has a vertical asymptote or when x approaches infiniti?
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That was an A or B question...not yes or no. I am assuming your mean vertical asymptotes. I need to fill in that gap in my videos but it will be about a week before I can get that recorded.
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I'm sorry for the late reply. I found a video already. Thanks for your reply though, I really appreciate the fact that you are willing to help :)
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what made you come to the conclusion at 10:38? like how were you able to tell that 1/3 made f(x)=f(1)???
in the first example (whether the function is continuous at a=1) do u have to find only one single limit (either that approaches from the left or that approaches from the right)?