A Tale of Three Functions | Intro to Limits Part II

We numerically and graphically investigate what happens as we approach the interesting point. Through this, we define the notion of a limit.

Learning Objectives:
1) Given a graph, estimate the limit of a function as the variable approachs a point (possibly only from the left or right)
2) Given a table of values, estimate the limit of a function as the variable approachs a point (possibly only from the left or right)

Note: My apologies for the strange artifacting around the limit expressions. Technology is annoying.

Now it's your turn:
1) Summarize the big idea of this video in your own words
2) Write down anything you are unsure about to think about later
3) What questions for the future do you have? Where are we going with this content?
4) Can you come up with your own sample test problem on this material? Solve it!

Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master calculus means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.

This video is part of a Calculus course taught by Dr. Trefor Bazett at the University of Cincinnati.

BECOME A MEMBER:

MATH BOOKS & MERCH I LOVE:

[Artur.Baranov]

your explanation skills are amazing! it's a real puzzle why so little views.. there should be hundreds of thousands!

[berargumen]

This is the clearest explanation of limit in YouTube, thanks.

[nebthegamerartist]

As a 7th grader, never imagined calculus could be this easy to understand, THANK YOU

[Jjdumott]

“The limit doesn’t care about what happens at the point it only cares about what happens as you get really close to it” Wise words

[jakecarlo]

This was a very clarifying way of approaching limits (no pun intended) - definitely the right thing at the right time for me + great production value, so thank you.

[inziify]

You are gem of a teacher and speaker.. You express yourself very clearly and I understand very easily whatever you speak sir.

[ekalavyain]

Under rated channel with excellent quality of teaching.

[Anne-gd]

Now I know that limit is not the mess or any kinda 'cause of dismay for mathematics students. .but it's kinda tool for indicating the behavior of functions. .or how limit concern 'bout how function approaches the particular value but not for the value of function at that specific point. It cares how the function behaves around a particular point instead of at that point. .

Thanking you! !

[joshuaisemperor]

Thank you very much for making such great videos! I really like the style you explain all these concepts. The more "story like" explaining and the extra information, like applications of some concept, make the proces of understanding and learning so much more intuitively. I wished more people teach in this way instead of just writing all formal definitions and such down. These kind of videos make me want to actually learn more about different and more advanced kinds of math. Again, thank you!

[jaydean]

Dr Bazett, it always a pleasure listening to your lectures(I've seen many), the world would be a better place(& smarter) with more professors like you. Thanks

[chetankhangar]

Limit defines the value of around the x and not the exact value
Is like the speed of vehicle around 9:10 and not the exact speed at 9:10
It may happened that 9:10 speedbreak was there and speed reduces
So limit of a function don't care at that point bt what happened arround it
You explained it very well.

[sudarshanreddyt]

really thankyou for doing this kind of graphical explantions

[shyamdas]

I am going to watch all the videos of Calculus I, II and III. Thank you, sir.

[josephmalone]

A limit is the height of the point, it is y value except for removable discontinuities.

[rockyjoe]

6:01 err didn't catch that one professor Trefor, I still don't understand why did we choose that specific open point to do the limit with instead of the other other point?

[skhalil]

Hi can anyone provide me the book name referred by @dr.trefor at the end of his video?