Continuity of Functions
Best of the Web
This website gives you a few more examples of different functions and a discussion of continuity at different points. You’ll see some of the craziest examples that mathematicians can cook up. No, that doesn't include ramen and peanut butter sandwiches.
This page discusses continuity and limits with a clear set of definitions and a number of examples. Like an oak tree, this page will firmly plant these ideas in your noggin. What, your oak trees don't do that?
If you've ever thought about the age-old question of applying the human genome project to function splicing, wonder no more: here's a description of the different types of discontinuities in functions.
If you often ask yourself, "Do I use a square bracket or do I use a parenthesis?" (we do it all the time), this link will come to your rescue. With an unparalleled explanation of interval notation, you'll never need to ask yourself this question again.
When you first saw the intermediate value theorem, it probably resembled the Russian language more than it did a mathematical idea. This video gives a very clear description of the IVT. Ура!
You may think the intermediate value theorem is about as useful as a pogo stick in a grocery store. That's just silly. How else would you reach the top shelf? This video will show you some practical uses for the theorem…in math, anyway.
This video gives you a few more-complicated examples on how to use the intermediate value theorem. These are the questions your teacher may use to trick you. Don’t succumb.
Let Dr. X explain the extreme value theorem to you in plain and simple terms. No, he won’t be able to help you with your mutant ability to grow out your fingernails at an inexplicably fast rate.
This is the type of question your teacher will ask you to solve on the continuity exam, and this video will show you how to solve the problem and bag those 10 extra puntos.
Tools and Games
This online tool helps teach the extreme value theorem. Unlike a gym membership, however, you can only use this theorem when the interval is closed.