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# AP Calculus AB

An interactive log for students and parents in my AP Calculus class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

## Wednesday, October 19, 2005

### Continuity

In today's class we learned if a function is continous or discontinous. According to Sarah's blog a continous function is predictable. In order for a function to be continous it should have no breaks, no holes, and no jumps. A function is continous it must have a limits at every x value, meaning it should have no breaks in its graph. Also it should have no holes, meaning f(x) cannot have an undefined point or any kind of vertical asymptotes. Then an important key to continuity is that if f(x) is continous, then for every x=a in the function, lim x->c f(x)=f(c). In other words, the function should exist at the height indicated by the function. Then Mr. Clark pointed to us that we should know about the Intermediate Value Theorem. It just states that if a function f is continous in a given interval [a,b], and k is a number between f(a) and f(b), then there exists at least one number c in (a,b) for which f(c) =k.

Basically that's all we learned in class today and we mostly spend our time doing our exercises. Btw some of the information I put in this summary are from Sarah's blog. Thanks Sarah! I guess that's all for now, because I still have to catch up on a lot of things. That's all folks!!!