In this lesson we are going to talk about continuity and the intermediate value theorem. In fact, intermediate value theorem represents the application of the continuity. First, we will give definitions of continuity and the intermediate value theorem. Simple illustration will be given just to clarify the meaning of intermediate value theorem. Later on, we will do some examples where we will be looking for places at which the function is not continuous, such are: removable discontinuities, jump discontinuities, and infinite discontinuities. We will also be looking for places where the function is not even defined because these are discontinuities as well.
Be careful in your
- it is a function composition!
Also take care in
carrying out the subtraction
realize we are subtracting off the entire quantity given by
The work here for
is famous and involves a couple famous limits.
If you know how to
compute derivatives directly, you can check your result by this
Limit Definition of the Derivative
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.