- Calculus Lab Hours: evening hours are out for the moment
- MTWR: 8:30 am -3:30 pm
- F: 8:30-noon
- How did it go Thursday?
- What problems are occuring with the homework?
- You have a new assignment:
- Read 2.3 for Thursday
- Begin your 2.2 on-line IMathAS (http://www.norsemathology.org/homework) homework assignment (due next Tuesday, 2/26, by midnight)
- By hand: pp. 59--, #53, 56, 61 (due next Thursday, 2/28, in class)
- Definition of a (finite) limit
- What is it about real data that causes trouble?
- We want to look at functions defined by formulas, so that the idea of a limit makes sense. For that reason, we leave behind the Keeling curve for the moment.
- So we've got to be able to refine our subdivisions continually, forever, more finely....
- Consider f(x)=|x|
- Graphical and Numerical Investigation
- Let's take a look at #2, p. 57, and perform an investigation
- This is an example of a function with a hole in it.
- What kind of functions have "holes in them"?
- What else can go wrong?
- Theorem 1
- Proof of the constant rule
- Proof of the linear rule
- One-sided limits
- What functions would be different on one side of a point
than they are on the other?
- postage
- general costs of items in bulk
- What functions would be different on one side of a point
than they are on the other?
- Infinite limits
- There are two kinds of infinite limits.
- In this section, we're horning in on a constant value of x, and finding that the function is growing "out of bounds"
- Example: