Day 2, Mat128: Calculus A

Here's the link to the Zoom recording of the last session.

I'll post the link to today's later (here it is). These zooms will continue through the next week. Nice to see so many of you here today!

please read Section 1.2 in our text, and carry out Preview Activity 1.2.1 (bring your work to class -- I'll be "evaluating" these for real next time!).

Please fill out the card, indicating

1. Name (that you want me to call you)
2. Hometown
3. What is your calling? ("a calling has to do with one's larger purpose, personhood, deepest values, and the gift one wishes to give the world.... A calling is about the use one makes of a career." David Orr, Earth in Mind)
4. What is your dream job?
5. What is something special about you?

The key to that will be something called an "indeterminate form", and limits. We'll get a look at that in the activity we do next, but it's hinted at by thinking about average velocity: as we noted last time, it's a change in $y$ over a change in $x$:

\[ AV = \frac{\textrm{change in y}}{\textrm{change in x}} \]

Now what happens as that "change in $x$" approaches 0? (that's the "limit" part!)

If all is well in the world, then the ratio becomes indeterminate because the "change in $y$" also approaches 0! And everyone knows what $\frac{0}{0}$ is, right? (that's the "indeterminate" part!)