Excel Projects in Calculus part 2

This is the second of my posts on Excel projects in Calculus.  I had two main goals with this project.  First, I wanted to explore some limits and see some limitations of technology.  Then I wanted to help explore a type of word problem and drive home the idea of always checking the end points of the interval.  If you need background, see my first post:

First Excel in Calculus post.
** If you want the Word and Excel copies, @me (@robebymathdude) on Twitter **

For question 2, I had the students explore the two limits definitions of e (going to 0 and going to infinity)  You will notice I asked them to look at the formula and then match that formula to the correct limit. 

Then in parts b, d, and d I had them explore the other thing: in Excel there is an overflow error sometimes.  (This is inspired by a twitter conversation Chris Robbins @Grallator  and I had)  There was a good bit of confusion with the students over this, and I had to walk most of them through this to finally get the idea I was aiming at.  Which is fine, but a heads up if you do this in your classes.

The other part of this project was the standard something is out in the water, and we have to decide how far down the shore to run before swimming type of problem.  I used a lifeguard in this case.

I wanted the students to have to wrestle with the boundaries, so I did four different variations on the basic problem.  I first varied the running speed, then the swimming speed, then the total distance along the shore, then the total distance out.  I also arranged the step size for increasing the speeds to make sure we got to the boundary case in most instances.  I then programmed the Excel squares with conditional formatting to highlight red when that happened.  You can see some of that on my example sheet.

This proved interesting, as there were a couple of students who had no red cells.  (It was my fault, they happened to have zeros in just the right places!)  So they asked me, and I started by asking them to compare mine and theirs, and why might I use the color red.  It was generally a good discussion. 

The case where we changed the distance was more trouble for the students, as you ended up with almost a calculus of variations type of problem.  But given they are Calculus I students, most of them gave reasonable answers about what seemed to be happening.