The Rule of Three and other oddities

WARNING:  THIS LAB IS SERIOUSLY INCOMPLETE AT THE MOMENT.  I GOT SIDETRACKED INTO WORKING ON SOME OTHER COOL LABS WHEN I REALLY SHOULD HAVE BEEN WORKING ON THIS.  I WILL, HOWEVER, ADD TO THIS OVER TIME...

Finding where two functions intersect

We want to find out where two functions intersect:

Let's start with the graph this time:

Taking a limit

We want to take the following limit:  

Using the "Rule of three", we want to investigate this numerically, graphically, and symbolically.  Let's start with the numbers: