Math 3066 -- Assignment 19: Limits

Due: November 5th

The idea of a limit is one of the "big ideas" in higher level mathematics.  The concept of a limit is accessible to middle school children who have access to technology like a spreadsheet.  Using Excel, solve this problem:

Imagine a cube shaped box that measures 1 foot on each side.  Stacked on this box is a box with all the dimensions exactly half of the box below.  So the second box measures 1/2 foot on each side and the total stack height is 1.5 feet.  This process of stacking a box half as big on all dimensions as the top box continues.  The question is how many boxes will be required to make a stack 10 feet tall?  How about 5 feet tall? 

Extensions of this problem are to change the size of that initial box, change the proportions of the "new" box (i.e. what if the new box is 90% of the original), another pattern is 1/2, 1/3, 1/4, 1/5, ... and to look for patterns in the boxes.

In class we will look at three problems.  Your assignment is to print out a short paragraph explaining why the limit exists (when it exists).  Your print out should include the Excel tables showing the limits (or lack thereof).