EMAT 3500Assignment #8
The Spreadsheet in Mathematics Explorations
Model and explore the following problems using a spreadsheet &
write-up the results, observations, etc. of ANY TWO of your investigations.
1. Construct a graph of any rational function h(x) = f(x)/g(x) where f(x) and g(x) are polynomials by generating a table of values with the x values in one column and the y values in another. Then using this table of values, calculate the limit of h(x) as x approaches:
2. Generate a Fibonnaci sequence in the first column using f(0) = 1, f(1) = 1,
f(n) = f(n-1) + f(n-2)
a. Construct the ratio of each pair of adjacent terms in the Fibonnaci sequence. What happens as n increases? What about the ratio of every second term? etc.
b. Explore sequences where f(0) and f(1) are some arbitrary integers other than 1. If f(0)=1 and f(1) = 3, then your sequence is a Lucas Sequence. All such sequences, however, have the same limit of the ratio of successive terms.
3. Problem: Place four numbers in the first row as follows
A B C D
For each successive row replace the entries by the absolute value of the difference of the entry just above and the entry just to the right in the previous row. In the fourth position use the absolute value of the difference of the fourth and the first (i.e. cycle)... spreadsheet code = abs(A1-B1)
|A-B| |B-C| |C-D| |D-A|
Will the process lead to a 0 in all 4 entries for some row?
What is the largest number of rows before a zero row is generated?
(If your answer is less than 10, you should try again)