You must complete the project in a group of two students. Normally, all members of the group will receive the same grade; however, the instructor reserves the right to conduct individual interviews over the content of the project and to assign different grades to different members of the group.
In this project, you will use explore how the graph of rational function, f(x)/g(x), compares with the graph of the f ′(x)/g ′(x) and f ′′(x)/g ′′(x), etc. You will need to describe the relationship of the graphs. You will be graded on the quality and clarity of your written presentation as well as the mathematical accuracy of your paper.
To label your work, use comments. For example, use the following to start your project (after every line, use SHIFT-ENTER to execute):
(* Your Name *)
(* Partner's Name *)
(* Math2431-100 *)
(* Summer 2012 *)
(* Project 3 *)
Consider the rational function f(x) = (2x3 + 5x2)/(xsin(x)).
Define the function as follows:
h[x_]:=2x^3 + 5x^2
f[x]near x = 0. What do you notice (i.e., what is the limit of f(x) as x approaches 0)?
j[x]:=h'[x]/g'[x]near x = 0. What do you notice?
k[x]:=h''[x]/g''[x]near x = 0. What do you notice?
l[x]:=h'''[x]/g'''[x]near x = 0. What do you notice? Why is this different from the above answers?
Please follow these guidelines when preparing your report: