MATH 261, Spring 2001 Due Date: Name(s):
Extra Project 15.2b: A Strange Function
Objective
If you have not already done so, read Section 15.2 of the text. In this project we investigate a function
that exhibits some very strange behavior.
Narrative
While Maple can help understand what the graph of a function f(x, y) looks like, it is not without flaw.
There are some functions which it will inevitably have difficulty graphing. In this project we consider one
such function.
Task
1. Explain why Maple might have difficulty correctly drawing the graph of f(x, y) = (x2
- y2
)/(x2
+ y2
)
over a square such as [-1, 1]×[-1, 1]. (Hint: Consider what would happen if Maple were to try to draw
the graph by plotting just points. What would happen if y was fixed at 0, and you approached the
origin along the x-axis? What would happen if x was fixed at 0, and you approached the origin along
the y-axis?)
2. Describe what the graph of f(x, y) = (x2
- y2
)/(x2
+ y2
) looks like near the origin.