Jonathan Rogness
Sample Lab Report 1B
Math 2374 Section 20
1/29/02

[If you wish, you can include some sort of introduction like the following:]

Mathematica has powerful tools for graphing functions, and the purpose of this lab is to become accustomed to the various commands at our disposal.

Exercise 1

In problem 13 on page 16, I matched the following equations and graphs:

(a) with (1)
(b) with (3)
(c) with (2)
(d) with (4)
(e) with (5)
(f) with (6)

was particularly easy to match to its graph, which is shown here.

First, notice that B(x,y) is not continuous at the origin, which explains the strange looking part of the graph in the center.  The reason B(x,y) is not continuous there is that B(0,0) is not defined; the denominator is zero if x and y are both 0.

Another obvious feature of the graph is the "straight line" on top.  Whenever y=0, 1, assuming x is not equal to zero as well.  So above the line y=0 -- i.e. on the x-axis -- the surface always has a height of one.  Although it's not as obvious, there's also a straight line at the bottom of this graph.  Along the y-axis, where x=0, we have B(0,y)=-1 for all values of y.  This line on the bottom is a bit more visible in the following picture:

So the graph of B has two straight lines, one at height one above the x-axis, and one at height -1 below the y-axis, and the rest of the surface is like a piece of rubber stretching between the two lines.  This stretching can't be done at the origin, so we have a discontinuity at (0,0).

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