Chapter 3: Functions of Several Variables
Section 3.1: Functions and Their Graphs
Example 3.1.4
Graph the surface zx,y defined implicitly by the equation xy+zcoshz−1=1.
Solution
Maple Solution - Interactive
The "Plots" option in the Context Panel branches to two choices: 3-D Implicit Plot, and Plot Builder. Figure 3.1.4(a) is the result of selecting 3-D Implicit Plot, along with the axis-order x,y,z. Notice that the grid density is modest, namely, ten points in each direction, and that −5≤x,y,z≤5. Any modification to this graph would have to be done interactively, with the Context Panel for the graph, and with the Plot toolbar.
Figure 3.1.4(a) Via Plots≻3-D Implicit Plot
Figure 3.1.4(b) Via Plot Builder with Options
Figure 3.1.4(b) is generated with the Plot Builder where options can be applied before the graph is finalized. The default window −10≤x,y,z≤10 in the Plot Builder (Basic Options) has been changed to −3≤x,y,z≤3, and the Style changed to surfacecontour, Axes Style to frame, and (3-D Options) Lighting Model to none. The Grid Size (3-D Options) has been changed to 20,20,20 from the default 10,10,10, a change that means 8,000 sample points are used instead of the default 1,000.
Maple Solution - Coded
Figure 3.1.4(b) can be obtained via the implicitplot3d command, implemented as shown below. (Select Evaluate from the Contour Panel.)
plots:-implicitplot3dxy+zcoshz−1=1,x=−3..3,y=−3..3,z=−3..3,style=surfacecontour,lightmodel=none,axes=frame,grid=20,20,20
<< Previous Example Section 3.1 Next Example >>
© Maplesoft, a division of Waterloo Maple Inc., 2024. All rights reserved. This product is protected by copyright and distributed under licenses restricting its use, copying, distribution, and decompilation.
For more information on Maplesoft products and services, visit www.maplesoft.com
Download Help Document
