Chapter 3: Functions of Several Variables
Section 3.1: Functions and Their Graphs
Graph the surface zx,y defined implicitly by the equation x⁢y+z⁢coshz−1=1.
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.)
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