James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

892 Chapter 14 Partial Derivatives
and y.] The graph of h has the equation z − 4x 2 1 y 2 , which is the elliptic paraboloid
that we sketched in Example 12.6.4. Horizontal traces are ellipses and vertical traces
are parabolas (see Figure 9).
z
FIGURE 9
Graph of hsx, yd − 4x 2 1 y 2
x
y
■
z
Computer programs are readily FIGURE available 9 for graphing functions of two variables.
In most such programs, traces Graph in the of vertical h(x, y)=4≈+¥ planes x − k and y − k are drawn for
equally spaced values of k and parts of the graph are eliminated using hidden line
removal.
Fig ure 10 shows computer-generated graphs of several functions. Notice that we get
7et140109
an especially good picture of a function when rotation is used to give views from dif-
04/26/10
MasterID: 01534
z
x
x
y
(a) f(x, y)=(≈+3¥)e _≈_¥
z
(b) f(x, y)=(≈+3¥)e _≈_¥
z
x
y
x
y
FIGURE 10
(c) f(x, y)=sin x+sin y
sin x sin y
(d) f(x, y)=
xy
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