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

902 chapter 14 Partial Derivatives
;
56. If Vsx, yd is the electric potential at a point sx, yd in the
xy-plane, then the level curves of V are called equipotential
curves because at all points on such a curve the electric
potential is the same. Sketch some equipotential curves if
Vsx, yd − cysr 2 2 x 2 2 y 2 , where c is a positive constant.
59. f sx, yd − e 2sx 2 1y 2 dy3
ssinsx 2 d 1 cossy 2 dd
60. f sx, yd − cos x cos y
61–66 Match the function (a) with its graph (labeled A–F below)
and (b) with its contour map (labeled I–VI). Give reasons for your
choices.
57–60 Use a computer to graph the function using various
domains and viewpoints. Get a printout of one that, in your
opinion, gives a good view. If your software also produces level
curves, then plot some contour lines of the same function and
61. z − sinsxyd 62. z − e x cos y
compare with the graph.
63. z − sinsx 2 yd 64. z − sin x 2 sin y
57. f sx, yd − xy 2 2 x 3 (monkey saddle) Graphs and Contour Maps for Exercises 35–40
x 2 y
65. z − s1 2 x 2 ds1 2 y 2 d
66. z −
58. f sx, yd − xy 3 2 yx 3 (dog saddle)
1 1 x 2 1 y 2
A z
B z
C z
x
y
x
y
x
y
D z
E z
F
7et1401x59-3
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MasterID: 01555
x
z
y
x
y
x
y
I
y
7et1401x59-2
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MasterID: 01555
II
y
III
y
x
x
x
IV V VI
y
y
y
x
x
x
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