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620
CHAPTER 15
DIFFERENTIATION IN SEVERAL VARIABLES
(ET CHAPTER 14)
i
B
D
E
C
P
A
ii
iii
400
450
0
1
2 km
Contour interval
=
10 meters
470
iv
44.
Match the contour maps (A) and (B) in Figure 23 with the two functions
f
(
x
,
y
)
=
x
−
2
y
and
g
(
x
,
y
)
=
2
x
−
y
.
c
=
−
2
y
xx
c
=
−
2
c
=
0
c
=
2
c
=
0
c
=
2
2
−
2
−
1
2
1
y
2
−
2
2
(A)
(B)
1
−
1
−
2
FIGURE 23
SOLUTION
The level curves of the function
f
(
x
,
y
)
=
x
−
2
y
are the lines
x
−
2
y
=
c
or
y
=
x
2
−
c
2
.Theleve
l
curves of
g
(
x
,
y
)
=
2
x
−
y
are the lines 2
x
−
y
=
c
or
y
=
2
x
−
c
. The slope of the lines in the contour map of
g
is
greater than the slope in the contour map of
f
. Therefore (A) is a contour map of
f
and (B) is a contour map of
g
.
45.
Which linear function has the contour map shown in Figure 24 (with level curve
c
=
0 as indicated),
assuming that the contour interval is
m
=
6? What if
m
=
3?
c
=
0
6
3
−
6
−
3
−
1
−
2
2
1
x
y
FIGURE 24
We denote the linear function by
f
(
x
,
y
)
=
α
x
+
β
y
+
γ
(1)
The level curves of
f
are
x
+
y
+
=
c
(2)
By the given information, the level curve for
c
=
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This note was uploaded on 02/13/2010 for the course MATH MATH 32A taught by Professor Park during the Fall '09 term at UCLA.
 Fall '09
 Park
 Multivariable Calculus

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