Evaluate the integral.
147)
1
0
y y2+ 7x dx
147)
A)
1
3(7x + 1)3/2 –1
3(7x)3/2
B)
2
15 y(y2+ 7)3/2 –2
15 (y2+ 1)3/2
C)
1
6(7x + 1)3/2 –1
6(7x + 7)3/2
D)
2
21 y(y2+ 7)3/2 –2
21 y4
Evaluate the double integral.
148)
8
1
ln x
0
ey dy dx
148)
A)
49
2
B)
81
2
C)
81
4
D)
49
4
Solve the problem.
149)
Determine which coordinate plane (i.e. xy–plane, yz–plane, or xz–plane) the graph of the equation
z= – 4 is parallel to.
149)
A)
yz–plane
B)
xz–plane
C)
xy–plane
150)
The base radius and the height of a cylindrical can tank were measured at 40 cm and 45 cm.The
percentage errors in these measurements do not exceed 0.2 for the base radius and 0.5 for the
height. Approximate the worst possible percentage error in the volume of the can. Assume that the
sides and ends of the can are of negligible thickness.
150)
A)
0.7%
B)
1.4%
C)
1%
D)
0.9%
Find fx(x, y).
151)
f(x, y) = y ln 1
x
151)
A)
fx(x, y) =y
x2
B)
fx(x, y) = – 1
x
C)
fx(x, y) = – y
x
D)
fx(x, y) = – y
x2
Solve the problem.
152)
Let f(x, y) =10x –8y2–2
Find lim
h
0
f(x, y + h) – f(x, y)
h
152)
A)
–16y
B)
–16y –2
C)
10 –16y2
D)
10x –16y2
153)
Determine if the graph of the equation y= 0 is a plane identical to, parallel to (but not identical to),
or perpendicular to the xz–plane.
153)
A)
Parallel
B)
Perpendicular
C)
Identical
D)
None of these
Evaluate the function.
154)
Find f(7, –8) when f(x, y) =9x + 2y – 6.
154)
A)
32
B)
39
C)
47
D)
41
54
Find the partial derivative.
155)
f(x, y) =x3– 7x2y – 4xy3. Find fy(x, y).
155)
A)
x3– 14xy – 12xy2
B)
–7x2– 4xy2
C)
–7x2y – 12y2
D)
–7x2– 12xy2
Solve the problem.
156)
Find three positive numbers whose sum is 84 and whose product is a maximum.
156)
A)
42, 21, and 21
B)
42, 42, and 42
C)
28, 21, and 21
D)
28, 28, and 28
157)
Production of television sets is given by P(x,y) = 100 2
3 x–2/3 +2
5 y–1/3 –4, where x is work hours
and y is the amount of capital. If 27 work hours and 64 units of capital are used, what is the
production output?
157)
A)
108,909
B)
2,213,415
C)
22,134
D)
1089
Find the indicated relative minimum or maximum.
158)
Minimum of f(x, y) =x2+y2,
subject to x – 3y = 6
158)
A)
f9
5, –7
5=26
5
B)
f–3
5, –11
5=26
5
C)
f–9
5, –13
5= 10
D)
f3
5, –9
5=18
5
55
Use the region R to evaluate the double integral.
159)
(x + y) dx dy
R
R bounded by xy = 4, x + y = 5
159)
A)
12
B)
8
C)
9
D)
6
Find the second–order partial derivative.
160)
Find fxx when f(x, y) = ln 2x + 9y .
160)
A)
–4
2x + 9y 2
B)
18
2x + 9y
C)
–18
2x + 9y 2
D)
–81
2x + 9y 2
Solve the problem.
161)
A farmer has 200 m of fencing. Find the dimensions of the rectangular field of maximum area that
can be enclosed by this amount of fencing.
161)
A)
40 m by 60 m
B)
50 m by 50 m
C)
20 m by 80 m
D)
50 m by 150 m
Find the second–order partial derivative.
162)
Find fxy when f(x, y) =x
x + y .
162)
A)
x – y
(x + y)3
B)
x
(x + y)3
C)
y – x
(x + y)3
D)
2y
(x + y)3(x + y)3
Evaluate the function.
163)
Find f(0, 1, –1) when f(x, y, z) =8x–3yz +2x.
163)
A)
–2
B)
3
C)
4
D)
–3
Find the partial derivative.
164)
Find fx(2, 4) when f(x, y) = ln xy + x + y + 1 .
164)
A)
1
3
B)
ln 15
C)
1
15
D)
3
ln 15
Evaluate dw.
165)
w =8x53y ln (4z);
x =6, y =9, z =8,
dx = – 0.02, dy =0.03, dz =0.03
165)
A)
–16,804.08
B)
–17,459.05
C)
–15,591.92
D)
3079.28
Find the average value of the function f over the region R.
166)
f(x, y) =1
xy ; 1 x 7, 1 y 7
166)
A)
ln 7
6
2
B)
ln 7
36
C)
ln 7
49
D)
ln 7
7
2
Use the region R to evaluate the double integral.
167)
x2y2 dx dy
R
R bounded by 0 x y, 1 y 3
167)
A)
370
3
B)
364
9
C)
370
9
D)
364
3
Find fx(x, y).
168)
f(x, y) = x ln (2x +5y)
168)
A)
fx(x, y) =2x
2x +5y + ln (2x +5y)
B)
fx(x, y) =2x
2x +5y
C)
fx(x, y) = ln (2x +5y)
D)
fx(x, y) = ln (2x +5y) +2
2x +5y
58
Answer Key
Testname: C9
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Answer Key
Testname: C9
Answer Key
Testname: C9
Answer Key
Testname: C9
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Answer Key
Testname: C9