Find the producer surplus for the supply curve at the given sales level, x.
125)
p =x2; x =4
125)
A)
$2.67
B)
$64
C)
$12
D)
$42.67
126)
p =2– x; x = 0
126)
A)
$1.75
B)
$1
C)
$0
D)
$2.30
Solve the problem.
127)
An object moves in such a way that its velocity (in meters per second) after time t (in seconds) is
given by
v = t2+ 3t + 10.
Find the distance traveled by the object during the first four seconds.
127)
A)
38.0 m
B)
64.0 m
C)
45.3 m
D)
85.3 m
Let f(x) be the function pictured in the graph. Determine whether the given integral is positive, negative, or zero.
128)
4
0
f(x)dx
128)
A)
Cannot be determined
B)
Zero
C)
Negative
D)
Positive
Solve the problem.
129)
Calculate the present value of a continuous income stream of $500 per year for 10 years at an
interest rate of 3% compounded continuously.
129)
A)
$12,346.97
B)
$5830.98
C)
$4319.70
D)
$29,013.64
130)
Find a function f(x) with the following property: f'(x) = – 1
4 – x , f(2) = 0.
130)
A)
f(x) = ln 1
4 – x +1
2
B)
f(x) = – ln 4 – x + 2
C)
f(x) = ln 4 – x – 2
D)
f(x) = – (4 – x)–2+1
2
E)
none of these
Find the volume generated by revolving about the x–axis the region bounded by the following graph.
131)
y =49 –x2, x = 0, x =7
131)
A)
686
3
B)
14
C)
1372
3
D)
196
132)
Use a Riemann sum to approximate the area under the graph of f(x) on the given interval. Use the
right endpoints.
f(x) =4x3; 0 x 3, n = 6
132)
A)
441
4=110.25
B)
225
16 =14.06
C)
441
16 =27.56
D)
225
4=56.25
Find the producer surplus for the supply curve at the given sales level, x.
133)
p = – 2x2; x = 1
133)
A)
–$1.33
B)
–$0.67
C)
$5
D)
–$4
134)
Suppose that a colony of fruit flies is growing exponentially with growth constant 0.04 . If there are
currently 30,000 flies present, what will be the average population over the next 6 months?
134)
A)
30,000(e0.02 – 1)
B)
75,000(e0.24 – 1)
C)
60,000(e0.24 – 1)
D)
1,500,000(e0.02 – 1)
E)
none of these
Find the value of k that makes the antidifferentiation formula true.
135)
(7 – x)–1 dx = k ln|7 – x| + C
135)
A)
1
B)
–1
C)
1
7
D)
–1
7
Determine the average value of f(x) over the interval from x = a to x = b.
136)
f(x) =4x +1; a =5, b =7
136)
A)
49
B)
25
C)
4
D)
50
137)
What is the area under the curve f(x) = 3x2+ 2x + 1 from x = – 3
2 to x = – 1
2?
137)
A)
9
4
B)
51
4
C)
15
4
D)
–15
4
E)
none of these
37
Refer to the figure to evaluate the definite integral.
138)
Evaluate
10
–5
f(x)dx
f(x)
5
–1
5x2+5
x –5
–5 5 10
138)
A)
475
6
B)
275
6
C)
275
3
D)
275
2
Find f such that the given conditions are satisfied.
139)
f'(x) = x –5, f(3) = – 4
139)
A)
f(x) =x2
2–5x +13
2
B)
f(x) =x2–5x
C)
f(x) =x2–5x +2
D)
f(x) =x2
2–5x +15
2
Compute the area of the shaded region.
140)
4
y = x +4y = – x +4
–4 4
140)
A)
32
B)
8
C)
16
D)
2
Solve the problem.
141)
Suppose that f and g are continuous and that
10
6
f(x) dx = – 3 and
10
6
g(x) dx =9.
Find
6
10
g(x) – f(x) dx .
141)
A)
–12
B)
6
C)
12
D)
–6
142)
Find the future value of an investment in which money is deposited steadily so that $200 per year is
being invested at 7.5%, compounded continuously for 30 years.
142)
A)
$27,967.30
B)
$22,633.96
C)
$25,300.63
D)
$169,754.72
For a particular commodity, the quantity produced and the unit price are given by the coordinates of the point where the
supply and demand curves intersect. Determine the point of intersection for the following supply and demand curves.
143)
Demand curve: p = – 2x +8, Supply curve: p =4x +3
143)
A)
–2, $12
B)
5
6, $6.33
C)
4, $0
D)
–3
2 , $2.04
144)
A company estimates that its marginal profit for producing a product is given by
MP(q) = 60 – 0.12q where MP(q) is in dollars per unit. Given that P = – 500 when q = 0, find the total
profit realized from selling 300 units of product.
144)
A)
$7700
B)
$12,100
C)
$6700
D)
$4100
Find the producer surplus for the supply curve at the given sales level, x.
145)
p =1–5x; x = 1
145)
A)
$0.20
B)
–$4
C)
$5
D)
–$2.50
Determine the average value of f(x) over the interval from x = a to x = b.
146)
f(x) =7–x2; a = – 2, b =4
146)
A)
–7
9
B)
35
9
C)
3
D)
–5
3
Calculate.
147)
1
0
e3x –1
(x + 1)2 dx
147)
A)
1
3e3+7
6
B)
1
3e3–5
6
C)
1
3e3– e –1
2
D)
1
3e +7
6
E)
none of these
Solve the problem.
148)
The rate at which an assembly line worker’s efficiency E (expressed as a percent) changes with
respect to time t is given by E'(t) =75 –6t, where t is the number of hours since the worker’s shift
began. Assuming that E(1) =92, find E(t).
148)
A)
E(t) =75t –3t2+164
B)
E(t) =75t –6t2+20
C)
E(t) =75t –3t2+92
D)
E(t) =75t –3t2+20
Answer Key
Testname: C6
41
Answer Key
Testname: C6
42
Answer Key
Testname: C6
Answer Key
Testname: C6
Answer Key
Testname: C6