Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the integral.
1)
(3x8– 7x3+ 7) dx
A)
9x9–7
4x4+ 7x + C
B)
9x9–7
3x4+ 7x + C
C)
1
3x9–7
3x4+ 7x + C
D)
1
3x9–7
4x4+ 7x + C
Answer:
D
2)
11x–6 dx
A)
B)
C)
11
5x
7
+ C
D)
Answer:
A
3)
12x3x dx
A)
B)
C)
11
5x9/2 + C
D)
Answer:
A
4)
3 dx
A)
B)
C)
3 + C
D)
Answer:
A
5)
5(t2– 5t – 2) dt
A)
B)
C)
5t3– 5t2– 2t + C
D)
Answer:
A
6)
(3x5–8x3+ 2) dx
A)
1
2x6– 2x4+ 2x + C
B)
1
6x6–1
4x4+ 2x + C
C)
3
4x4– 4x2+ C
D)
3
5x5–8
3x3+ 2x + C
Answer:
A
1
7)
6 +x2
xdx
A)
B)
C)
3
x2+x2+ C
D)
Answer:
B
8)
x3– 7
xdx
A)
B)
C)
1
4x4– 7x2+ C
D)
Answer:
D
9)
–3
3x
– 4 x dx
A)
–9
2x2/3 –8
3x3/2 + C
B)
x2/3 – 2x3/2 + C
C)
–2x2/3 – 6x3/2 + C
D)
–3 ln x1/3 – 2x3/2 + C
Answer:
A
10)
9x– 5 dx .
A)
B)
C)
9
4x6+ C
D)
Answer:
A
11)
9e 0.2x dx.
A)
B)
C)
45e0.2x + C
D)
Answer:
C
12)
2
t–7et dt
A)
B)
C)
2 ln t–7et+ C
D)
Answer:
C
13)
5ex–1
x dx
A)
B)
C)
5ex–2
x2+ C
D)
Answer:
D
2
14)
23x4–x–3 dx
A)
B)
C)
6
7x6/7 +1
2x2+ C
D)
Answer:
D
15)
(5 +x3)(4 –x2) dx
A)
20 –5
3x3+x4–1
6x6+ C
B)
20x –5
3x3+5
3x4–1
6x6+ C
C)
20x –5
3x3+x4–1
6x6+ C
D)
20x –5
3x3+x4–1
6+ C
Answer:
C
Provide an appropriate response.
16)
Find f(x) if f'(x) =7
x4 and f(1) = 4.
A)
B)
C)
–7
3x–3– 3
D)
Answer:
A
17)
Find f(x) if f'(x) =3
x5 and f 1
2= 1.
A)
B)
C)
–4
5x–4+ 13
D)
Answer:
A
Solve the problem.
18)
The rate of change in a person‘s body temperature, with respect to the dosage of x milligrams of a drug, is given
by D'(x) =3
x + 6 . One milligram raises the temperature 2.5°C. Find the function giving the total change.
A)
D(x) =3 ln x + 6 + 2.5
B)
D(x) = ln 3
x + 6 – 3.3
C)
D(x) =3 ln x + 6 – 3.3
D)
D(x) = ln 3
x + 6 – 2.5
Answer:
C
19)
Find the cost function if the marginal cost function is C'(x) =18x –11 and the fixed cost is $2.
A)
C(x) =9x2–11x +1
B)
C(x) =18x2–11x +2
C)
C(x) =18x2–11x +1
D)
C(x) =9x2–11x +2
Answer:
D
3
20)
A company finds that consumer demand quantity changes with respect to price at a rate given by
D'(p) = – 2500
p2. Find the demand function if the company knows that 827 units of the product are demanded
when the price is $5 per unit.
A)
B)
C)
D(p) =5000
p+827
D)
Answer:
A
21)
A newspaper is launching a new advertising campaign in order to increase the number of daily subscribers.
The newspaper currently (t = 0) has 26,000 daily subscribers and management expects that number, S(t), to
grow at the rate of S'(t) = 80t1/2 subscribers per day, where t is the number of days since the campaign began.
How long (to the nearest day) should the campaign last if the newspaper wants the number of daily subscribers
to grow to 49,000?
A)
B)
C)
57 days
D)
Answer:
C
22)
The marginal revenue from the sale of compact discs is given by R'(x) = 190 – 8x and R(0) = 0, where R(x) is the
revenue in dollars. Find the price–demand equation.
A)
B)
C)
p = 190 – 4x
D)
Answer:
C
23)
A computer manufacturer has found that its expenditure rate per day (in hundreds of dollars) on a certain type
of job is given by C‘(x) = 10x + 6, where x is the number of days since the start of the job. Find the expenditure if
the job takes 8 days.
A)
B)
C)
$36,800
D)
Answer:
C
24)
An rock’s acceleration at time t is given by a(t) = 16t, and its initial velocity is 35. Find the velocity function v(t).
A)
B)
C)
v(t) = 16t2+ 35
D)
Answer:
B
Find the integral.
25)
(–x8+4)6x7 dx
A)
–8
7(–x8+ 4)7+ C
B)
–1
7(–x8+ 4)7+1
8x8+ C
C)
–1
56 (–x8+4)7+ C
D)
–56(–x8+ 4)7+ C
Answer:
C
26)
e7x +4 dx
A)
B)
C)
(7x + 4) e7x + 4 + C
D)
Answer:
D
4
27)
1
3 – 2x dx
A)
B)
C)
– 2 ln 3 – 2x + C
D)
Answer:
D
28)
ln 8x
x dx
A)
B)
C)
(ln 8x)2
16 + C
D)
Answer:
D
29)
t e– 7t2 dt
A)
B)
C)
1
7e– 7t2+ C
D)
Answer:
B
30)
7x6dx
(4 +x7)4
A)
B)
C)
–1
3(4 +x7)3+ C
D)
Answer:
C
31)
t2
37+t3
dt
A)
B)
C)
1
2t3(7 +t3)2/3 + C
D)
Answer:
A
32)
x3x4+3dx
A)
B)
C)
2
3(x4+3)3/2 + C
D)
Answer:
D
33)
4x + 1
4x2+ 2x + 3 dx
A)
1
2(4x2+ 2x + 3)2+ C
B)
2
(4x2+ 2x + 3)2+ C
C)
2 ln 4x2+ 2x + 3 + C
D)
1
2 ln 4x2+ 2x + 3 + C
Answer:
D
5
34)
(2 + 2x)e(4x + 2x2) dx
A)
1
2e(4x + 2x2)+ C
B)
e[(1/2)(4x + 2x2)] + C
C)
e[2(4x + 2x2)] + C
D)
2e(4x + 2x2)+ C
Answer:
A
35)
x2
5x3+ 8 dx
A)
B)
C)
15 ln (5x3– 8) + C
D)
Answer:
D
Solve the problem.
36)
The rate of expenditure for maintenance of a particular machine is given by M'(x) = 12x x2+ 5, where x is time
measured in years. Total maintenance costs through the second year are $105. Find the total maintenance
function.
A)
M(x) = 12(x2+ 5)3/2 – 3
B)
M(x) = 4(x2+ 5)3/2 – 3
C)
M(x) = 4(x2+ 5)3/2 – 93
D)
M(x) = 12(x2+ 5)3/2 – 93
Answer:
B
37)
The management of an oil company estimates that oil will be pumped from a producing field at a rate given by
R(t) =56
t + 7 for 0 t 20, where R(t) is the rate of production in thousands of barrels per year, t years after
pumping begins. How many barrels of oil, Q(t), will be produced the first five years? (Round answer to the
nearest thousand barrels.)
A)
296 thousand barrels
B)
46 thousand barrels
C)
148 thousand barrels
D)
92 thousand barrels
Answer:
D
38)
The marginal price for a weekly demand of x bottles of cough medicine in a drug store is given by
p'(x) =
–13,300
(5x +40)2. Find the price–demand equation if the weekly demand is 125 when the price of a bottle of
cough medicine is $4. What is the weekly demand (to the nearest bottle) when the price is $3?
A)
p(x) =5,320
5x + 40 ; 347 bottles
B)
p(x) =2,660
5x + 40 ; 169 bottles
C)
p(x) =5,320
5x + 40 – 4; 144 bottles
D)
p(x) = – 2,660
5x + 40 + 8; 98 bottles
Answer:
B
6
39)
A manufacturing company is ready to introduce a new product with a national sales campaign. After extensive
test marketing, the market research department estimates that sales (in millions of dollars) will increase at the
monthly rate of S'(t) = 10 – 10e–0.2t for 0 t 24, t months after the national campaign has started. What will the
total sales be five months after the beginning of the campaign if we assume zero sales at the beginning of the
campaign? (Round the answer to the nearest million.)
A)
B)
C)
$18 million
D)
Answer:
C
40)
A company has found that the marginal cost of a new production line (in thousands) is C'(x) =9
x + e , where x is
the number of years the line is in use. Find the total cost function for the production line (in thousands). The
fixed cost is $20,000.
A)
C(x) =ln (x + e)
9+ 11
B)
C(x) =ln (x + e)
9+ 20
C)
C(x) = 9 ln (x + e) + 11
D)
C(x) = 9 ln (x + e) + 20
Answer:
C
Provide an appropriate response.
41)
Find the general solution for the differential equation y’=30x2
A)
B)
C)
x3+ C
D)
Answer:
A
42)
Find the general solution for the differential equation y‘ =8e3x
A)
B)
C)
8
3 e3x + C
D)
Answer:
C
43)
Find the general solution for the differential equation dx
dt = – 3x
A)
B)
C)
x =e–3t + C
D)
Answer:
A
44)
Find the particular solution for the differential equation y’ = 4x + 7; y(0) = – 12.
A)
B)
C)
y = 2x2+ 7x – 6
D)
Answer:
D
45)
Find the particular solution for the differential equation dy
dx =1
2 + x ; y(0) = 3
A)
y = ln 2 + x +ln 2
3
B)
y = ln 2 + x + ln 2 + 3
C)
y = ln 2 + x
D)
y = ln 2 + x – ln 2 + 3
Answer:
D
7
46)
Find the particular solution for the differential equation y’ = 4xe2x ; y(0) = 20.
A)
y = 4xe2x –e2x + 21
B)
y = 4xe2x –e2x + 22
C)
y = 2xe2x + 20
D)
y = 2xe2x –e2x + 21
Answer:
D
Match the differential equation with the appropriate slope field.
47)
dy
dx = x – y
A)
B)
C)
D)
Answer:
C
8
48)
dy
dx = y + 2
A)
B)
C)
D)
Answer:
A
9
49)
dy
dx =x
y
A)
B)
C)
D)
Answer:
B
10
50)
dy
dx =x2–y2
A)
B)
C)
D)
Answer:
D
Provide an appropriate response.
51)
Graph the following example of unlimited growth: y =550e0.17t, 0 t 12, 0 y 4500.
11