Exam
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
1)
The given graph is that of the derivative of a function f. Using information obtained from
the graph of f’ and the fact that f(–1) = – 4
3 and f(–3) = 0, sketch the graph of f.
1)
1
2)
The given graph is that of the derivative of a function f. Using information obtained from
the graph of f’ and the fact that f(–1) = –2
3 and f(1) =2
3, sketch the graph of f.
2)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
3)
Find the exact value of 3/2
/2 5 cos x dx.
3)
A)
B)
C)
D)
4)
Convert to radian measure. Leave your answer in terms of .
440°
4)
A)
B)
C)
D)
Find the derivative.
5)
y = (sin x)7
5)
A)
y’ = 7(sin x)6
B)
y’ = 7(cos x)6 sin x
C)
y’ = 7(cos x)6
D)
y’ = 7(sin x)6 cos x
6)
Integrate: x2 sin(7x3– 6) dx
6)
A)
1
21 cos(7x3– 6) + C
B)
–1
21 cos(7x3– 6) + C
C)
21 cos(7x3– 6) + C
D)
–21 cos(7x3– 6) + C
7)
Find the indefinite integral cos 2t dt.
7)
A)
B)
C)
D)
8)
Evaluate cos 30°.
8)
A)
B)
C)
D)
9)
Find the exact value of 3/4
/4 2cos x dx.
9)
A)
B)
C)
D)
10)
Find the indefinite integral sin x cos6 x dx.
10)
A)
B)
C)
D)
11)
Use a calculator to find the value (to four decimal places) of sin 321.5°.
11)
A)
B)
C)
D)
Find the derivative.
12)
d
dx[cos (x3+ 8) + sin (9x5)]
12)
A)
–3x2 sin (x3+ 8) + 45x4 cos (9x5)
B)
3x cos (x2+ 8) + 45x sin (9x4)
C)
–sin (x3+ 8) + cos (9x5)
D)
–3x sin (x3+ 8) + 45x cos (9x5)
Solve the problem.
13)
A department store has revenue from the sale of electrical kitchen appliances that is given
approximately by R(t) = 2.2 + 2.2 cos t
23 for 0 t 52, where R(t) is revenue in hundreds of dollars
for a week of sales t weeks after January 1. What is the total revenue (to the nearest hundred
dollars) earned from t = 10 to t = 16?
13)
A)
B)
C)
D)
Provide an appropriate response.
14)
Use a calculator to find the value (to four decimal places) of cos 36.93°
14)
A)
B)
C)
D)
15)
Find the slope of the graph f(x) =23 sin x at x =
3.
15)
A)
B)
C)
D)
16)
Use a calculator to find the value (to four decimal places) of sin 261.5°.
16)
A)
B)
C)
D)
17)
Find the indefinite integral sin 2t dt.
17)
A)
B)
C)
D)
Find the derivative.
18)
y =8 cos 8x
18)
A)
B)
C)
D)
Provide an appropriate response.
19)
Find the area under the curve y = cos x from 0 to
2.
19)
A)
B)
C)
D)
Solve the problem.
20)
The number of Canadian geese (in thousands) counted at a certain checkpoint in their migration is
given by O(t) = 5 + 5 cos (t/6), where t is time in months and t = 0 is October. Find the number of
geese passing the checkpoint between October and November.
20)
A)
B)
C)
D)
Provide an appropriate response.
21)
Use a calculator to evaluate the definite integral 3.5
0sin x dx. (Express the answer as a decimal
rounded to four places.)
21)
A)
B)
C)
D)
22)
Find the exact value of cos + sin 0.
22)
A)
B)
C)
D)
6
Solve the problem.
23)
The intensity of light I at time t hours after sunrise and at a depth of x feet below the ocean surface
is given by I(x,t) =Ioe–kx sin3t
D , where D is the length of daylight in hours, Io is the intensity of
light on the surface of the water at midday, and k is a positive constant. Assume D = 14, Io= 50,
and k =0.006. In a study of the effect of light on ocean plants, a scientist needs to determine the
minimum depth x at which a plant would never at any time be exposed to an intensity of light
greater than 25. What is this minimum depth?
23)
A)
B)
C)
D)
Find the derivative.
24)
d
dx[sin(x2– 7)]4
24)
A)
– 8x cos(x2– 7)sin(x2– 7)]
B)
–4x[sin (x2– 7)]3cos(x2– 7)
C)
4x sin(x2– 7)
D)
8x cos(x2– 7)[sin (x2– 7)]3
D
Provide an appropriate response.
25)
Convert to radian measure. Leave your answer in terms of .
42°
25)
A)
B)
C)
D)
A
Find the derivative.
26)
y = sin 3 e-3x
26)
A)
-9 e-3x cos 3 e-3x
B)
e-3x cos 3 e-3x
C)
cos 3 e-3x
D)
9e-3x cos 3 e-3x
A
D
Provide an appropriate response.
27)
Find the exact value of sin
2+ sin 3
2.
27)
A)
B)
C)
D)
28)
Find the area under the curve y = sin x from
2 to .
28)
A)
B)
C)
D)
29)
Integrate: (cos x)8 sin x dx
29)
A)
B)
C)
D)
Solve the problem.
30)
The revenue from the sale of electric blankets is seasonal, with maximum revenue in the winter. Let
the revenue received from the sale of heaters be approximated by R(x) = 18 cos 2x + 600, where x
is time in years, measured from January 1. Find R'(x) for August 1st.
30)
A)
B)
C)
D)
Find the derivative.
31)
y =4tan5x
31)
A)
B)
C)
D)
Provide an appropriate response.
32)
Graph the function y = sin x.
32)
A)
B)
C)
D)
33)
Graph the function y = –cos x.
33)
A)
B)
C)
D)
34)
Graph the function y = x cos x.
34)
A)
B)
C)
D)
35)
Find the indefinite integral – 6x3 sin x4 dx.
35)
A)
B)
C)
D)
Use a graphing calculator to graph the function using the given viewing window parameters.
36)
y = cos x –
2
36)
A)
B)
C)
D)
Provide an appropriate response.
37)
Find the exact value of cos
2+ sin 3
2 .
37)
A)
B)
C)
D)
38)
Find the slope of the graph f(x) =21 cos x at x =
4.
38)
A)
B)
C)
D)
39)
Find the indefinite integral 4 sin (6x) dx.
39)
A)
–2
3 cos (6x) + C
B)
4 cos (6x) + C
C)
– 24 cos (6x) + C
D)
2
3 cos (6x) + C
40)
Find the exact value of /2
02 sin x dx.
40)
A)
B)
C)
D)
Find the derivative.
41)
y =x3 cos (8x2)
41)
A)
y’ = – 16x4 sin (8x2)
B)
y’ = 16x4 sin (8x2) + 3x2 cos (8x2)
C)
y’ = – 16x4 sin (8x2) + 3x2 cos (8x2)
D)
y’ = sin (8x2) + 3x2 cos (8x2)
Provide an appropriate response.
42)
Evaluate cos 5
6 .
42)
A)
B)
C)
D)
43)
Integrate: 12 sin x cos xdx
43)
A)
–18(cos x)3/2 + C
B)
18(cos x)3/2 + C
C)
8(cos x)3/2 + C
D)
–8(cos x)3/2 + C
Find the derivative.
44)
y = cos x4
44)
A)
B)
C)
D)
Provide an appropriate response.
45)
Evaluate sin 30°.
45)
A)
B)
C)
D)
46)
Use a calculator to find the value (to four decimal places) of sin 54.25°.
46)
A)
B)
C)
D)
Find the derivative.
47)
d
dx cos(x2– 1)
47)
A)
x sin(x2–1)[cos (x2– 1)]1/2
B)
– x sin(x2–1)[cos (x2– 1)]–1/2
C)
x sin(x2–1)[cos (x2– 1)]–1/2
D)
– 2 x [cos (x2– 1)]–1/2
Provide an appropriate response.
48)
Evaluate sin 45°.
48)
A)
B)
C)
D)
Solve the problem.
49)
The profit for the sale of tennis rackets in a sporting goods store is given approximately by
P(t) = 9 – 9 cos t
15 for 0 t 52, where P(t) is profit in thousands of dollars for a week of sales t
weeks after January 1. What is the rate of change of profit six weeks after the first of the year?
(Express the answer to the nearest dollar.)
49)
A)
B)
C)
D)
50)
The temperature in Fairbanks (in °F) is approximated by T(x) = 37 sin 2
365(x – 101) + 25, where
T(x) is the temperature on day x, with x = 1 corresponding to Jan 1 and x = 365 corresponding to
Dec 31. Estimate the temperature, to the nearest degree, on day 309.
50)
A)
B)
C)
D)
Provide an appropriate response.
51)
Use a calculator to find the function value to four decimal places.
csc 81° 44′ 59″
51)
A)
B)
C)
D)
Find the derivative.
52)
y = (cos x)5
52)
A)
y’ = 5(cos x)4
B)
y’ = –5 (sin x)4
C)
y’ = –5x4 sin x5
D)
y’ = –5 sin x(cos x)4
Solve the problem.
53)
In a large city, the amount of sulfur dioxide pollutant released into the atmosphere due to the
burning of coal and oil for heating purposes is given approximately by
P(n) = 3 + cos n
26 for 0 n 104, where P(n) is the amount of sulfur dioxide in tons released during
the nth week after January 1. How many tons (to the nearest ton) of pollutants were emitted into
the atmosphere from n = 0 to n = 65?
53)
A)
B)
C)
D)
54)
Sales of snow shovels are seasonal. Suppose the sale of snow shovels (in dollars) in Maine is
approximated by s(t) = 10,000 + 10,000 cos
6 t, where t is time in months and t = 0 is October. What
are the sales in December?
54)
A)
B)
C)
D)
Find the derivative.
55)
y = 8 sin x3
55)
A)
B)
C)
D)
Provide an appropriate response.
56)
Use a graphing calculator to estimate f'(a) for the given value of a.
f(x) =x2 sin x; a = – 2
56)
A)
B)
C)
D)
57)
Find the indefinite integral (– 2 sin t + cos (5t)) dt.
57)
A)
2 cos t –1
5 sin (5t) + C
B)
2 cos t +1
5 sin (5t) + C
C)
2 cos t + 5 sin (5t) + C
D)
– 2 cos t – 5 sin (5t) + C
58)
Use a calculator to find the function value to four decimal places.
cot 62.3°
58)
A)
B)
C)
D)
Find the derivative.
59)
y =16x sin 18x
59)
A)
288x cos 16x + 16 sin 18x
B)
288x cos 18x + 16 sin 18x
C)
–288x cos 18x + 16 sin 18x
D)
288x cos 18x + sin 18x
Provide an appropriate response.
60)
Find the exact value of /2
0cos2x sin x dx.
60)
A)
B)
C)
D)
Find the derivative.
61)
y = 5 sin (4x – 8)
61)
A)
y’ = 5 cos (4x – 8)
B)
y’ = 20 cos (4x – 8)
C)
y’ = 4 sin (4x – 8)
D)
y’ = – 4 cos (4x – 8)
Use a graphing calculator to graph the function using the given viewing window parameters.
62)
y = sin x –
4
62)
18
A)
B)
C)
D)
Provide an appropriate response.
63)
Convert to radian measure. Leave your answer in terms of .
327°
63)
A)
B)
C)
D)
Answer Key
Testname: C8
Answer Key
Testname: C8