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Stewart_Essential Calc_2e ch01sec01
MULTIPLE CHOICE
1. The graph of the function
is given. State the value of
.
a.
b.
c.
d.
e.
ANS: C
MSC: Bimodal
2. The graphs of
a. 4, 2
PTS: 1
NOT: Section 1.1
and
DIF:
Medium
are given. For what values of x is
REF: 1.1.3b
?
b. 0
c.
d. –4, 12
e.
ANS: D
MSC: Bimodal
PTS: 1
NOT: Section 1.1
DIF:
Medium
REF: 1.1.4b
3. The graph shown gives the weight of a certain person as a function of age. Find the age at
which the person started an exercise program.
a.
b.
c.
d.
e.
54
38
20
35
ANS: C
MSC: Bimodal
4. If
PTS: 1
NOT: Section 1.1
DIF:
, find and simplify
Medium
, where
REF: 1.1.9
.
a.
b.
c.
d.
ANS: C
MSC: Bimodal
5. If
PTS: 1
NOT: Section 1.1
DIF:
Easy
, evaluate the difference quotient
REF: 1.1.21
.
a.
b.
c.
d. h
e. none of these
ANS: E
MSC: Bimodal
PTS: 1
NOT: Section 1.1
DIF:
Medium
REF: 1.1.22
6. Find the domain of the function.
a. (–, 0)
b.
c.
d. (–, 0)  (0, )
ANS: D
MSC: Bimodal
PTS: 1
NOT: Section 1.1
DIF:
Easy
REF: 1.1.25
7. Find the domain and sketch the graph of the function. What is its range?
f (x) =
a. D: (– , ); R: [–1, )
c. D: (– , ); R: (– , 3]
y
–2
y
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
b. D: (– , ); R: (– , 0]
5
6
7
(3, )
8
x
–2
–1
–1
1
2
3
d. D: (– , ); R: [0, )
4
5
6
7
8
x
y
y
4
10
3
9
2
8
1
7
6
–1
–1
1
2
3
4
5
6
7
8
9
x
5
–2
4
–3
3
–4
2
–5
1
–6
1
ANS: C
MSC: Bimodal
PTS: 1
NOT: Section 1.1
8. Find an expression for the function
DIF:
2
3
Medium
4
5
6
7
8
9
10
x
REF: 1.1.39
whose graph is the bottom half of the parabola
.
a.
b.
c.
d.
e.
ANS: B
MSC: Bimodal
PTS: 1
NOT: Section 1.1
9. A rectangle has perimeter
length of one of its sides.
DIF:
Medium
REF: 1.1.45
m. Express the area of the rectangle as a function
of the
a.
b.
c.
d.
e.
ANS: B
MSC: Bimodal
PTS: 1
NOT: Section 1.1
10. An open rectangular box with volume
the box as a function
of the length
a.
DIF:
Medium
REF: 1.1.47
has a square base. Express the surface area of
of a side of the base.
b.
c.
d.
e.
ANS: B
MSC: Bimodal
PTS: 1
NOT: Section 1.1
DIF:
Medium
REF: 1.1.51
11. Determine whether the function whose graph is given is even, odd, or neither.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
a. Even
b. Neither
c. Odd
ANS: A
MSC: Bimodal
12. If the point
graph?
PTS: 1
NOT: Section 1.1
DIF:
Medium
REF: 1.1.55
is on the graph of an even function, what other point must also be on the
a.
b.
c.
d.
e. None of these
ANS: D
MSC: Bimodal
PTS: 1
NOT: Section 1.1
DIF:
Medium
REF: 1.1.57a
13. Which of the following graphs is neither even nor odd?
a.
b.
c.
ANS: C
MSC: Bimodal
PTS: 1
NOT: Section 1.1
DIF:
Medium
NUMERIC RESPONSE
1. The graphs of
and
are given.
Find the values of
and
.
ANS:
,
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 1.1.4a
NOT: Section 1.1
2. Find the domain of the function.
ANS:
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 1.1.26
NOT: Section 1.1
REF: 1.1.60
3. Find the domain of the function.
ANS:
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 1.1.27
NOT: Section 1.1
4. Determine whether f is even, odd, or neither.
ANS: even
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 1.1.56
NOT: Section 1.1
SHORT ANSWER
1. Refer to the graph of the function f in the following figure.
y
5
4
3
f = ( x)
2
1
–4
–3
–2
–1
–1
1
2
3
4
5
6
7
8 x
–2
–3
–4
–5
a. Find f (1).
b. Find the value of x for which (i)
c. Find the domain and range of f.
and (ii)
.
ANS:
a. 0
b. (i) 2 (ii) 1, 3
c. D: [1, 4], R: [–3, 1]
PTS: 1
NOT: Section 1.1
DIF:
Easy
REF: 1.1.3a
MSC: Short Answer
2. If f (x) =
find f (–4), f (0), and f (1).
ANS:
f (–4) = 19, f (0) = 3, f (1) = 1.
PTS: 1
NOT: Section 1.1
DIF:
Easy
REF: 1.1.19
MSC: Short Answer
3. Determine whether the function is even, odd, or neither.
ANS:
Odd
PTS: 1
NOT: Section 1.1
DIF:
Medium
REF: 1.1.63
MSC: Short Answer
Stewart_Essential Calc_2e ch01sec02
MULTIPLE CHOICE
1. The relationship between the Fahrenheit and Celsius temperature scales is given by the
linear function.
What is the F-intercept and what does it represent?
a.
, Fahrenheit temperature corresponding to
b. 32, Fahrenheit temperature corresponding to
c. 32, Celsius temperature corresponding to
d. 0, Fahrenheit temperature corresponding to
e.
, Celsius temperature corresponding to
ANS: B
MSC: Bimodal
PTS: 1
NOT: Section 1.2
DIF:
Medium
REF: 1.2.9b
2. The monthly cost of driving a car depends on the number of miles driven. Julia found that in
October it cost her
to drive
mi and in July it cost her
to drive
mi.
Express the monthly cost C as a function of the distance driven d assuming that a linear
relationship gives a suitable model.
a.
b.
c.
d.
e.
ANS: D
MSC: Bimodal
PTS: 1
NOT: Section 1.2
DIF:
Medium
REF: 1.2.14a
3. Many physical quantities are connected by inverse square laws, that is, by power functions
of the form
.
In particular, the illumination of an object by a light source is inversely proportional to the
square of the distance from the source. Suppose that after dark you are in a room with just
one lamp and you are trying to read a book. The light is too dim and so you move
the distance to the lamp. How much brighter is the light?
a.
times
b. 9 times
c.
d.
times
times
e.
times
ANS: B
MSC: Bimodal
PTS: 1
NOT: Section 1.2
DIF:
Medium
REF: 1.2.15
NUMERIC RESPONSE
1. The relationship between the Fahrenheit and Celsius temperature scales is given by the
linear function.
Complete the table and find the slope.
ANS:
; slope =
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 1.2.9a
NOT: Section 1.2
2. It makes sense that the larger the area of a region, the larger the number of species that
inhabit the region. Many ecologists have modeled the species-area relation with a power
function and, in particular, the number of species S of bats living in caves in central Mexico
has been related to the surface area A measured in
of the caves by the equation
(a) The cave called mission impossible near puebla, mexico, has surface area of
How many species of bats would expect to find in that cave?
(b) If you discover that
species of bats live in cave estimate the area of the cave.
ANS:
a) species
b)
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 1.2.16
NOT: Section 1.2
.
Stewart_Essential Calc_2e ch01sec03
MULTIPLE CHOICE
1. Use the graph of the function to state the value of
, if it exists.
a.
b.
c.
d.
e. does not exist
ANS: E
MSC: Bimodal
PTS: 1
NOT: Section 1.3
DIF:
2. Use the graph of the function to state the value of
Medium
REF: 1.3.15
if it exists.
a.
b. 1
c.
d.
e. does not exist
ANS: E
MSC: Bimodal
PTS: 1
NOT: Section 1.3
DIF:
Medium
REF: 1.3.18
3. Estimate the value of the following limit by graphing the function
.
Round your answer correct to two decimal places.
a. 3.18
b.
c.
d.
e.
ANS: E
MSC: Bimodal
PTS: 1
NOT: Section 1.3
DIF:
Medium
REF: 1.3.20a
NUMERIC RESPONSE
1. By graphing the function
and zooming in toward the point where the graph crosses the y-axis, estimate the value of
ANS:
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 1.3.19a
NOT: Section 1.3
2. Evaluate the function
at the given numbers (correct to six decimal places). Use the results to guess the value of the
limit
ANS:
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 1.3.21a
NOT: Section 1.3
SHORT ANSWER
1. Complete the table by computing
at the given values of x, accurate to five decimal
places. Use the results to guess at the indicated limit, if it exists, to three decimal places.
x
ANS:
x
–0.34483
–0.33445
–0.33344
–0.33322
–0.33223
–0.32258
–0.333
PTS:
1
DIF:
Medium
REF: 1.3.11
MSC: Short Answer
NOT: Section 1.3
2. Complete the table by computing
at the given values of x, accurate to five decimal
places. Use the results to guess at the indicated limit, if it exists, to three decimal places.
x
4.9
4.99
4.999
5.001
5.01
5.1
4.9
0.1001
4.99
0.10001
4.999
0.1
5.001
0.1
5.01
0.09999
5.1
0.0999
ANS:
x
0.1
PTS: 1
NOT: Section 1.3
DIF:
Medium
REF: 1.3.12
MSC: Short Answer
3. Complete the table by computing
at the given values of x, accurate to five decimal
places. Use the results to guess at the indicated limit, if it exists, to three decimal places.
ANS:
0.20858
0.20008
0.2
0.2
0.20008
0.20858
0.2
PTS: 1
NOT: Section 1.3
DIF:
Medium
REF: 1.3.13
MSC: Short Answer
Stewart_Essential Calc_2e ch01sec04
MULTIPLE CHOICE
1. Find the limit
a.
b.
c.
d.
.
12
–12
6
–1
ANS: A
MSC: Bimodal
PTS: 1
NOT: Section 1.4
DIF:
Easy
REF: 1.4.3
PTS: 1
NOT: Section 1.4
DIF:
Medium
REF: 1.4.4
PTS: 1
NOT: Section 1.4
DIF:
Medium
REF: 1.4.11
2. Evaluate the limit.
a.
b.
c.
d.
e.
ANS: C
MSC: Bimodal
3. Find the limit.
a.
b.
c.
d.
e.
ANS: C
MSC: Bimodal
4. Find the limit
a. 2
, if it exists.
b. 5
c. 3
d. Does not exist
ANS: B
MSC: Bimodal
PTS: 1
NOT: Section 1.4
5. Find the limit
DIF:
Medium
REF: 1.4.13
DIF:
Easy
REF: 1.4.14
DIF:
Medium
REF: 1.4.17
.
a.
b.
c.
d. 1
ANS: B
MSC: Bimodal
PTS: 1
NOT: Section 1.4
6. Evaluate the limit, if it exists.
a.
b. 1
c.
d.
e. does not exist
ANS: D
MSC: Bimodal
7. Find the limit
a.
b.
PTS: 1
NOT: Section 1.4
, if it exists.
c.
d. Does not exist
ANS: C
MSC: Bimodal
PTS: 1
NOT: Section 1.4
DIF:
Medium
NUMERIC RESPONSE
1. Find the limit.
ANS:
2
15
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 1.4.5
NOT: Section 1.4
2. Evaluate the limit.
ANS:
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 1.4.19
NOT: Section 1.4
3. Evaluate the limit.
ANS: 0
PTS: 1
DIF: Medium
MSC: Numerical Response
SHORT ANSWER
1. Find the limit
, if it exists.
REF: 1.4.37
NOT: Section 1.4
REF: 1.4.21
ANS:
PTS: 1
NOT: Section 1.4
DIF:
2. Find the limit
Medium
REF: 1.4.12
MSC: Short Answer
Easy
REF: 1.4.23
MSC: Short Answer
.
ANS:
PTS: 1
NOT: Section 1.4
DIF:
Stewart_Essential Calc_2e ch01sec05
MULTIPLE CHOICE
1. Choose an equation from the following that expresses the fact that a function f is
continuous at the number .
a.
b.
c.
d.
e.
ANS: D
MSC: Bimodal
PTS: 1
NOT: Section 1.5
DIF:
Medium
REF: 1.5.1
DIF:
Medium
REF: 1.5.11
DIF:
Medium
REF: 1.5.28
2. If f and g are continuous functions with
a.
b.
c.
d.
e.
ANS: D
MSC: Bimodal
PTS: 1
NOT: Section 1.5
3. Use continuity to evaluate the limit.
a.
b. 1
c. 0
d.
e.
ANS: C
MSC: Bimodal
PTS: 1
NOT: Section 1.5
4. Determine where f is discontinuous.
a. 0 only
b.
c.
only
d.
e.
only
ANS: D
MSC: Bimodal
PTS: 1
NOT: Section 1.5
DIF:
Medium
REF: 1.5.31
5. For what value of the constant c is the function f continuous on
a.
b.
c.
d.
e.
ANS: E
MSC: Bimodal
PTS: 1
NOT: Section 1.5
DIF:
Medium
REF: 1.5.33
NUMERIC RESPONSE
1. For
determine whether f is continuous from the right, from the left, or neither.
ANS: neither
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 1.5.3b
NOT: Section 1.5
2. Determine where f is discontinuous.
ANS:
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 1.5.16
NOT: Section 1.5
Stewart_Essential Calc_2e ch01sec06
MULTIPLE CHOICE
1. Let
Find the following limits.
a.
and
b. both
c. both 1
d.
and
e.
and
ANS: A
MSC: Bimodal
PTS: 1
NOT: Section 1.6
DIF:
Medium
REF: 1.6.13
PTS: 1
NOT: Section 1.6
DIF:
Easy
REF: 1.6.19
2. Find the limit.
a. 5
2
b. 2
7
c. 2
5
d. 7
5
e. 5
7
ANS: D
MSC: Bimodal
3. Find the limit.
a.
b.
c.
d.
e.
ANS: D
MSC: Bimodal
PTS: 1
NOT: Section 1.6
DIF:
Easy
REF: 1.6.32
DIF:
Medium
REF: 1.6.35
4. Find the vertical asymptotes of the function.
a.
b.
c.
d.
e. None of these
ANS: E
MSC: Bimodal
PTS: 1
NOT: Section 1.6
NUMERIC RESPONSE
1. For the function f whose graph is shown, state the following.
ANS:
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 1.6.1d
NOT: Section 1.6