Test Bank for Precalculus, 6th Edition

Name: Test Bank for Precalculus, 6th Edition
Brand: Academic Documents Platform
Price: 29.99 USD
Availability: InStock
Author: Sophia Lee

Test Bank for Precalculus, 6th Edition helps you familiarize yourself with exam formats and key concepts.

Sophia Lee

Contributor

4.9

175

about 2 months ago

Preview (31 of 1051)

Ch. 11 Introduction to Calculus
11.1 Finding Limits Using Tables and Graphs
1 Understand Limit Notation
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Choose the table which contains the best values of x for finding the requested limit of the given function.
1) lim
x→2
(x2 + 8x - 2)
A) x 1.9 1.99 1.999 2.001 2.01 2.1
f(x)
B) x 0.9 0.99 0.999 1.001 1.01 1.1
f(x)
C) x -1.9 -1.99 -1.999 2.001 2.01 2.1
f(x)
D) x -0.9 -0.99 -0.999 1.001 1.01 1.1
f(x)
2) lim
x→1
x4 - 1
x - 1
A) x 0.9 0.99 0.999 1.001 1.01 1.1
f(x)
B) x 1.9 1.99 1.999 1.001 1.01 1.1
f(x)
C) x -0.9 -0.99 -0.999 -1.001 -1.01 -1.1
f(x)
D) x 0.1 0.19 0.119 1.99 1.09 1.9
f(x)
Page 1

3) lim
x→0
sin 2x
x
A) x -0.03 -0.02 -0.01 0.01 0.02 0.03
f(x)
B) x -0.01 -0.02 -0.03 0.03 0.02 0.01
f(x)
C) x -0.3 -0.2 -0.1 0.1 0.2 0.3
f(x)
D) x 0.03 0.02 0.01 0.001 0.002 0.003
f(x)
Translate the given limit notation into a sentence.
4) lim
x→4
( x - 2) = 0
A) The limit of x - 2 as x approaches 4 equals the number 0.
B) The limit of x - 2 as x approaches 0 equals the number 4.
C) The limit of x - 4 as x approaches 2 equals the number 0.
D) The limit of x - 4 as x approaches 0 equals the number 2.
5) lim
x→0
sin 2x
x = 2
A) The limit of sin 2x
x as x approaches 0 equals the number 2.
B) The limit of sin 2x
x as x approaches 2 equals the number 0.
C) The limit of sin 2x
x as x approaches 0 from the left equals the number 2.
D) The limit of sin 2x
x as x approaches 0 from the right equals the number 2.
2 Find Limits Using Tables
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Complete the table for the function and find the indicated limit.
1) lim
x→2
(x2 + 8x - 2)
x 1.9 1.99 1.999 2.001 2.01 2.1
f(x)
A) 16.810; 17.880; 17.988; 18.012; 18.120; 19.210
limit = 18.0
B) 5.043; 5.364; 5.396; 5.404; 5.436; 5.763
limit = 5.40
C) 16.692; 17.592; 17.689; 17.710; 17.808; 18.789
limit = 17.70
D) 6.810; 7.880; 7.988; 8.012; 8.120; 9.210
limit = 8.0
Page 2

2) lim
x→1
x4 - 1
x - 1
x 0.9 0.99 0.999 1.001 1.01 1.1
f(x)
A) 3.439; 3.940; 3.994; 4.006; 4.060; 4.641
limit = 4.0
B) 1.032; 1.182; 1.198; 1.201; 1.218; 1.392
limit = 1.210
C) 4.595; 5.046; 5.095; 5.105; 5.154; 5.677
limit = 5.10
D) 7.439; 7.940; 7.994; 8.006; 8.060; 8.641
limit = 8.0
3) lim
x→0
x3 - 6x + 8
x - 2
x -0.1 -0.01 -0.001 0.001 0.01 0.1
f(x)
A) -4.09476; -4.00995; -4.00100; -3.99900; -3.98995; -3.89526
limit = -4.0
B) -1.22843; -1.20298; -1.20030; -1.19970; -1.19699; -1.16858
limit = -1.20
C) -2.18529; -2.10895; -2.10090; -2.09910; -2.09096; -2.00574
limit = -2.10
D) 4.09476; 4.00995; 4.00100; 3.99900; 3.98995; 3.89526
limit = 4.0
4) lim
x→0
(x2 - 5)
x -0.1 -0.01 -0.001 0.001 0.01 0.1
f(x)
A) -4.9900; -4.9999; -5.0000; -5.0000; -4.9999; -4.9900
limit = -5.0
B) -1.4970; -1.4999; -1.5000; -1.5000; -1.4999; -1.4970
limit = -1.50
C) -2.9910; -2.9999; -3.0000; -3.0000; -2.9999; -2.9910
limit = -3.0
D) 1.4970; 1.4999; 1.5000; 1.5000; 1.4999; 1.4970
limit = 1.50
5) lim
x→0
sin 2x
x
x -0.03 -0.02 -0.01 0.01 0.02 0.03
f(x)
A) 1.9988, 1.9995, 1.9999, 1.9999, 1.9995, 1.9988
limit = 2
B) 1.9988, 1.9995, 1.9999, 1.9999, 1.9995, 1.9988
limit = 0
C) 1.9988, 1.9995, 1.9999, 1.9999, 1.9995, 1.9988
limit = 1
D) 1.9988, 1.9995, 1.9999, 1.9999, 1.9995, 1.9988
limit = -2
Page 3

Loading page 4...

6) lim
x→0
x2
sin x
x -0.03 -0.02 -0.01 0.01 0.02 0.03
f(x)
A) -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300
limit = 0
B) -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300
limit = 1
C) -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300
limit = 0.1
D) -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300
limit = -1
7) lim
x→ -7
x2 - 49
x + 7
x -7.1 -7.01 -7.001 -6.999 -6.99 -6.9
f(x)
A) -14.1, -14.01, -14.001, -13.999, -13.99, -13.9
limit = -14
B) 7.1, 7.01, 7.001, 6.999, 6.99, 6.9
limit = 7
C) -14.1, -14.01, -14.001, -13.999, -13.99, -13.9
limit = -14
D) -7.1, -7.01, -7.001, -6.999, -6.99, -6.9
limit = -7
8) lim
x→0
1 - cos x
sin x
x -0.03 -0.02 -0.01 0.01 0.02 0.03
f(x)
A) -0.0150, -0.0100, -0.0050, 0.0050, 0.0100, 0.0150
limit = 0
B) -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300
limit = 1
C) -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300
limit = 0.1
D) -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300
limit = -1
9) lim
x→0
f(x), where f(x) = x + 5 if x < 0
3x + 5 if x ≥ 0
x -0.1 -0.01 -0.001 0.001 0.01 0.1
f(x)
A) 4.9, 4.99, 4.999, 5.003, 5.03, 5.3
limit = 5
B) 2.9, 2.99, 2.999, 3.003, 3.03, 3.3
limit = 3
C) 0.9, 0.99, 0.999, 1.003, 1.03, 1.3
limit = 1
D) 1.9, 1.99, 1.999, 2.003, 2.03, 2.3
limit = 2
Page 4

Loading page 5...

3 Find Limits Using Graphs
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
The graph of a function is given. Use the graph to find the indicated limit and function value, or state that the limit
or function value does not exist.
1) a. lim
x→0
f(x) b. f(0)
x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
y
4
3
2
1
-1
-2
-3
-4
x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
y
4
3
2
1
-1
-2
-3
-4
A) a. lim
x→0
f(x) = 0
b. f(0) = 0
B) a. lim
x→0
f(x) = 0
b. f(0) = 2
C) a. lim
x→0
f(x) = -2
b. f(0) = -2
D) a. lim
x→0
f(x) does not exist
b. f(0) does not exist
2) a. lim
x→0
f(x) b. f(0)
x-10-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10
y
1
-1
x-10-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10
y
1
-1
A) a. lim
x→0
f(x) = 1
b. f(0) = 1
B) a. lim
x→0
f(x) = 0
b. f(0) = 0
C) a. lim
x→0
f(x) = -1
b. f(0) = -1
D) a. lim
x→0
f(x) does not exist
b. f(0) does not exist
Page 5

Loading page 6...

3) a. lim
x→0
f(x) b. f(0)
A) a. lim
x→0
f(x) = 1
b. f(0) does not exist
B) a. lim
x→0
f(x) = -1
b. f(0) does not exist
C) a. lim
x→0
f(x) = 0
b. f(0) = 0
D) a. lim
x→0
f(x) does not exist
b. f(0) does not exist
4) a. lim
x→0
f(x) b. f(0)
x-2 -1 1 2 3 4 5
y
10
8
6
4
2
-2
x-2 -1 1 2 3 4 5
y
10
8
6
4
2
-2
A) a. lim
x→0
f(x) = 0
b. f(0) = 6
B) a. lim
x→0
f(x) = 6
b. f(0) = 6
C) a. lim
x→0
f(x) = 6
b. f(0) = 0
D) a. lim
x→0
f(x) does not exist
b. f(0) = 6
Page 6

Loading page 7...

5) a. lim
x→0
f(x) b. f(0)
A) a. lim
x→0
f(x) = 0
b. f(0) does not exist
B) a. lim
x→0
f(x) = 1
b. f(0) = 1
C) a. lim
x→0
f(x) = -1
b. f(0) does not exist
D) a. lim
x→0
f(x) does not exist
b. f(0) does not exist
6) a. lim
x → 1
f(x) b. f(1)
x-3 -2 -1 1 2
y2
1
-1
-2
-3
-4
x-3 -2 -1 1 2
y2
1
-1
-2
-3
-4
A) a. lim
x → 1
f(x) = -3
b. f(1) = -3
B) a. lim
x → 1
f(x) = 3
b. f(1) = 3
C) a. lim
x → 1
f(x) = 1
b. f(1) = 1
D) a. lim
x → 1
f(x) does not exist
b. f(1) = -3
Page 7

Loading page 8...

7) a. lim
x→1
f(x) b. f(1)
x1 2 3 4 5
y
4
3
2
1
-1
x1 2 3 4 5
y
4
3
2
1
-1
A) a. lim
x→1
f(x) = 3
b. f(1) = 3
B) a. lim
x→1
f(x) = 1
b. f(1) = 3
C) a. lim
x→1
f(x) = 0
b. f(1) = 0
D) a. lim
x→1
f(x) does not exist
b. f(1) does not exist
8) a. lim
x→2
f(x) b. f(2)
x1 2 3 4 5
y
5
4
3
2
1
x1 2 3 4 5
y
5
4
3
2
1
A) a. lim
x→2
f(x) = 2
b. f(2) = 1
B) a. lim
x→2
f(x) = 1
b. f(2) = 1
C) a. lim
x→2
f(x) = 1
b. f(2) = 2
D) a. lim
x→2
f(x) does not exist
b. f(2) = 1
Page 8

Loading page 9...

9) a. lim
x → 1
f(x) b. f(1)
x-3 -2 -1 1 2
y2
1
-1
-2
-3
-4
x-3 -2 -1 1 2
y2
1
-1
-2
-3
-4
A) a. lim
x → 1
f(x) = -3
b. f(1) = 1
B) a. lim
x → 1
f(x) = -3
b. (1) = -3
C) a. lim
x → 1
f(x) = 1
b. f(1) = -3
D) a. lim
x → 1
f(x) = -3
b. f(1) does not exist
Use the graph and the viewing rectangle shown below the graph to find the indicated limit.
10) lim
x→-2
(x2 - 2)
[-6, 6, 1] by [-6, 6, 1]
A) lim
x→-2
(x2 - 2) = 2 B) lim
x→-2
(x2 - 2) = -6
C) lim
x→-2
(x2 - 2) = 6 D) lim
x→-2
(x2 - 2) = -2
Page 9

Loading page 10...

Loading page 11...

Loading page 12...

Loading page 13...

Loading page 14...

4 Find One-Sided Limits and Use Them to Determine If a Limit Exists
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
The graph of a function is given. Use the graph to find the indicated limit and function value, or state that the limit
or function value does not exist.
1) a. lim
x→3
f(x) b. f(3)
x1 2 3 4 5
y
5
4
3
2
1
x1 2 3 4 5
y
5
4
3
2
1
A) a. lim
x→3
f(x) does not exist
b. f(3) = 5
B) a. lim
x→3
f(x) = 5
b. f(3) = 5
C) a. lim
x→3
f(x) = 3
b. f(3) = 5
D) a. lim
x→3
f(x) = 4
b. f(3) does not exist
2) a. lim
x→1
f(x) b. f(1)
x-2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
x-2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
A) a. lim
x→1
f(x) does not exist
b. f(1) = 2
B) a. lim
x→1
f(x) = 1
b. f(1) = 2
C) a. lim
x→1
f(x) = 2
b. f(1) = 2
D) a. lim
x→1
f(x) = 1
b. f(1) = 0
Page 14

Loading page 15...

Loading page 16...

5) a. lim
x→-1/2
f(x) b. f(-1/2)
A) a. lim
x→-1/2
f(x) = -1
b. f(-1/2) = -1
B) a. lim
x→-1/2
f(x) = -2
b. f(-1/2) = -1
C) a. lim
x→-1/2
f(x) = 0
b. f(-1/2) does not exist
D) a. lim
x→-1/2
f(x) does not exist
b. f(-1/2) = -1
6) a. lim
x→3-
f(x) b. f(3)
x1 2 3 4 5
y
5
4
3
2
1
x1 2 3 4 5
y
5
4
3
2
1
A) a. lim
x→3-
f(x) = 3
b. f(3) = 5
B) a. lim
x→3-
f(x) = 3
b. f(3) = 3
C) a. lim
x→3-
f(x) = 3
b. f(3) does not exist
D) a. lim
x→3-
f(x) does not exist
b. f(3) = 5
Page 16

Loading page 17...

7) a. lim
x→3+
f(x) b. f(3)
x1 2 3 4 5
y
5
4
3
2
1
x1 2 3 4 5
y
5
4
3
2
1
A) a. lim
x→3+
f(x) = 5
b. f(3) = 5
B) a. lim
x→3+
f(x) = 3
b. f(3) = 3
C) a. lim
x→3+
f(x) = 3
b. f(3) does not exist
D) a. lim
x→3+
f(x) does not exist
b. f(3) = 5
8) a. lim
x→1+
f(x) b. f(1)
x-2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
x-2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
A) a. lim
x→1+
f(x) = 2
b. f(1) = 2
B) a. lim
x→1+
f(x) = 2
b. f(1) = 1
C) a. lim
x→1+
f(x) = 1
b. f(1) = 0
D) a. lim
x→1+
f(x) does not exist
b. f(1) = 2
Page 17

Loading page 18...

9) a. lim
x→-1-
f(x) b. f(-1)
A) a. lim
x→-1-
f(x) = -1
b. f(-1) does not exist
B) a. lim
x→-1-
f(x) = 0
b. f(-1) = 1
C) a. lim
x→-1-
f(x) = -1
b. f(-1) = 1
D) a. lim
x→-1-
f(x) does not exist
b. f(-1) does not exist
10) a. lim
x→-2+
f(x) b. f(-2)
A) a. lim
x→-2+
f(x) = -2
b. f(-2) = -2
B) a. lim
x→-2+
f(x) = -1
b. f(-2) does not exist
C) a. lim
x→-2+
f(x) = -2
b. f(-2) = -1
D) a. lim
x→-2+
f(x) does not exist
b. f(-2) = -1
Page 18

Loading page 19...

11) a. lim
x→2.5-
f(x) b. f(2.5)
A) a. lim
x→2.5-
f(x) = 1
b. f(2.5) = 1
B) a. lim
x→2.5-
f(x) = 2
b. f(2.5) = 1
C) a. lim
x→2.5-
f(x) = 0
b. f(2.5) = 2
D) a. lim
x→2.5-
f(x) does not exist
b. f(2.5) = 2
12) a. lim
x→1-
f(x) b. f(1)
x-2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
x-2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
A) a. lim
x→1-
f(x) = 1
b. f(1) = 2
B) a. lim
x→1-
f(x) = 2
b. f(1) = 2
C) a. lim
x→1-
f(x) = 1
b. f(1) = 1
D) a. lim
x→1-
f(x) does not exist
b. f(1) = 2
Page 19

Loading page 20...

5 Solve Apps: Use Limits
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) You are riding your motorcycle along a freeway traveling x miles per hour. The function
f(x) = 0.0014x2 + x + 9 describes the recommended safe distance, f(x), in feet, between your motorcycle and
the other motorcycles on the freeway. Use the values in the table below to solve this exercise.
x 49.9 49.99 49.999 → ← 50.001 50.01 50.1
f(x) 93.76 93.976 93.998 → ← 94.002 94.024 94.24
Find lim
x→50
f(x). Describe what this means in terms of your motorcycle's speed and the recommended safe
distance.
A) 94; This means that the recommended safe distance between motorcycles traveling at 50 miles per
hour is 94 feet.
B) 50; This means that the recommended safe distance between motorcycles traveling at 50 miles per
hour is 50 feet.
C) 93.999; This means that the recommended safe distance between motorcycles traveling at 50 miles per
hour is 93.999 feet.
D) lim
x→ 50
f(x) does not exist.
Page 20

Loading page 21...

2) You rent a moving van from a company that charges $10 per hour plus $0.50 per mile. The van is driven 40
miles in the first hour. The figure below shows the graph of the cost, f(x), in dollars, as a function of the
miles, x, that you drive the van.
(i) Find lim
x→ 20
f(x). Interpret the limit, referring to miles driven and cost.
(ii) For the first hour hour only, what is the rental cost approaching as the mileage gets closer to 40?
(iii) What is the cost to rent the van at the start of the second hour?
A) (i) 20; the cost to rent the van for one hour and drive it 20 miles is $20.
(ii) $30
(iii) $40
B) (i) 30; the cost to rent the van for one hour and drive it 20 miles is $30.
(ii) $40
(iii) $40
C) (i) 40; the cost to rent the van for one hour and drive it 20 miles is $40.
(ii) $30
(iii) $40
D) (i) 20; the cost to rent the van for one hour and drive it 20 miles is $20.
(ii) $30
(iii) $30
3) You are building a screened-in porch attached to your house. Because the house will be used for one side
of the enclosure, only three sides will need to be enclosed. You have 24 yards of material to enclose the
three walls. The function f(x) = x(24 - 2x) describes the area of the screened-in porch that you can enclose,
f(x), in square yards, if the width of the screened-in porch is x yards
X Y1
5.7
5.8
5.9
6
6.1
6.2
6.3
71.82
71.92
71.98
71.98
71.92
71.82
Y1 = X * (24 - 2X)
(i) Use the table shown to find lim
x→ 6
f(x).
(ii) Use the graph of f(x) = x(24- 2x) shown to find lim
x→ 6
f(x). Do you get the same limit as you did in part
(i)? What information about the limit is shown by the graph that might not be obvious from the table?
Page 21

Loading page 22...

[-5, 15, 5] by [0, 80, 10]
A) (i) 72
(ii) 72; Yes, the same limit is obtained. The graph shows that the limit is the maximum area.
B) (i) 80
(ii) 80; Yes, the same limit is obtained. The graph shows that the limit is the maximum area.
C) (i) 72
(ii) 80; No, the same limit is not obtained. The graph shows that the limit is the maximum amount of
material that can be used.
D) (i) 80
(ii) 72; No, the same limit is not obtained. The graph shows that the limit is the maximum amount of
material that can be used.
11.2 Finding Limits Using Properties of Limits
1 Find Limits of Constant Functions and the Identity Function
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit
properties can be applied.
1) lim
x→10
-6
A) -6 B) 10 C) 6 D) 0
2) lim
x→-8
x
A) -8 B) 8 C) 0 D) 1
2 Find Limits Using Properties of Limits
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit
properties can be applied.
1) lim
x→-7
15x3
A) -5145 B) -7 C) -343 D) 15
2) lim
x→0
(x2 - 5)
A) -5 B) 5 C) 0 D) does not exist
Page 22

Loading page 23...

3) lim
x→2
(x2 + 8x - 2)
A) 18 B) -18 C) 0 D) does not exist
4) lim
x→2
(x3 + 5x2 - 7x + 1)
A) 15 B) 29 C) 0 D) does not exist
5) lim
x→0
( x - 2)
A) -2 B) 0 C) 2 D) does not exist
6) lim
x→1
(3x2 - 19)2
A) 256 B) -352 C) 144 D) 100
7) lim
x→4
(x - 4)( x - 2)
A) 0 B) 2 C) 4 D) does not exist
8) lim
x→1
(x2 - 2)3
A) -1 B) 1 C) 3 D) -3
9) lim
x→3 (3x2 - 2x + 2)2
A) 529 B) -529 C) 81 D) does not exist
10) lim
x→1
3x - 2
A) 1 B) 2 C) -1 D) does not exist
11) lim
x→1
2x - 7
4x + 5
A) - 5
9 B) - 1
2 C) - 7
5 D) does not exist
12) lim
x→1
2x - 7
4x + 5
A) - 5
9 B) - 1
2 C) - 7
5 D) does not exist
13) lim
x→5
x2 - 2x - 15
x + 3
A) 0 B) -8 C) 5 D) does not exist
14) lim
x→0
x3 - 6x + 8
x - 2
A) -4 B) 0 C) 4 D) does not exist
Page 23

Loading page 24...

15) lim
x→1
3x2 + 7x - 2
3x2 - 4x + 2
A) 8 B) - 7
4 C) 0 D) does not exist
16) lim
x→2 [(x - 3)3(5x + 1)2]
A) -121 B) 121 C) -288 D) does not exist
17) lim
x→7
x - 7
x - 49
A) 1
6 - 7
42 B) 0 C) 7
42 - 1
6 D) does not exist
3 Find One-Sided Limits Using Properties of Limits
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
A piecewise function is given. Use the properties of limits to find the indicated limits, or state that the limit does
not exist.
1) f(x) = 4x - 3 if x < 1
-3x + 4 if x > 1
a. lim
x→1-
f(x) b. lim
x→1+
f(x) c. lim
x→1
f(x)
A) a. 1
b. 1
c. 1
B) a. 1
b. 1
c. does not exist
C) a. -3
b. 4
c. does not exist
D) a. 4
b. -3
c. does not exist
2) f(x) = x2 - 1 if x < 0
-4 if x ≥ 0
a. lim
x→-5-
f(x) b. lim
x→-5+
f(x) c. lim
x→-5
f(x)
A) a. 24
b. 24
c. 24
B) a. -1
b. -4
c. does not exist
C) a. -4
b. -1
c. does not exist
D) a. -1
b. -4
c. -4
3) f(x) =
1
x - 5 if x > 5
x2 - 2x if x ≤ 5
a. lim
x→5-
f(x) b. lim
x→5+
f(x) c. lim
x→5
f(x)
A) a. 15
b. does not exist
c. does not exist
B) a. does not exist
b. 15
c. does not exist
C) a. 15
b. does not exist
c. 15
D) a. does not exist
b. 15
c. 15
Page 24

Loading page 25...

4) f(x) =
x2 - 9
x - 3 if x ≠ 3
5 if x = 3
a. lim
x→3-
f(x) b. lim
x→3+
f(x) c. lim
x→3
f(x)
A) a. 6
b. 6
c. 6
B) a. 6
b. 6
c. 5
C) a. 3
b. 3
c. does not exist
D) a. 3
b. 3
c. 5
5) f(x) =
4x - 5 if x < 1
1 if x = 1
-3x - 4 if x > 1
a. lim
x→1-
f(x) b. lim
x→1+
f(x) c. lim
x→1
f(x)
A) a. -1
b. -7
c. does not exist
B) a. -7
b. -1
c. does not exist
C) a. -1
b. -7
c. -8
D) a. -7
b. -1
c. -8
6) f(x) =
6 - x if x < 1
4 if x = 1
x2 + 4 if x > 1
a. lim
x→1-
f(x) b. lim
x→1+
f(x) c. lim
x→1
f(x)
A) a. 5
b. 5
c. 5
B) a. 5
b. 4
c. does not exist
C) a. 4
b. 6
c. does not exist
D) a. 5
b. 5
c. 4
4 Find Limits of Fractional Expressions in Which the Limit of the Denominator is Zero
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit
properties can be applied.
1) lim
x→1
x4 - 1
x - 1
A) 4 B) 2 C) 0 D) does not exist
2) lim
x→-3
x2 - 2x - 15
x + 3
A) -8 B) 0 C) 5 D) does not exist
3) lim
x→0
x3 + 12x2 - 5x
5x
A) -1 B) 0 C) 5 D) does not exist
4) lim
x→1
x3 + 5x2 + 3x - 9
x - 1
A) 16 B) -16 C) 0 D) does not exist
Page 25

Loading page 26...

5) lim
x→0
4 + x - 2
x
A) 1
4 B) 1
2 C) 4 D) 0
6) lim
x→9
1
x - 1
9
x - 9
A) - 1
81 B) 1
9 C) 0 D) does not exist
7) lim
x→4
x - 4
x - 2
A) 4 B) 1/4 C) 0 D) does not exist
8) lim
x→4
x - 2
x - 4
A) 1/4 B) 4 C) 0 D) does not exist
9) lim
x→5
x2 - 25
x3 - 125
A) 2
15 B) - 2
15 C) 1
15 D) does not exist
10) lim
h→0
(x + h)3 - x3
h
A) 3x2 B) 0 C) 3x2 + 3xh + h2 D) does not exist
11.3 Limits and Continuity
1 Determine Whether a Function is Continuous at a Number
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the definition of continuity to determine whether f is continuous at a.
1) f(x) = 5x4 - 9x3 + x - 6
a = 0
A) Continuous B) Not continuous
2) f(x) = 3x4 - 9x3 + x - 5
a = 5
A) Continuous B) Not continuous
3) f(x) = 5
x + 2
a = -2
A) Not continuous B) Continuous
Page 26

Loading page 27...

4) f(x) = 5
x - 8
a = 0
A) Continuous B) Not continuous
5) f(x) = x + 7
x + 2
a = -7
A) Continuous B) Not continuous
6) f(x) = x - 6
x + 3
a = 0
A) Continuous B) Not continuous
7) f(x) = x + 7
x + 3
a = -3
A) Not continuous B) Continuous
8) f(x) = 7
x2 + 8x
a = 0
A) Not continuous B) Continuous
9) f(x) = 1
x2 - 9x
a = 9
A) Not continuous B) Continuous
10) f(x) = 1
x2 - 3x
a = -1
A) Continuous B) Not continuous
11) f(x) = x2 - 16
x - 4
a = 0
A) Continuous B) Not continuous
12) f(x) = x2 - 64
x - 8
a = 8
A) Not continuous B) Continuous
13) f(x) = x2 - 5, if x < 0
3, if x ≥ 0
a = -4
A) Continuous B) Not continuous
Page 27

Loading page 28...

14) f(x) =
4x + 3, if x < 1
1, if x = 1
4x - 7, if x > 1
a = 1
A) Not continuous B) Continuous
15) f(x) =
1
x + 4 , if x > -4
x2 - 4x, if x ≤ -4
a = -4
A) Not continuous B) Continuous
2 Determine For What Numbers a Function is Discontinuous
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine for what numbers, if any, the given function is discontinuous.
1) f(x) = 2x + 5
A) None B) 5
2 C) - 5
2 D) -5
2) f(x) = -3x2 + 5x
A) None B) - 5
6 C) 5
6 D) -3
3) f(x) = -3 cos x
A) None B) 0 C) 1 D) -3
4) f(x) = 4 tan x
A) nπ
2 and - nπ
2 B) 0 C) nπ
4 and - nπ
4 D) None
5) f(x) = 2x - 1
x2 - 25
A) -5 and 5 B) 5 C) -5 and 5 and - 1
2 D) None
6) f(x) = x- 4 if x ≤ 4
x2 -8 if x > 4
A) 4 B) None C) -4, 4 D) 0
7) f(x) = x- 3 if x ≤ 3
x2 if x > 3
A) 3 B) [the set of numbers 1, 2, 3, . . . 8]
C) [the set of numbers 1, 2, 3, . . . 9] D) None
8) f(x) =
x2 - 9
x - 3 if x ≠ 3
6 if x = 3
A) None B) 3 C) 9 D) 3, 9
Page 28

Loading page 29...

9) f(x) =
8x if x < 7
55 if x = 7
x2 + 7 if x > 7
A) 7 B) 0, 7 C) 8, 7 D) None
3 Solve Apps: Limits and Continuity
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
1) The figure shows the cost of renting a car, f(x), as a function of distance driven, x, in miles, for distances
not exceeding 70 miles.
Cost
(dollars)
x
y
x
y
49
47
45
43
41
39
37
20 40 60
Distance (miles)
(i) Find lim
x→60-
f(x).
(ii) Find lim
x→60+
f(x).
(iii) What can you conclude about lim
x→60
f(x)? How is this shown by the graph?
(iv) What aspect of costs of renting a car causes the graph to jump vertically by the same amount at its
discontinuities?
Page 29

Loading page 30...

2) The following piecewise function gives the tax owed, T(x), by a single taxpayer on a taxable income of x
dollars.
T(x) =
0.11x if 0 < x ≤ 7593
759.30 + 0.18(x - 7593) if 7593 < x ≤ 31,687
5096.22 + 0.26(x - 31,687) if 31,687 < x ≤ 72,784
15,781.44 + 0.29(x - 72,784) if 72,784 < x ≤ 149,897
38,144.21 + 0.32(x - 149,897) if 149,897 < x ≤ 325,127
94,217.81 + 0.36(x - 325,127) if x > 325,127
(i) Determine whether T is continuous at 7593.
(ii) Determine whether T is continuous at 31,687.
(iii) If T had discontinuities, use one of these discontinuities to describe a situation where it might be
advantageous to earn less money in taxable income.
11.4 Introduction to Derivatives
1 Find Slopes and Equations of Tangent Lines
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the slope of the tangent line to the graph of f at the given point.
1) f(x) = -2x + 20 at (8, 4)
A) -2 B) 20 C) -20 D) - 1
2
2) f(x) = x2 + 5x at (4, 36)
A) 13 B) 9 C) 3 D) 21
3) f(x) = 5x2 + x at (-4, 76)
A) -39 B) -41 C) 6 D) -14
4) f(x) = -4x2 + 7x at (5, -65)
A) -33 B) 33 C) -13 D) 3
5) f(x) = 2x2 + x - 3 at (4, 33)
A) 17 B) 15 C) 5 D) 19
6) f(x) = x2 + 11x - 15 at (1, -3)
A) 13 B) -9 C) 26 D) 11
7) f(x) = x at (64, 8)
A) 1
16 B) 4 C) 16 D) 1
4
8) f(x) = 3
x at (1, 3)
A) -3 B) 3 C) 6 D) 3
2
Find the slope-intercept equation of the tangent line to the graph of f at the given point.
9) f(x) = x2 + 5x at (4, 36)
A) y = 13x - 16 B) y = 13x - 72 C) y = 2x - 5 D) y = 2x + 5
Page 30

Loading page 31...

30 more pages available. Scroll down to load them.

Preview Mode

100%

Study Now!

XY-Copilot AI

Unlimited Access

Secure Payment

Instant Access

24/7 Support

AI Assistant

Document Details

Subject

Mathematics

Test Bank for Precalculus, 6th Edition

Study Now!

Document Details

Related Documents

Test Bank for Biocalculus: Calculus for Life Sciences, 1st Edition

Test Bank for Current Medical Diagnosis and Treatment 2023 (Ie), 62nd Edition (Chapters 27)

Test Bank For Math in Our World, 4th Edition

Single Variable Calculus, 8th Edition Test Bank

Test Bank for Calculus: Concepts and Contexts, Enhanced 4th Edition

Test Bank For Discrete Mathematics With Applications, 5th Edition

Test Bank for Calculus, 10th Edition

Test Bank for Calculus of a Single Variable, 10th Edition

Test Bank for Algebra for College Students, 8th Edition

Test Bank For College Geometry: A Problem Solving Approach with Applications, 2nd Edition