Applied Calculus 8th Edition
by Waner and Costenoble, Chapter 1 to 9
TEST BANK
,Table of contents
1. Functions And Applications.
2. Nonlinear Functions And Models.
3. Introduction To The Derivative.
4. Techniques Of Differentiation.
5. Applications Of The Derivative.
6. The Integra.
7. Further Integration Techniques And Applications Of The Integral.
8. Functions Of Several Variables.
9. Trigonometric Models.
,Chapter 1 Functions and Applications
Section 1.1
1. Using the table: a. ƒ(0) 2 b. ƒ(2) 05
2. Using the table: a. ƒ( 1) 4 b. ƒ(1) 1
3. Using the table: a. ƒ(2) ƒ( 2) 05 2 25 b. ƒ( 1)ƒ( 2) (4)(2) 8
c. 2ƒ( 1) 2(4) 8
4. Using the table: a. ƒ(1) ƒ( 1) 1 4 5 b. ƒ(1)ƒ( 2) ( )(2) 2
c. 3ƒ( 2) 3(2) 6
5. From the graph, we estimate: a. ƒ(1) 20 b. ƒ(2) 30
In a similar way, we find: c. ƒ(3) 30 d. ƒ(5) 20\\e. ƒ(3) ƒ(2) 30 30 0
f. ƒ(3 2) ƒ(1) 20
6. From the graph, we estimate: a. ƒ(1) 20 b. ƒ(2) 10
In a similar way, we find: c. ƒ(3) 10 d. ƒ(5) 20 \\e. ƒ(3) ƒ(2) 10 10 0
f. ƒ(3 2) ƒ(1) 20
7. From the graph, we estimate: a. ƒ( 1) 0 b. ƒ(1) 3 since the solid dot is on (1 3)
ƒ(3) ƒ( ) 3 ( 3)
In a similar way, we estimate c. ƒ(3) 3 d. Since ƒ(3) 3 and ƒ(1) 3 3
3 1 3 1
3
© 2024 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, Solutions Section 1.1
8. From the graph, we estimate: a. ƒ( 3) 3 b. ƒ( 1) 2 since the solid dot is on ( 1 2)
In a similar way, we estimate c. ƒ(1) 0
ƒ(3) ƒ(1) 2 0
d. Since ƒ(3) 2 and ƒ(1) 0 1
3 1 3 1
1
9. ƒ( ) with its natural domain.
2
The natural domain consists of all x for which ƒ(x) makes sense: all real numbers other than 0
1 1 63
a. Since 4 is in the natural domain, ƒ(4) is defined, and ƒ(4) 4 4
42 16 16
b. Since 0 is not in the natural domain, ƒ(0) is not defined.
1 1
c. Since 1 is in the natural domain, ƒ( 1) 1 1 2
( 1) 2 1
2
10. ƒ(x) x2 with domain [2 $)
x
2 1 16 3
a. Since 4 is in [2 ) ƒ(4) is defined, and ƒ(4) 42
4 2 2
b. Since 0 is not in [2 ) ƒ(0) is not defined. c. Since 1 is not in [2 ) ƒ(1) is not defined
11. ƒ( ) { + 10 with domain [ 10 0)
a. Since 0 is not in [ 10 0) ƒ(0) is not defined. b. Since 9 is not in [ 10 0) ƒ(9) is not defined.
c. Since 10 is in [ 10 0) ƒ( 10) is defined, and ƒ( 10) { 10 + 10 {0 0
12. ƒ( ) {9 2 with domain ( 3 3)
a. Since 0 is in ( 3 3) ƒ(0) is defined, and ƒ(0) {9 0 3
b. Since 3 is not in ( 3 3) ƒ(3) is not defined. . Since 3 is not in ( 3 3) ƒ( 3) is not defined.
13. ƒ(x) 4x 3
a. ƒ( 1) 4( 1) 3 4 3 7 b. ƒ(0) 4(0) 3 0 3 3
c. ƒ(1) 4(1) 3 4 3 1 d. Substitute y for x to obtain ƒ(y) 4y 3
e. Substitute (a + b) for x to obtain ƒ(a + b) 4(a + b) 3
14. ƒ( ) 3 +4
a. ƒ( 1) 3( 1) + 4 3+4 7 b. ƒ(0) 3(0) + 4 0 + 4 4
c. ƒ(1) 3(1) + 4 3+4 1 d. Substitute y for x to obtain ƒ(y) 3y + 4
e. Substitute ( + b) for to obtain ƒ( + b) 3( + b) + 4
15. ƒ(x) x2 + 2x + 3
a. ƒ(0) (0)2 + 2(0) + 3 0+0+3 3 b. ƒ(1) 12 + 2(1) + 3 1+2+3 6
4
© 2024 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
by Waner and Costenoble, Chapter 1 to 9
TEST BANK
,Table of contents
1. Functions And Applications.
2. Nonlinear Functions And Models.
3. Introduction To The Derivative.
4. Techniques Of Differentiation.
5. Applications Of The Derivative.
6. The Integra.
7. Further Integration Techniques And Applications Of The Integral.
8. Functions Of Several Variables.
9. Trigonometric Models.
,Chapter 1 Functions and Applications
Section 1.1
1. Using the table: a. ƒ(0) 2 b. ƒ(2) 05
2. Using the table: a. ƒ( 1) 4 b. ƒ(1) 1
3. Using the table: a. ƒ(2) ƒ( 2) 05 2 25 b. ƒ( 1)ƒ( 2) (4)(2) 8
c. 2ƒ( 1) 2(4) 8
4. Using the table: a. ƒ(1) ƒ( 1) 1 4 5 b. ƒ(1)ƒ( 2) ( )(2) 2
c. 3ƒ( 2) 3(2) 6
5. From the graph, we estimate: a. ƒ(1) 20 b. ƒ(2) 30
In a similar way, we find: c. ƒ(3) 30 d. ƒ(5) 20\\e. ƒ(3) ƒ(2) 30 30 0
f. ƒ(3 2) ƒ(1) 20
6. From the graph, we estimate: a. ƒ(1) 20 b. ƒ(2) 10
In a similar way, we find: c. ƒ(3) 10 d. ƒ(5) 20 \\e. ƒ(3) ƒ(2) 10 10 0
f. ƒ(3 2) ƒ(1) 20
7. From the graph, we estimate: a. ƒ( 1) 0 b. ƒ(1) 3 since the solid dot is on (1 3)
ƒ(3) ƒ( ) 3 ( 3)
In a similar way, we estimate c. ƒ(3) 3 d. Since ƒ(3) 3 and ƒ(1) 3 3
3 1 3 1
3
© 2024 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, Solutions Section 1.1
8. From the graph, we estimate: a. ƒ( 3) 3 b. ƒ( 1) 2 since the solid dot is on ( 1 2)
In a similar way, we estimate c. ƒ(1) 0
ƒ(3) ƒ(1) 2 0
d. Since ƒ(3) 2 and ƒ(1) 0 1
3 1 3 1
1
9. ƒ( ) with its natural domain.
2
The natural domain consists of all x for which ƒ(x) makes sense: all real numbers other than 0
1 1 63
a. Since 4 is in the natural domain, ƒ(4) is defined, and ƒ(4) 4 4
42 16 16
b. Since 0 is not in the natural domain, ƒ(0) is not defined.
1 1
c. Since 1 is in the natural domain, ƒ( 1) 1 1 2
( 1) 2 1
2
10. ƒ(x) x2 with domain [2 $)
x
2 1 16 3
a. Since 4 is in [2 ) ƒ(4) is defined, and ƒ(4) 42
4 2 2
b. Since 0 is not in [2 ) ƒ(0) is not defined. c. Since 1 is not in [2 ) ƒ(1) is not defined
11. ƒ( ) { + 10 with domain [ 10 0)
a. Since 0 is not in [ 10 0) ƒ(0) is not defined. b. Since 9 is not in [ 10 0) ƒ(9) is not defined.
c. Since 10 is in [ 10 0) ƒ( 10) is defined, and ƒ( 10) { 10 + 10 {0 0
12. ƒ( ) {9 2 with domain ( 3 3)
a. Since 0 is in ( 3 3) ƒ(0) is defined, and ƒ(0) {9 0 3
b. Since 3 is not in ( 3 3) ƒ(3) is not defined. . Since 3 is not in ( 3 3) ƒ( 3) is not defined.
13. ƒ(x) 4x 3
a. ƒ( 1) 4( 1) 3 4 3 7 b. ƒ(0) 4(0) 3 0 3 3
c. ƒ(1) 4(1) 3 4 3 1 d. Substitute y for x to obtain ƒ(y) 4y 3
e. Substitute (a + b) for x to obtain ƒ(a + b) 4(a + b) 3
14. ƒ( ) 3 +4
a. ƒ( 1) 3( 1) + 4 3+4 7 b. ƒ(0) 3(0) + 4 0 + 4 4
c. ƒ(1) 3(1) + 4 3+4 1 d. Substitute y for x to obtain ƒ(y) 3y + 4
e. Substitute ( + b) for to obtain ƒ( + b) 3( + b) + 4
15. ƒ(x) x2 + 2x + 3
a. ƒ(0) (0)2 + 2(0) + 3 0+0+3 3 b. ƒ(1) 12 + 2(1) + 3 1+2+3 6
4
© 2024 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
