, CONTENTS
Chapter 1 Functions, Graphs, and Limits ............................................................... 1
Chapter 2 Differentiation.......................................................................................66
Chapter 3 Applications of the Derivative ...........................................................145
Chapter 4 Exponential and Logarithmic Functions ...........................................247
Chapter 5 Integration and Its Applications.........................................................309
Chapter 6 Techniques of Integration ..................................................................367
Chapter 7 Functions of Several Variables ..........................................................416
Chapter 8 Trigonometric Functions....................................................................497
Chapter 9 Probability and Calculus ....................................................................548
Chapter 10 Series and Taylor Polynomials ..........................................................580
Chapter 11 Differential Equations ........................................................................646
Appendix A Precalculus Review ............................................................................683
Appendix B Alternate Introduction to the Fundamental Theorem
of Calculus ..........................................................................................700
Checkpoints .............................................................................................................704
Tech Tutors .............................................................................................................757
, C H A P T E R 1
Functions, Graphs, and Limits
Section 1.1 The Cartesian Plane and the Distance Formula ....................................2
Section 1.2 Graphs of Equations ...............................................................................8
Section 1.3 Lines in the Plane and Slope ................................................................17
Quiz Yourself ...............................................................................................................27
Section 1.4 Functions...............................................................................................30
Section 1.5 Limits ....................................................................................................38
Section 1.6 Continuity .............................................................................................45
Review Exercises ..........................................................................................................51
Test Yourself ...............................................................................................................62
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, C H A P T E R 1
Functions, Graphs, and Limits
Section 1.1 The Cartesian Plane and the Distance Formula
Skills Warm Up
1. (3 − 6)2 + ⎡⎣1 − ( −5)⎤⎦
2
= (−3)2 + 62 8. (6 − 2) + ( − 2 − y )
2 2
= 52
2
= 9 + 36 ⎛ − 2) + ( −2 − y ) ⎞⎟ = ( )
2
(6
2 2
⎜ 52
⎝ ⎠
= 45
= 3 5
(6 − 2) + ( −2 − y ) = 52
2 2
42 + ( −2 − y ) = 52
2
(−2 − 0)2 ⎣ 7 − ( −3)⎤⎦ (−2)2 + ( −4)
2 2
2. + ⎡− = 16 + ( −2 − y ) = 52
2
= 4 + 16 (−2 − y )
2
= 36
= 20 −2 − y = ± 6
= 2 5 − y = ±6 + 2
y = ∓6 − 2
5 + ( −4) 1
3. = y = −8, 4
2 2
−3 + ( −1) −4 x + ( −5)
4. = = −2 9. = 7
2 2 2
x + ( −5) = 14
5. 27 + 12 = 3 3 + 2 3 = 5 3
x = 19
6. 8 − 18 = 2 2 − 3 2 = − 2 −7 + y
10. = −3
2
7. (3 − x ) 2 + (7 − 4)
2
= 45 −7 + y = −6
2
y =1
⎛ + (7 − 4) ⎞⎟ = ( )
2
(3 − x )
2 2
⎜ 45
⎝ ⎠
(3 − x ) 2 + (7 − 4) = 45
2
(3 − x )
2
+ 32 = 45
(3 − x ) 2 + 9 = 45
(3 − x )
2
= 36
3 − x = ±6
− x = −3 ± 6
x = 3∓ 6
x = −3, 9
y y
1. 2.
(−5, 3) 3 (−3, 5) 6
2
4
1 (2, 0)
x 2 (5, 1)
−5 −4 −3 −2 −1 2 3
−2
(1, −1) x
−4 −2 2 4 6
(−2, − 4) −3 (−6, − 1) −2 (2, −2)
−4 −4 (0, −4)
−5
(1, −6) −6
−6
2 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Chapter 1 Functions, Graphs, and Limits ............................................................... 1
Chapter 2 Differentiation.......................................................................................66
Chapter 3 Applications of the Derivative ...........................................................145
Chapter 4 Exponential and Logarithmic Functions ...........................................247
Chapter 5 Integration and Its Applications.........................................................309
Chapter 6 Techniques of Integration ..................................................................367
Chapter 7 Functions of Several Variables ..........................................................416
Chapter 8 Trigonometric Functions....................................................................497
Chapter 9 Probability and Calculus ....................................................................548
Chapter 10 Series and Taylor Polynomials ..........................................................580
Chapter 11 Differential Equations ........................................................................646
Appendix A Precalculus Review ............................................................................683
Appendix B Alternate Introduction to the Fundamental Theorem
of Calculus ..........................................................................................700
Checkpoints .............................................................................................................704
Tech Tutors .............................................................................................................757
, C H A P T E R 1
Functions, Graphs, and Limits
Section 1.1 The Cartesian Plane and the Distance Formula ....................................2
Section 1.2 Graphs of Equations ...............................................................................8
Section 1.3 Lines in the Plane and Slope ................................................................17
Quiz Yourself ...............................................................................................................27
Section 1.4 Functions...............................................................................................30
Section 1.5 Limits ....................................................................................................38
Section 1.6 Continuity .............................................................................................45
Review Exercises ..........................................................................................................51
Test Yourself ...............................................................................................................62
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, C H A P T E R 1
Functions, Graphs, and Limits
Section 1.1 The Cartesian Plane and the Distance Formula
Skills Warm Up
1. (3 − 6)2 + ⎡⎣1 − ( −5)⎤⎦
2
= (−3)2 + 62 8. (6 − 2) + ( − 2 − y )
2 2
= 52
2
= 9 + 36 ⎛ − 2) + ( −2 − y ) ⎞⎟ = ( )
2
(6
2 2
⎜ 52
⎝ ⎠
= 45
= 3 5
(6 − 2) + ( −2 − y ) = 52
2 2
42 + ( −2 − y ) = 52
2
(−2 − 0)2 ⎣ 7 − ( −3)⎤⎦ (−2)2 + ( −4)
2 2
2. + ⎡− = 16 + ( −2 − y ) = 52
2
= 4 + 16 (−2 − y )
2
= 36
= 20 −2 − y = ± 6
= 2 5 − y = ±6 + 2
y = ∓6 − 2
5 + ( −4) 1
3. = y = −8, 4
2 2
−3 + ( −1) −4 x + ( −5)
4. = = −2 9. = 7
2 2 2
x + ( −5) = 14
5. 27 + 12 = 3 3 + 2 3 = 5 3
x = 19
6. 8 − 18 = 2 2 − 3 2 = − 2 −7 + y
10. = −3
2
7. (3 − x ) 2 + (7 − 4)
2
= 45 −7 + y = −6
2
y =1
⎛ + (7 − 4) ⎞⎟ = ( )
2
(3 − x )
2 2
⎜ 45
⎝ ⎠
(3 − x ) 2 + (7 − 4) = 45
2
(3 − x )
2
+ 32 = 45
(3 − x ) 2 + 9 = 45
(3 − x )
2
= 36
3 − x = ±6
− x = −3 ± 6
x = 3∓ 6
x = −3, 9
y y
1. 2.
(−5, 3) 3 (−3, 5) 6
2
4
1 (2, 0)
x 2 (5, 1)
−5 −4 −3 −2 −1 2 3
−2
(1, −1) x
−4 −2 2 4 6
(−2, − 4) −3 (−6, − 1) −2 (2, −2)
−4 −4 (0, −4)
−5
(1, −6) −6
−6
2 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
