they illustrate how business concepts are applied in real-world scenarios. Group discussions and practicing sample case studies can aid in refining analytical skills.________________________________________
Student Solutions Manual
for
SINGLE VARIABLE CALCULUS
EIGHTH EDITION
by
DANIEL ANDERSON
University of Iowa
JEFFERY A. COLE
Anoka-Ramsey Community College
DANIEL DRUCKER
Wayne State University
, ■ ABBREVIATIONS AND SYMBOLS
CD concave downward
CU concave upward
D the domain of f
FDT First Derivative Test
HA horizontal asymptote(s)
I interval of convergence
IP inflection point(s)
R radius of convergence
VA vertical asymptote(s)
CAS
indicates the use of a computer algebra system.
PR
1 indicates the use of the Product Rule.
QR
indicates the use of the Quotient Rule.
CR
indicates the use of the Chain Rule.
H
indicates the use of l’Hospital’s Rule.
= indicates the use of Formula j in the Table of Integrals in the back endpapers.
s
indicates the use of the substitution {u = sin x, du = cos x dx}.
c
indicates the use of the substitution {u = cos x, du = —sin x dx}.
they illustrate how business concepts are applied in real-world scenarios. Group discussions and practicing sample case studies can aid in refining analytical skills.________________________________________
■ CONTENTS
■ DIAGNOSTIC TESTS 1
1 ■ FUNCTIONS AND LIMITS 9
1.1 Four Ways to Represent a Function 9
1.2 Mathematical Models: A Catalog of Essential Functions 14
1.3 New Functions from Old Functions 18
1.4 The Tangent and Velocity Problems 25
1.5 The Limit of a Function 27
1.6 Calculating Limits Using the Limit Laws 32
1.7 The Precise Definition of a Limit 37
1.8 Continuity 41
Review 47
Principles of Problem Solving 53
they illustrate how business concepts are applied in real-world scenarios. Group discussions and practicing sample case studies can aid in refining analytical skills.________________________________________
2 ■ DERIVATIVES 57
2.1 Derivatives and Rates of Change 57
, 2.2 The Derivative as a Function 63
2.3 Differentiation Formulas 70
2.4 Derivatives of Trigonometric Functions 77
2.5 The Chain Rule 80
2.6 Implicit Differentiation 86
2.7 Rates of Change in the Natural and Social Sciences 92
2.8 Related Rates 97
2.9 Linear Approximations and Differentials 101
Review 104
Problems Plus 113
they illustrate how business concepts are applied in real-world scenarios. Group discussions and practicing sample case studies can aid in refining analytical skills.________________________________________
3 ■ APPLICATIONS OF DIFFERENTIATION 119
3.1 Maximum and Minimum Values 119
3.2 The Mean Value Theorem 124
3.3 How Derivatives Affect the Shape of a Graph 127
3.4 Limits at Infinity; Horizontal Asymptotes 137
3.5 Summary of Curve Sketching 144
3.6 Graphing with Calculus and Calculators 154
3.7 Optimization Problems 162
3.8 Newton’s Method 174
3.9 Antiderivatives 178
Review 183
Problems Plus 193
4 ■ INTEGRALS 199
4.1 Areas and Distances 199
4.2 The Definite Integral 205
4.3 The Fundamental Theorem of Calculus 211
4.4 Indefinite Integrals and the Net Change Theorem 216
4.5 The Substitution Rule 219
Review 224
Problems Plus 229
5 ■ APPLICATIONS OF INTEGRATION 233
5.1 Areas Between Curves 233
, 5.2 Volumes 240
5.3 Volumes by Cylindrical Shells 248
5.4 Work 253
5.5 Average Value of a Function 256
Review 257
Problems Plus 261
they illustrate how business concepts are applied in real-world scenarios. Group discussions and practicing sample case studies can aid in refining analytical skills.________________________________________
6 ■ INVERSE FUNCTIONS:
Exponential, Logarithmic, and Inverse Trigonometric Functions 265
6.1 Inverse Functions 265
6.2 Exponential Functions and 6.2* The Natural Logarithmic
Their Derivatives 268 Function 285
6.3 Logarithmic 6.3* The Natural Exponential
Functions 275 Function 291
6.4 Derivatives of Logarithmic 6.4* General Logarithmic and
Functions 280 Exponential Functions 298
6.5 Exponential Growth and Decay 302
6.6 Inverse Trigonometric Functions 305
6.7 Hyperbolic Functions 310
6.8 Indeterminate Forms and l’Hospital’s Rule 315
Review 323
Problems Plus 331
7 ■ TECHNIQUES OF INTEGRATION 335
7.1 Integration by Parts 335
7.2 Trigonometric Integrals 341
7.3 Trigonometric Substitution 344
7.4 Integration of Rational Functions by Partial Fractions 350
7.5 Strategy for Integration 358
7.6 Integration Using Tables and Computer Algebra Systems 365
7.7 Approximate Integration 368
7.8 Improper Integrals 376
Review 383
Problems Plus 391
8 ■ FURTHER APPLICATIONS OF INTEGRATION 395
8.1 Arc Length 395
8.2 Area of a Surface of Revolution 399
Student Solutions Manual
for
SINGLE VARIABLE CALCULUS
EIGHTH EDITION
by
DANIEL ANDERSON
University of Iowa
JEFFERY A. COLE
Anoka-Ramsey Community College
DANIEL DRUCKER
Wayne State University
, ■ ABBREVIATIONS AND SYMBOLS
CD concave downward
CU concave upward
D the domain of f
FDT First Derivative Test
HA horizontal asymptote(s)
I interval of convergence
IP inflection point(s)
R radius of convergence
VA vertical asymptote(s)
CAS
indicates the use of a computer algebra system.
PR
1 indicates the use of the Product Rule.
QR
indicates the use of the Quotient Rule.
CR
indicates the use of the Chain Rule.
H
indicates the use of l’Hospital’s Rule.
= indicates the use of Formula j in the Table of Integrals in the back endpapers.
s
indicates the use of the substitution {u = sin x, du = cos x dx}.
c
indicates the use of the substitution {u = cos x, du = —sin x dx}.
they illustrate how business concepts are applied in real-world scenarios. Group discussions and practicing sample case studies can aid in refining analytical skills.________________________________________
■ CONTENTS
■ DIAGNOSTIC TESTS 1
1 ■ FUNCTIONS AND LIMITS 9
1.1 Four Ways to Represent a Function 9
1.2 Mathematical Models: A Catalog of Essential Functions 14
1.3 New Functions from Old Functions 18
1.4 The Tangent and Velocity Problems 25
1.5 The Limit of a Function 27
1.6 Calculating Limits Using the Limit Laws 32
1.7 The Precise Definition of a Limit 37
1.8 Continuity 41
Review 47
Principles of Problem Solving 53
they illustrate how business concepts are applied in real-world scenarios. Group discussions and practicing sample case studies can aid in refining analytical skills.________________________________________
2 ■ DERIVATIVES 57
2.1 Derivatives and Rates of Change 57
, 2.2 The Derivative as a Function 63
2.3 Differentiation Formulas 70
2.4 Derivatives of Trigonometric Functions 77
2.5 The Chain Rule 80
2.6 Implicit Differentiation 86
2.7 Rates of Change in the Natural and Social Sciences 92
2.8 Related Rates 97
2.9 Linear Approximations and Differentials 101
Review 104
Problems Plus 113
they illustrate how business concepts are applied in real-world scenarios. Group discussions and practicing sample case studies can aid in refining analytical skills.________________________________________
3 ■ APPLICATIONS OF DIFFERENTIATION 119
3.1 Maximum and Minimum Values 119
3.2 The Mean Value Theorem 124
3.3 How Derivatives Affect the Shape of a Graph 127
3.4 Limits at Infinity; Horizontal Asymptotes 137
3.5 Summary of Curve Sketching 144
3.6 Graphing with Calculus and Calculators 154
3.7 Optimization Problems 162
3.8 Newton’s Method 174
3.9 Antiderivatives 178
Review 183
Problems Plus 193
4 ■ INTEGRALS 199
4.1 Areas and Distances 199
4.2 The Definite Integral 205
4.3 The Fundamental Theorem of Calculus 211
4.4 Indefinite Integrals and the Net Change Theorem 216
4.5 The Substitution Rule 219
Review 224
Problems Plus 229
5 ■ APPLICATIONS OF INTEGRATION 233
5.1 Areas Between Curves 233
, 5.2 Volumes 240
5.3 Volumes by Cylindrical Shells 248
5.4 Work 253
5.5 Average Value of a Function 256
Review 257
Problems Plus 261
they illustrate how business concepts are applied in real-world scenarios. Group discussions and practicing sample case studies can aid in refining analytical skills.________________________________________
6 ■ INVERSE FUNCTIONS:
Exponential, Logarithmic, and Inverse Trigonometric Functions 265
6.1 Inverse Functions 265
6.2 Exponential Functions and 6.2* The Natural Logarithmic
Their Derivatives 268 Function 285
6.3 Logarithmic 6.3* The Natural Exponential
Functions 275 Function 291
6.4 Derivatives of Logarithmic 6.4* General Logarithmic and
Functions 280 Exponential Functions 298
6.5 Exponential Growth and Decay 302
6.6 Inverse Trigonometric Functions 305
6.7 Hyperbolic Functions 310
6.8 Indeterminate Forms and l’Hospital’s Rule 315
Review 323
Problems Plus 331
7 ■ TECHNIQUES OF INTEGRATION 335
7.1 Integration by Parts 335
7.2 Trigonometric Integrals 341
7.3 Trigonometric Substitution 344
7.4 Integration of Rational Functions by Partial Fractions 350
7.5 Strategy for Integration 358
7.6 Integration Using Tables and Computer Algebra Systems 365
7.7 Approximate Integration 368
7.8 Improper Integrals 376
Review 383
Problems Plus 391
8 ■ FURTHER APPLICATIONS OF INTEGRATION 395
8.1 Arc Length 395
8.2 Area of a Surface of Revolution 399
