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SOLUTIONS CONTENTS
Survey/Applied/Business Calculus
TAN 6th Ed
CHAPTER 1 PRELIMINARIES
1.1 Precalculus Review I 1
1.2 Precalculus Review II 12
1.3 The Cartesian Coordinate System 22
1.4 Straight Lines 29
Review Exercises, Group Discussion, Exploring with Technology 42
CHAPTER 2 FUNCTIONS, LIMITS, AND THE DERIVATIVE
2.1 Functions and Their Graphs 52
2.2 The Algebra of Functions 77
2.3 Functions and Mathematical Models 85
2.4 Limits 104
2.5 One-Sided Limits and Continuity 117
2.6 The Derivative 129
Review Exercises, Group Discussion, Exploring with Technology 148
CHAPTER 3 DIFFERENTIATION
3.1 Basic Rules of Differentiation 165
3.2 The Product and Quotient Rules 177
3.3 The Chain Rule 193
3.4 Marginal Functions in Economics 209
3.5 Higher-Order Derivatives 219
3.6 Implicit Differentiation and Related Rates 227
3.7 Differentials 245
Review Exercises, Group Discussion, Exploring with Technology 253
CHAPTER 4 APPLICATIONS OF THE DERIVATIVE
4.1 Applications of the First Derivative 268
4.2 Applications of the Second Derivative 292
4.3 Curve Sketching 313
4.4 Optimization I 349
4.5 Optimization II 371
Review Exercises, Group Discussion, Exploring with Technology 383
CHAPTER 6 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
5.1 Exponential Functions  409
5.2 Logarithmic Functions  418
5.3 Compound Interest  425
5.4 Differentiation of Exponential Functions  433
5.5 Differentiation of Logarithmic Functions  451
5.6 Exponential Functions as Mathematical Models  459
Review Exercises, Group Discussion, Exploring with Technology  471
CHAPTER 6 INTEGRATION
6.1 Antiderivatives and the Rules of Integration  483
6.2 Integration by Substitution  495
6.3 Area and the Definite Integral  508
6.4 The Fundamental Theorem of Calculus  513
6.5 Evaluating Definite Integrals  520
6.6 Area Between Two Curves  529
6.7 Applications of the Definite Integral to Business and Economics  543
Review Exercises, Group Discussion, Exploring with Technology  548
CHAPTER 7 ADDITIONAL TOPICS IN INTEGRATION
7.1 Integration by Parts  562
7.2 Integration Using Tables of Integrals  573
7.3 Numerical Integration  582
7.4 Improper Integrals  595
7.5 Applications of Probability to Calculus  602
Review Exercises, Group Discussion, Exploring with Technology  608
CHAPTER 8 CALCULUS OF SEVERAL VARIABLES
8.1 Functions of Several Variables 619
8.2 Partial Derivatives  625
8.3 Maxima and Minima of Functions of Several Variables  634
8.4 The Method of Least Squares  646
8.5 Constrained Maxima and Minima and the Method of Lagrange Multipliers 661
8.6 Double Integrals 673
Review Exercises, Group Discussion, Exploring with Technology 682

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