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CHAPTER 1 FUNCTIONS
1.1 Lines and Linear Functions ......................................................................................................... 28
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1.2 The Least Squares Line ............................................................................................................... 39
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1.3 Properties of Functions ................................................................................................................ 46
1.4 Quadratic Functions; Translation and Reflection ........................................................................ 54
1.5 Polynomial and Rational Functions............................................................................................. 66
Chapter 1 Review Exercises .................................................................................................................. 76
CHAPTER 2 EXPONENTIAL, LOGARITHMIC, AND TRIGONOMETRIC FUNCTIONS
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Extended Application: Using Extrapolation to Predict Life Expectancy............................................... 88
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2.1 Exponential Functions ................................................................................................................. 89
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Extended Application: Power Functions ............................................................................................... 133
CHAPTER 3 THE DERIVATIVE
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3.1 Limits........................................................................................................................................... 134
3.2 Continuity .................................................................................................................................... 145
3.3 Rates of Change........................................................................................................................... 152
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3.4 Definition of the Derivative......................................................................................................... 163
3.5 Graphical Differentiation............................................................................................................. 178
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Chapter 3 Review Exercises .................................................................................................................. 182
Extended Application: A Model for Drugs Administered Intravenously .............................................. 194
, CHAPTER 4 CALCULATING THE DERIVATIVE
4.1 Techniques for Finding Derivatives ............................................................................................ 196
4.2 Derivatives of Products and Quotients ........................................................................................ 205
4.3 The Chain Rule............................................................................................................................ 212
4.4 Derivatives of Exponential Functions ......................................................................................... 221
4.5 Derivatives of Logarithmic Functions ......................................................................................... 239
4.6 Derivatives of Trigonometric Functions...................................................................................... 248
Chapter 4 Review Exercises .................................................................................................................. 253
Extended Application: Managing Renewable Resources ...................................................................... 263
CHAPTER 5 GRAPHS AND THE DERIVATIVE
5.1 Increasing and Decreasing Functions .......................................................................................... 265
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5.2 Relative Extrema ......................................................................................................................... 278
5.3 Higher Derivatives, Concavity, and the Second Derivative Test ................................................ 293
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5.4 Curve Sketching .......................................................................................................................... 316
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Chapter 5 Review Exercises .................................................................................................................. 336
Extended Application: A Drug Concentration Model for Orally Administered Medications ............... 360
CHAPTER 6 APPLICATIONS OF THE DERIVATIVE
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6.1 Absolute Extrema ........................................................................................................................
6.2 Applications of Extrema ..............................................................................................................
6.3 Implicit Differentiation................................................................................................................
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6.4 Related Rates ............................................................................................................................... 399
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6.5 Differentials: Linear Approximation ........................................................................................... 406
Chapter 6 Review Exercises .................................................................................................................. 410
Extended Application: A Total Cost Model for a Training Program..................................................... 421
CHAPTER 7 INTEGRATION
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7.1 Antiderivatives............................................................................................................................. 423
7.2 Substitution..................................................................................................................................
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429
7.3 Area and the Definite Integral ..................................................................................................... 437
7.4 The Fundamental Theorem of Calculus....................................................................................... 451
7.5 The Area Between Two Curves................................................................................................... 465
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Chapter 7 Review Exercises .................................................................................................................. 480
Extended Application: Estimating Depletion Dates for Minerals.......................................................... 493
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CHAPTER 8 FURTHER TECHNIQUES AND APPLICATIONS OF INTEGRATION
8.1 Numerical Integration.................................................................................................................. 494
8.2 Integration by Parts...................................................................................................................... 508
8.3 Volume and Average Value......................................................................................................... 517
8.4 Improper Integrals ....................................................................................................................... 525
Chapter 8 Review Exercises .................................................................................................................. 533
Extended Application: Flow Systems .................................................................................................... 545
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