Calculus: Graphical, Numerical, Algebraic, AP Edition

by Finney, Ross L.; Demana, Franklin; Waits, Bert K.; Kennedy, Daniel

• ISBN13: 9780132014083
• ISBN10: 0132014084
• Edition: 3rd
• Format: Hardcover
• Copyright: 2006-02-01
• Publisher: Savvas Learning Company

Table of Contents

Prerequisites for Calculus	2	(56)
Lines	3	(9)
Increments
Slope of a Line
Parallel and Perpendicular Lines
Equations of Lines
Applications
Functions and Graphs	12	(10)
Functions
Domains and Ranges
Viewing and Interpreting Graphs
Even Functions and Odd Functions---Symmetry
Functions Defined in Pieces
Absolute Value Function
Composite Functions
Exponential Functions	22	(8)
Exponential Growth
Exponential Decay
Applications
The Number e
Parametric Equations	30	(7)
Relations
Circles
Ellipses
Lines and Other Curves
Functions and Logarithms	37	(9)
One-to-One Functions
Inverses
Finding Inverses
Logarithmic Functions
Properties of Logarithms
Applications
Trigonometric Functions	46	(12)
Radian Measure
Graphs of Trigonometric Functions
Periodicity
Even and Odd Trigonometric Functions
Transformations of Trigonometric Graphs
Inverse Trigonometric Functions
Key Terms	55	(1)
Review Exercises	56	(2)
Limits and Continuity	58	(40)
Rates of Change and Limits	59	(11)
Average and Instantaneous Speed
Definition of Limit
Properties of Limits
One-sided and Two-sided Limits
Sandwich Theorem
Limits Involving Infinity	70	(8)
Finite Limits as x → ± ∞
Sandwich Theorem Revisited
Infinite Limits as x → α
End Behavior Models
``Seeing'' Limits as x → ± ∞
Continuity	78	(9)
Continuity at a Point
Continuous Functions
Algebraic Combinations
Composites
Intermediate Value Theorem for Continuous Functions
Rates of Change and Tangent Lines	87	(11)
Average Rates of Change
Tangent to a Curve
Slope of a Curve
Normal to a Curve
Speed Revisited
Key Terms	95	(1)
Review Exercises	95	(3)
Derivatives	98	(88)
Derivative of a Function	99	(10)
Definition of a Derivative
Notation
Relationship Between the Graphs of f and f'
Graphing the Derivative from Data
One-sided Derivatives
Differentiability	109	(7)
How f'(a) Might Fail to Exist
Differentiability Implies Local Linearity
Derivatives on a Calculator
Differentiability Implies Continuity
Intermediate Value Theorem for Derivatives
Rules for Differentiation	116	(11)
Positive Integer Powers, Multiples, Sums, and Differences
Products and Quotients
Negative Integer Powers of x
Second and Higher Order Derivatives
Velocity and Other Rates of Change	127	(14)
Instantaneous Rates of Change
Motion along a Line
Sensitivity to Change
Derivatives in Economics
Derivatives of Trigonometric Functions	141	(7)
Derivative of the Sine Function
Derivative of the Cosine Function
Simple Harmonic Motion
Jerk
Derivatives of Other Basic Trigonometric Functions
Chain Rule	148	(9)
Derivative of a Composite Function
``Outside-Inside'' Rule
Repeated Use of the Chain Rule
Slopes of Parametrized Curves
Power Chain Rule
Implicit Differentiation	157	(8)
Implicitly Defined Functions
Lenses, Tangents, and Normal Lines
Derivatives of Higher Order
Rational Powers of Differentiable Functions
Derivatives of Inverse Trigonometric Functions	165	(7)
Derivatives of Inverse Functions
Derivative of the Arcsine
Derivative of the Arctangent
Derivative of the Arcsecant
Derivatives of the Other Three
Derivatives of Exponential and Logarithmic Functions	172	(14)
Derivative of ex
Derivative of αx
Derivative of In x
Derivative of logαx
Power Rule for Arbitrary Real Powers
Calculus at Work	181	(1)
Key Terms	181	(1)
Review Exercises	181	(5)
Applications of Derivatives	186	(76)
Extreme Values of Functions	187	(9)
Absolute (Global) Extreme Values
Local (Relative) Extreme Values
Finding Extreme Values
Mean Value Theorem	196	(9)
Mean Value Theorem
Physical Interpretation
Increasing and Decreasing Functions
Other Consequences
Connecting f' and f'' with the Graph of f	205	(14)
First Derivative Test for Local Extrema
Concavity
Points of Inflection
Second Derivative Test for Local Extrema
Learning about Functions from Derivatives
Modeling and Optimization	219	(14)
Examples from Mathematics
Examples from Business and Industry
Examples from Economics
Modeling Discrete Phenomena with Differentiable Functions
Linearization and Newton's Method	233	(13)
Linear Approximation
Newton's Method
Differentials
Estimating Change with Differentials
Absolute, Relative, and Percentage Change
Sensitivity to Change
Related Rates	246	(16)
Related Rate Equations
Solution Strategy
Simulating Related Motion
Key Terms	255	(1)
Review Exercises	256	(6)
The Definite Integral	262	(58)
Estimating with Finite Sums	263	(11)
Distance Traveled
Rectangular Approximation Method (RAM)
Volume of a Sphere
Cardiac Output
Definite Integrals	274	(11)
Riemann Sums
Terminology and Notation of Integration
Definite Integral and Area
Constant Functions
Integrals on a Calculator
Discontinuous Integrable Functions
Definite Integrals and Antiderivatives	285	(9)
Properties of Definite Integrals
Average Value of a Function
Mean Value Theorem for Definite Integrals
Connecting Differential and Integral Calculus
Fundamental Theorem of Calculus	294	(12)
Fundamental Theorem, Part 1
Graphing the Function ∫ x/α f(t)dt
Fundamental Theorem, Part 2
Area Connection
Analyzing Antiderivatives Graphically
Trapezoidal Rule	306	(14)
Trapezoidal Approximations
Other Algorithms
Error Analysis
Key Terms	315	(1)
Review Exercises	315	(4)
Calculus at Work	319	(1)
Differential Equations and Mathematical Modeling	320	(58)
Slope Fields and Euler's Method	321	(10)
Differential Equations
Slope Fields
Euler's Method
Antidifferentiation by Substitution	331	(10)
Indefinite Integrals
Leibniz Notation and Antiderivatives
Substitution in Indefinite Integrals
Substitution in Definite Integrals
Antidifferentiation by Parts	341	(9)
Product Rule in Integral Form
Solving for the Unknown Integral
Tabular Integration
Inverse Trigonometric and Logarithmic Functions
Exponential Growth and Decay	350	(12)
Separable Differential Equations
Law of Exponential Change
Continuously Compounded Interest
Radioactivity
Modeling Growth with Other Bases
Newton's Law of Cooling
Logistic Growth	362	(16)
How Populations Grow
Partial Fractions
The Logistic Differential Equation
Logistic Growth Models
Key Terms	372	(1)
Review Exercises	372	(4)
Calculus at Work	376	(2)
Applications of Definite Integrals	378	(41)
Integral As Net Change	379	(11)
Linear Motion Revisited
General Strategy
Consumption Over Time
Net Change from Data
Work
Areas in the Plane	390	(9)
Area Between Curves
Area Enclosed by Intersecting Curves
Boundaries with Changing Functions
Integrating with Respect to y
Saving Time with Geometry Formulas
Volumes	399	(13)
Volume As an Integral
Square Cross Sections
Circular Cross Sections
Cylindrical Shells
Other Cross Sections
Lengths of Curves	412	(7)
A Sine Wave
Length of Smooth Curve
Vertical Tangents, Corners, and Cusps
Applications from Science and Statistics	419	(15)
Work Revisited
Fluid Force and Fluid Pressure
Normal Probabilities
Calculus at Work	430	(1)
Key Terms	430	(1)
Review Exercises	430	(4)
Sequences, L'Hopital's Rule, and Improper Integrals	434	(38)
Sequences	435	(9)
Defining a Sequence
Arithmetic and Geometric Sequences
Graphing a Sequence
Limit of a Sequence
L'Hopital's Rule	444	(9)
Indeterminate Form 0/0
Indeterminate Forms ∞/∞, ∞ 0, and ∞ - ∞
Indeterminate Forms 1∞, 00, ∞0
Relative Rates of Growth	453	(6)
Comparing Rates of Growth
Using L'Hopital's Rule to Compare Growth Rates
Sequential versus Binary Search
Improper Integrals	459	(13)
Infinite Limits of Integration
Integrands with Infinite Discontinuities
Test for Convergence and Divergence
Applications
Key Terms	470	(1)
Review Exercises	470	(2)
Infinite Series	472	(58)
Power Series	473	(11)
Geometric Series
Representing Functions by Series
Differentiation and Integration
Identifying a Series
Taylor Series	484	(11)
Constructing a Series
Series for sin x and cos x
Beauty Bare
Maclaurin and Taylor Series
Combining Taylor Series
Table of Maclaurin Series
Taylor's Theorem	495	(8)
Taylor Polynomials
The Remainder
Remainder Estimation Theorem
Euler's Formula
Radius of Convergence	503	(10)
Convergence
nth-Term Test
Comparing Nonnegative Series
Ratio Test
Endpoint Convergence
Testing Convergence at Endpoints	513	(17)
Integral Test
Harmonic Series and p-series
Comparison Tests
Alternating Series
Absolute and Conditional Convergence
Intervals of Convergence
A Word of Caution
Key Terms	526	(1)
Review Exercises	526	(3)
Calculus at Work	529	(1)
Parametric, Vector, and Polar Functions	530	(88)
Parametric Functions	531	(7)
Parametric Curves in the Plane
Slope and Concavity
Arc Length
Cycloids
Vectors in the Plane	538	(10)
Two-Dimensional Vectors
Vector Operations
Modeling Planar Motion
Velocity, Acceleration, and Speed
Displacement and Distance Traveled
Polar Functions	548	(14)
Polar Coordinates
Polar Curves
Slopes of Polar Curves
Areas Enclosed by Polar Curves
A Small Polar Gallery
Key Terms	559	(1)
Review Exercises	560	(2)
APPENDIX
Formulas from Precalculus Mathematics	562	(4)
Mathematical Induction	566	(3)
Using the Limit Definition	569	(8)
Proof of the Chain Rule	577	(1)
Conic Sections	578	(25)
Hyperbolic Functions	603	(9)
A Brief Table of Integrals	612	(6)
Glossary	618	(11)
Selected Answers	629	(51)
Applications Index	680	(4)
Index	684