Calculus: Early Transcendentals 3rd Edition by William Briggs, ISBN-13: 978-0134763644

Calculus: Early Transcendentals 3rd Edition by William Briggs, ISBN-13: 978-0134763644

[PDF eBook eTextbook]

• Publisher: ‎ Pearson; 3rd edition (January 2, 2018)
• Language: ‎ English
• ‎1344 pages (Large file size: 63 MB)
  
• ISBN-10: ‎ 0134763645
• ISBN-13: ‎ 978-0134763644

For 3- to 4-semester courses covering single-variable and multivariable calculus, taken by students of mathematics, engineering, natural sciences, or economics.

The most successful new calculus text in the last two decades.

The much-anticipated 3rd Edition of Briggs’ Calculus Series retains its hallmark features while introducing important advances and refinements. Briggs, Cochran, Gillett, and Schulz build from a foundation of meticulously crafted exercise sets, then draw students into the narrative through writing that reflects the voice of the instructor. Examples are stepped out and thoughtfully annotated, and figures are designed to teach rather than simply supplement the narrative. The groundbreaking eBook contains approximately 700 Interactive Figures that can be manipulated to shed light on key concepts.

Table of Contents:

Contents
Preface
New to the Third Edition
New to MyLab Math
Noteworthy Features
Accuracy Checkers
Reviewers
Credits
Chapter 1
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 10
Chapter 12
Chapter 13
Chapter 15
Chapter 16
1 Functions
Chapter Preview
1.1 Review of Functions
Quick Check 1
Solution
Solution
Solution
Quick Check 2
Composite Functions
Solution
Solution
Solution
Solution
Solution
Quick Check 3
Secant Lines and the Difference Quotient
Solution
Solution
Quick Check 4
Symmetry
Quick Check 5
Solution
Section 1.1 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
1.2 Representing Functions
Using Formulas
Quick Check 1
Using Graphs
Linear Functions
Solution
Solution
Piecewise Functions
Solution
Solution
Power Functions
Quick Check 2
Root Functions
Rational Functions
Quick Check 3
Solution
Using Tables
Using Words
Solution
Solution
Transformations of Functions and Graphs
Solution
Quick Check 4
Solution
Section 1.2 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
1.3 Inverse, Exponential, and Logarithmic Functions
Exponential Functions
Properties of Exponential Functions
Quick Check 1
Quick Check 2
The Natural Exponential Function
Inverse Functions
Quick Check 3
One-to-One Functions
Solution
Existence of Inverse Functions
Quick Check 4
Solution
Finding Inverse Functions
Solution
Quick Check 5
Graphing Inverse Functions
Solution
Logarithmic Functions
Properties of Logarithmic Functions
Quick Check 6
Solution
Change of Base
Solution
Section 1.3 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
1.4 Trigonometric Functions and Their Inverses
Radian Measure
Quick Check 1
Trigonometric Functions
Solution
Quick Check 2
Trigonometric Identities
Reciprocal Identities
Pythagorean Identities
Double- and Half-Angle Identities
Quick Check 3
Solution
Graphs of the Trigonometric Functions
Transforming Graphs
Inverse Trigonometric Functions
Inverse Sine and Cosine
Quick Check 4
Solution
Graphs and Properties
Solution
Solution
Other Inverse Trigonometric Functions
Solution
Quick Check 5
Section 1.4 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
Chapter 1 Review Exercises
Chapter 1 Guided Projects
2 Limits
Chapter Preview
2.1 The Idea of Limits
Average Velocity
Solution
Quick Check 1
Instantaneous Velocity
Quick Check 2
Solution
Slope of the Tangent Line
Quick Check 3
Section 2.1 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
2.2 Definitions of Limits
Solution
Quick Check 1
Solution
One-Sided Limits
Solution
Solution
Solution
Quick Check 2
Section 2.2 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
2.3 Techniques for Computing Limits
Limits of Linear Functions
Solution
Limit Laws
Solution
Limits of Polynomial and Rational Functions
Quick Check 1
Solution
Quick Check 2
Solution
One-Sided Limits
Solution
Other Techniques
Solution
Quick Check 3
Solution
An Important Limit
Solution
The Squeeze Theorem
Solution
Quick Check 4
Trigonometric Limits
Solution
Section 2.3 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
2.4 Infinite Limits
An Overview
Infinite Limits
Solution
Quick Check 1
Solution
Finding Infinite Limits Analytically
Solution
Quick Check 2
Solution
Quick Check 3
Solution
Quick Check 4
Solution
Section 2.4 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
2.5 Limits at Infinity
Limits at Infinity and Horizontal Asymptotes
Solution
Quick Check 1
Infinite Limits at Infinity
Quick Check 2
Solution
End Behavior
Solution
Solution
Quick Check 3
Solution
End Behavior for and ln x
Solution
Quick Check 4
Section 2.5 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
2.6 Continuity
Continuity at a Point
Solution
Quick Check 1
Solution
Solution
Solution
Solution
Continuity on an Interval
Quick Check 2
Solution
Functions Involving Roots
Solution
Quick Check 3
Continuity of Transcendental Functions
Trigonometric Functions
Exponential Functions
Inverse Functions
Solution
Quick Check 4
Intermediate Value Theorem
Solution
Quick Check 5
Section 2.6 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
2.7 Precise Definitions of Limits
Moving Toward a Precise Definition
Solution
Quick Check 1
A Precise Definition
Solution
Quick Check 2
Solution
Limit Proofs
Solution
Solution
Justifying Limit Laws
Solution
Infinite Limits
Solution
Quick Check 3
Limits at Infinity
Section 2.7 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
Chapter 2 Review Exercises
Chapter 2 Guided Projects
3 Derivatives
Chapter Preview
3.1 Introducing the Derivative
Solution
Quick Check 1
Tangent Lines and Rates of Change
Quick Check 2
Solution
Solution
Quick Check 3
The Derivative
Solution
Quick Check 4
Interpreting the Derivative
Solution
Solution
Section 3.1 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
3.2 The Derivative as a Function
The Derivative Function
Solution
Quick Check 1
Derivative Notation
Quick Check 2
Solution
Quick Check 3
Quick Check 4
Solution
Graphs of Derivatives
Solution
Solution
Quick Check 5
Solution
Continuity
Quick Check 6
Solution
Section 3.2 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
3.3 Rules of Differentiation
The Constant and Power Rules for Derivatives
Quick Check 1
Solution
Quick Check 2
Constant Multiple Rule
Solution
Sum Rule
Quick Check 3
Solution
The Derivative of the Natural Exponential Function
Quick Check 4
Slopes of Tangent Lines
Solution
Solution
Quick Check 5
Higher-Order Derivatives
Solution
Quick Check 6
Section 3.3 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
3.4 The Product and Quotient Rules
Product Rule
Solution
Quick Check 1
Quotient Rule
Solution
Quick Check 2
Solution
Extending the Power Rule to Negative Integers
Quick Check 3
Solution
Combining Derivative Rules
Solution
Section 3.4 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
3.5 Derivatives of Trigonometric Functions
Two Special Limits
Solution
Quick Check 1
Derivatives of Sine and Cosine Functions
Quick Check 2
Solution
Derivatives of Other Trigonometric Functions
Solution
Quick Check 3
Solution
Higher-Order Trigonometric Derivatives
Quick Check 4
Solution
Section 3.5 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
3.6 Derivatives as Rates of Change
One-Dimensional Motion
Quick Check 1
Solution
Quick Check 2
Solution
Quick Check 3
Solution
Quick Check 4
Growth Models
Solution
Quick Check 5
Economics and Business
Solution
Quick Check 6
Solution
Section 3.6 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
3.7 The Chain Rule
Quick Check 1
Chain Rule Formulas
Quick Check 2
Solution
Solution
Solution
Solution
Chain Rule for Powers
Solution
The Composition of Three or More Functions
Solution
Quick Check 3
Solution
Proof of the Chain Rule
Section 3.7 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
3.8 Implicit Differentiation
Quick Check 1
Solution
Solution
Quick Check 2
Slopes of Tangent Lines
Quick Check 3
Solution
Solution
Higher-Order Derivatives of Implicit Functions
Solution
Section 3.8 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
3.9 Derivatives of Logarithmic and Exponential Functions
The Derivative of
Quick Check 1
Solution
Quick Check 2
The Derivative of bx
Solution
Solution
Quick Check 3
The General Power Rule
Solution
Solution
Solution
Derivatives of General Logarithmic Functions
Quick Check 4
Solution
Quick Check 5
Logarithmic Differentiation
Solution
Section 3.9 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
3.10 Derivatives of Inverse Trigonometric Functions
Inverse Sine and Its Derivative
Quick Check 1
Solution
Derivatives of Inverse Tangent and Secant
Inverse Tangent
Quick Check 2
Inverse Secant
Quick Check 3
Solution
Solution
Quick Check 4
Derivatives of Inverse Functions in General
Solution
Quick Check 5
Solution
Solution
Section 3.10 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
3.11 Related Rates
Solution
Quick Check 1
Solution
Quick Check 2
Solution
Quick Check 3
Solution
Quick Check 4
Section 3.11 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
Chapter 3 Review Exercises
Chapter 3 Guided Projects
4 Applications of the Derivative
Chapter Preview
4.1 Maxima and Minima
Absolute Maxima and Minima
Quick Check 1
Solution
Local Maxima and Minima
Solution
Critical Points
Solution
Quick Check 2
Locating Absolute Maxima and Minima
Solution
Solution
Section 4.1 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
4.2 Mean Value Theorem
Rolle’s Theorem
Quick Check 1
Solution
Mean Value Theorem
Quick Check 2
Solution
Solution
Consequences of the Mean Value Theorem
Quick Check 3
Section 4.2 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
4.3 What Derivatives Tell Us
Increasing and Decreasing Functions
Intervals of Increase and Decrease
Quick Check 1
Solution
Solution
Identifying Local Maxima and Minima
Quick Check 2
First Derivative Test
Solution
Solution
Quick Check 3
Absolute Extreme Values on Any Interval
Solution
Concavity and Inflection Points
Quick Check 4
Solution
Solution
Second Derivative Test
Quick Check 5
Solution
Recap of Derivative Properties
Section 4.3 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
4.4 Graphing Functions
Calculators and Analysis
Quick Check 1
Graphing Guidelines
Solution
Quick Check 2
Solution
Solution
Quick Check 3
Solution
Solution
Section 4.4 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
4.5 Optimization Problems
Quick Check 1
Solution
Quick Check 2
Solution
Quick Check 3
Section 4.5 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
4.6 Linear Approximation and Differentials
Linear Approximation
Quick Check 1
Solution
Quick Check 2
Solution
Quick Check 3
Solution
Quick Check 4
Linear Approximation and Concavity
Solution
A Variation on Linear Approximation
Solution
Quick Check 5
Differentials
Solution
Section 4.6 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
4.7 L’Hôpital’s Rule
L’ Hôpital’s Rule for the Form 0/0
Solution
Quick Check 1
Solution
Indeterminate Form
Quick Check 2
Solution
Related Indeterminate Forms: and
Solution
Quick Check 3
Solution
Indeterminate Forms and
Quick Check 4
Solution
Growth Rates of Functions
Quick Check 5
Quick Check 6
Solution
Solution
Pitfalls in Using l’Hôpital’s Rule
Section 4.7 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
4.8 Newton’s Method
Why Approximate?
Deriving Newton’s Method
Quick Check 1
Solution
Quick Check 2
When Do You Stop?
Solution
Solution
Pitfalls of Newton’s Method
Solution
Section 4.8 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
4.9 Antiderivatives
Thinking Backward
Quick Check 1
Solution
Quick Check 2
Indefinite Integrals
Solution
Indefinite Integrals of Trigonometric Functions
Solution
Quick Check 3
Solution
Other Indefinite Integrals
Solution
Solution
Introduction to Differential Equations
Quick Check 4
Solution
Motion Problems Revisited
Quick Check 5
Solution
Solution
Section 4.9 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
Chapter 4 Review Exercises
Chapter 4 Guided Projects
5 Integration
Chapter Preview
5.1 Approximating Areas Under Curves
Area Under a Velocity Curve
Quick Check 1
Solution
Quick Check 2
Approximating Areas by Riemann Sums
Quick Check 3
Solution
Solution
Quick Check 4
Solution
Sigma (Summation) Notation
Riemann Sums Using Sigma Notation
Solution
Alternative Solution
Section 5.1 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
5.2 Definite Integrals
Net Area
Solution
Quick Check 1
Quick Check 2
The Definite Integral
Notation
Evaluating Definite Integrals
Quick Check 3
Solution
Solution
Quick Check 4
Solution
Properties of Definite Integrals
Quick Check 5
Integral of a Sum
Constants in Integrals
Integrals Over Subintervals
Integrals of Absolute Values
Solution
Quick Check 6
Bounds on Definite Integrals
Nonnegative Integrand
Comparing Definite Integrals
Lower and Upper Bounds
Evaluating Definite Integrals Using Limits
Solution
Section 5.2 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
5.3 Fundamental Theorem of Calculus
Area Functions
Solution
Quick Check 1
Solution
Quick Check 2
Fundamental Theorem of Calculus
Quick Check 3
The Inverse Relationship Between Differentiation and Integration
Quick Check 4
Solution
Solution
Solution
Solution
Solution
Section 5.3 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
5.4 Working with Integrals
Integrating Even and Odd Functions
Quick Check 1
Solution
Average Value of a Function
Quick Check 2
Solution
Mean Value Theorem for Integrals
Quick Check 3
Solution
Section 5.4 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
5.5 Substitution Rule
Indefinite Integrals
Solution
Quick Check 1
Solution
Quick Check 2
Solution
Substitution 1
Substitution 2
General Formulas for Indefinite Integrals
Quick Check 3
Solution
Quick Check 4
Definite Integrals
Solution
Solution
Geometry of Substitution
Quick Check 5
Section 5.5 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
Chapter 5 Review Exercises
Chapter 5 Guided Projects
6 Applications of Integration
Chapter Preview
6.1 Velocity and Net Change
Velocity, Position, and Displacement
Quick Check 1
Quick Check 2
Solution
Future Value of the Position Function
Quick Check 3
Solution
Quick Check 4
Solution
Quick Check 5
Acceleration
Solution
Net Change and Future Value
Solution
Solution
Quick Check 6
Section 6.1 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
6.2 Regions Between Curves
Quick Check 1
Solution
Quick Check 2
Solution
Integrating with Respect to y
Solution
Quick Check 3
Solution
Quick Check 4
Section 6.2 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
6.3 Volume by Slicing
General Slicing Method
Quick Check 1
Solution
Solution
Quick Check 2
The Disk Method
Quick Check 3
Solution
Washer Method
Quick Check 4
Solution
Quick Check 5
Revolving about the y-Axis
Solution
Quick Check 6
Solution
Section 6.3 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
6.4 Volume by Shells
Cylindrical Shells
Solution
Quick Check 1
Solution
Solution
Solution
Quick Check 2
Restoring Order
Solution
Quick Check 3
Section 6.4 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
6.5 Length of Curves
Arc Length for y = f(x)
Quick Check 1
Solution
Solution
Solution
Solution
Arc Length for
Quick Check 2
Solution
Quick Check 3
Solution
Section 6.5 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
6.6 Surface Area
Some Preliminary Calculations
Quick Check 1
Quick Check 2
Surface Area Formula
Quick Check 3
Solution
Solution
Solution
Solution
Section 6.6 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
6.7 Physical Applications
Density and Mass
Quick Check 1
Solution
Quick Check 2
Work
Quick Check 3
Solution
Quick Check 4
Lifting Problems
Solution
Quick Check 5
Quick Check 6
Pumping Problems
Solution
Quick Check 7
Solution
Force and Pressure
Solution
Section 6.7 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
Chapter 6 Review Exercises
Chapter 6 Guided Projects
7 Logarithmic, Exponential, and Hyperbolic Functions
Chapter Preview
7.1 Logarithmic and Exponential Functions Revisited
Step 1: The Natural Logarithm
Properties of the Natural Logarithm
Domain, Range, and Sign
Derivative
Quick Check 1
Graph of ln x
Logarithm of a Product
Logarithm of a Quotient
Logarithm of a Power
Integrals
Solution
Step 2: The Exponential Function
Quick Check 2
Derivatives and Integrals
Quick Check 3
Solution
Step 3: General Logarithmic and Exponential Functions
Quick Check 4
Solution
Step 4: General Power Rule
Solution
Approximating e
Section 7.1 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
7.2 Exponential Models
Exponential Growth
Solution
Quick Check 1
Quick Check 2
Solution
Quick Check 3
A Financial Model
Solution
Resource Consumption
Solution
Exponential Decay
Quick Check 4
Radiometric Dating
Solution
Pharmacokinetics
Solution
Section 7.2 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
7.3 Hyperbolic Functions
Relationship Between Trigonometric and Hyperbolic Functions
Definitions, Identities, and Graphs of the Hyperbolic Functions
Solution
Quick Check 1
Quick Check 2
Derivatives and Integrals of Hyperbolic Functions
Solution
Quick Check 3
Solution
Quick Check 4
Inverse Hyperbolic Functions
Solution
Quick Check 5
Derivatives of the Inverse Hyperbolic Functions and Related Integral Formulas
Solution
Solution
Quick Check 6
Applications of Hyperbolic Functions
The Catenary
Solution
Velocity of a Wave
Solution
Quick Check 7
Section 7.3 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
Chapter 7 Review Exercises
Chapter 7 Guided Projects
8 Integration Techniques
Chapter Preview
8.1 Basic Approaches
Solution
Quick Check 1
Solution
Solution
Solution
Quick Check 2
Solution
Quick Check 3
Solution
Quick Check 4
Section 8.1 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
8.2 Integration by Parts
Integration by Parts for Indefinite Integrals
Solution
Solution
Quick Check 1
Solution
Solution
Integration by Parts for Definite Integrals
Solution
Quick Check 2
Solution
Quick Check 3
Section 8.2 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
8.3 Trigonometric Integrals
Integrating Powers of sin x or cos x
Solution
Quick Check 1
Integrating Products of Powers of sin x and cos x
Solution
Quick Check 2
Reduction Formulas
Solution
Integrating Products of Powers of tan x and sec x
Solution
Section 8.3 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
8.4 Trigonometric Substitutions
Integrals Involving
Quick Check 1
Solution
Solution
Integrals Involving or
Quick Check 2
Solution
Quick Check 3
Solution
Solution
Solution
Section 8.4 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
8.5 Partial Fractions
Method of Partial Fractions
Quick Check 1
The Key Idea
Simple Linear Factors
Quick Check 2
Solution
A Shortcut (Convenient Values)
Solution
Repeated Linear Factors
Solution
Quick Check 3
Irreducible Quadratic Factors
Solution
Solution
Long Division
Quick Check 4
Section 8.5 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
8.6 Integration Strategies
Integration Strategies
Rewrite the integrand
Solution
Quick Check 1
Try substitution
Solution
Quick Check 2
Quick Check 3
Recognize a common pattern present in the integrand
Solution
Be persistent
Solution
Multiple techniques
Solution
Section 8.6 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
8.7 Other Methods of Integration
Using Tables of Integrals
Solution
Solution
Solution
Quick Check 1
Symbolic Methods
Quick Check 2
Solution
Quick Check 3
Solution
Section 8.7 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
8.8 Numerical Integration
Absolute and Relative Error
Solution
Midpoint Rule
Quick Check 1
Solution
The Trapezoid Rule
Quick Check 2
Solution
Solution
Quick Check 3
Solution
Solution
Simpson’s Rule
Solution
Quick Check 4
Solution
Quick Check 5
Errors in Numerical Integration
Quick Check 6
Section 8.8 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
8.9 Improper Integrals
Infinite Intervals
Solution
Quick Check 1
Solution
Quick Check 2
Solution
Unbounded Integrands
Quick Check 3
Solution
Solution
Solution
The Comparison Test
Solution
Quick Check 4
Section 8.9 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
Chapter 8 Review Exercises
Chapter 8 Guided Projects
9 Differential Equations
Chapter Preview
9.1 Basic Ideas
Solution
Solution
Quick Check 1
Solution
Quick Check 2
Solution
Quick Check 3
Differential Equations in Action
Solution
Quick Check 4
Solution
Solution
Quick Check 5
Final Note
Section 9.1 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
9.2 Direction Fields and Euler’s Method
Direction Fields
Solution
Quick Check 1
Solution
Quick Check 2
Solution
Quick Check 3
Euler’s Method
Solution
Quick Check 4
Final Note
Section 9.2 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
9.3 Separable Differential Equations
Method of Solution
Quick Check 1
Solution
Quick Check 2
Solution
Quick Check 3
Solution
Quick Check 4
Logistic Equation Revisited
Solution
Section 9.3 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
9.4 Special First-Order Linear Differential Equations
Method of Solution
Quick Check 1
Solution
Quick Check 2
Solution
Quick Check 3
Solution
Newton’s Law of Cooling
Quick Check 4
Solution
Quick Check 5
Section 9.4 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
9.5 Modeling with Differential Equations
Population Models
Quick Check 1
Solution
Solution
Stirred Tank Reactions
Quick Check 2
Solution
Predator-Prey Models
Quick Check 3
Solution
Section 9.5 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
Chapter 9 Review Exercises
Chapter 9 Guided Projects
10 Sequences and Infinite Series
Chapter Preview
10.1 An Overview
Examples of Sequences
Quick Check 1
Solution
Solution
Quick Check 2
Solution
Limit of a Sequence
Solution
Solution
Solution
Infinite Series and the Sequence of Partial Sums
Solution
Quick Check 3
Quick Check 4
Solution
Quick Check 5
Summary
Section 10.1 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
10.2 Sequences
Limit of a Sequence and Limit Laws
Solution
Terminology for Sequences
Quick Check 1
Solution
Geometric Sequences
Quick Check 2
Solution
The Squeeze Theorem
Solution
Bounded Monotonic Sequence Theorem
An Application: Recurrence Relations
Solution
Quick Check 3
Growth Rates of Sequences
Quick Check 4
Solution
Formal Definition of a Limit of a Sequence
Solution
Section 10.2 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
10.3 Infinite Series
Quick Check 1
Geometric Sums and Series
Quick Check 2
Quick Check 3
Quick Check 4
Quick Check 5
Solution
Solution
Telescoping Series
Solution
Properties of Convergent Series
Quick Check 6
Solution
Quick Check 7
Section 10.3 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
10.4 The Divergence and Integral Tests
The Divergence Test
Solution
Quick Check 1
The Harmonic Series
The Integral Test
Solution
The p-series
Quick Check 2
Solution
Estimating the Value of Infinite Series
Quick Check 3
Solution
Section 10.4 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
10.5 Comparison Tests
The Comparison Test
Solution
Quick Check 1
The Limit Comparison Test
Quick Check 2
Solution
Section 10.5 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
10.6 Alternating Series
Alternating Harmonic Series
Quick Check 1
Alternating Series Test
Quick Check 2
Solution
Remainders in Alternating Series
Solution
Quick Check 3
Absolute and Conditional Convergence
Quick Check 4
Solution
Section 10.6 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
10.7 The Ratio and Root Tests
The Ratio Test
Solution
Quick Check 1
Quick Check 2
The Root Test
Solution
Section 10.7 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
10.8 Choosing a Convergence Test
Series Strategies
Categorize the Series
Solution
Quick Check 1
Apply the Divergence Test
Solution
Quick Check 2
Identify Special Series
Solution
Integral, Ratio, and Root Tests
Solution
Quick Check 3
Rational Terms
Solution
Section 10.8 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
Chapter 10 Review Exercises
Chapter 10 Guided Projects
11 Power Series
Chapter Preview
11.1 Approximating Functions with Polynomials
What Is a Power Series?
Polynomial Approximation
Linear and Quadratic Approximation
Solution
Taylor Polynomials
Quick Check 1
Solution
Quick Check 2
Quick Check 3
Approximations with Taylor Polynomials
Solution
Quick Check 4
Solution
Quick Check 5
Remainder in a Taylor Polynomial
Estimating the Remainder
Solution
Solution
Solution
Quick Check 6
Solution
Section 11.1 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
11.2 Properties of Power Series
Geometric Series as Power Series
Quick Check 1
Convergence of Power Series
Solution
Quick Check 2
Solution
Combining Power Series
Solution
Differentiating and Integrating Power Series
Solution
Quick Check 3
Solution
Quick Check 4
Section 11.2 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
11.3 Taylor Series
Taylor Series for a Function
Quick Check 1
Solution
Quick Check 2
Solution
Quick Check 3
Solution
Solution
Quick Check 4
The Binomial Series
Quick Check 5
Solution
Quick Check 6
Solution
Convergence of Taylor Series
Solution
Solution
Section 11.3 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
11.4 Working with Taylor Series
Limits by Taylor Series
Solution
Quick Check 1
Solution
Differentiating Power Series
Solution
Quick Check 2
Solution
Integrating Power Series
Solution
Representing Real Numbers
Solution
Quick Check 3
Representing Functions as Power Series
Solution
Solution
Section 11.4 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
Chapter 11 Review Exercises
Chapter 11 Guided Projects
12 Parametric and Polar Curves
Chapter Preview
12.1 Parametric Equations
Basic Ideas
Solution
Quick Check 1
Solution
Quick Check 2
Solution
Quick Check 3
Solution
Quick Check 4
Solution
Derivatives and Parametric Equations
Quick Check 5
Solution
Arc Length
Quick Check 6
Solution
Solution
Section 12.1 Exercises
Getting Started
Practice Exercises
Explorations and Challenges
Quick Check Answers
12.2 Polar Coordinates
Defining Polar Coordinates
Quick Check 1
Solution
Converting Between Cartesian and Polar Coordinates
Quick Check 2
Solution
Quick Check 3
Basic Curves in Polar Coordinates
Quick Check 4
Solution
Quick Check 5
Graphing in Polar Coordinates
Solution
Cartesian-to-Polar