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

Description

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