This is completed downloadable of Test Bank for Calculus Early Transcendentals: Briggs Cochran
Product Details:
- ISBN-10 ‏ : ‎ 0134763645
- ISBN-13 ‏ : ‎ 978-0134763644
- Author:Â Briggs Cochran
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Table of Content:
- 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 Method
- Solution
- Symmetry
- Quick Check 6
- Solution
- Solution
- Solution
- Using Graphing Utilities
- Solution
- Section 12.2 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 12.3 Calculus in Polar Coordinates
- Slopes of Tangent Lines
- Quick Check 1
- Solution
- Solution
- Quick Check 2
- Area of Regions Bounded by Polar Curves
- Solution
- Quick Check 3
- Solution
- Solution
- Solution
- Arc Length of a Polar Curve
- Quick Check 4
- Solution
- Section 12.3 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 12.4 Conic Sections
- Parabolas
- Quick Check 1
- Quick Check 2
- Solution
- Solution
- Reflection Property
- Ellipses
- Quick Check 3
- Solution
- Solution
- Hyperbolas
- Solution
- Quick Check 4
- Eccentricity and Directrix
- Quick Check 5
- Solution
- Polar Equations of Conic Sections
- Quick Check 6
- Solution
- Solution
- Section 12.4 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- Chapter 12 Review Exercises
- Chapter 12 Guided Projects
- 13 Vectors and the Geometry of Space
- Chapter Preview
- 13.1 Vectors in the Plane
- Basic Vector Operations
- Scalar Multiplication
- Quick Check 1
- Solution
- Vector Addition and Subtraction
- Quick Check 2
- Quick Check 3
- Solution
- Vector Components
- Quick Check 4
- Magnitude
- Solution
- Vector Operations in Terms of Components
- Solution
- Unit Vectors
- Quick Check 5
- Solution
- Quick Check 6
- Properties of Vector Operations
- Quick Check 7
- Applications of Vectors
- Velocity Vectors
- Solution
- Force Vectors
- Solution
- Solution
- Section 13.1 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 13.2 Vectors in Three Dimensions
- The xyz-Coordinate System
- Solution
- Quick Check 1
- Equations of Simple Planes
- Quick Check 2
- Solution
- Distances in xyz-Space
- Equation of a Sphere
- Solution
- Solution
- Quick Check 3
- Vectors in R3
- Quick Check 4
- Solution
- Magnitude and Unit Vectors
- Solution
- Quick Check 5
- Solution
- Section 13.2 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 13.3 Dot Products
- Two Forms of the Dot Product
- Quick Check 1
- Solution
- Quick Check 2
- Solution
- Properties of Dot Products
- Orthogonal Projections
- Quick Check 3
- Solution
- Applications of Dot Products
- Work and Force
- Solution
- Parallel and Normal Forces
- Solution
- Section 13.3 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 13.4 Cross Products
- The Cross Product
- Quick Check 1
- Solution
- Properties of the Cross Product
- Quick Check 2
- Solution
- Solution
- Solution
- Quick Check 3
- Applications of the Cross Product
- Torque
- Solution
- Magnetic Force on a Moving Charge
- Solution
- Section 13.4 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 13.5 Lines and Planes in Space
- Lines in Space
- Quick Check 1
- Solution
- Solution
- Quick Check 2
- Distance from a Point to a Line
- Quick Check 3
- Solution
- Solution
- Equations of Planes
- Quick Check 4
- Solution
- Solution
- Quick Check 5
- Solution
- Parallel and Orthogonal Planes
- Quick Check 6
- Solution
- Solution
- Section 13.5 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 13.6 Cylinders and Quadric Surfaces
- Cylinders and Traces
- Quick Check 1
- Solution
- Quadric Surfaces
- Quick Check 2
- Solution
- Quick Check 3
- Solution
- Quick Check 4
- Solution
- Quick Check 5
- Solution
- Solution
- Solution
- Quick Check 6
- Section 13.6 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- Chapter 13 Review Exercises
- Chapter 13 Guided Projects
- 14 Vector-Valued Functions
- Chapter Preview
- 14.1 Vector-Valued Functions
- Vector-Valued Functions
- Curves in Space
- Solution
- Quick Check 1
- Orientation of Curves
- Solution
- Solution
- Solution
- Limits and Continuity for Vector-Valued Functions
- Solution
- Quick Check 2
- Section 14.1 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 14.2 Calculus of Vector-Valued Functions
- The Derivative and Tangent Vector
- Solution
- Quick Check 1
- Unit Tangent Vector
- Quick Check 2
- Solution
- Derivative Rules
- Quick Check 3
- Solution
- Higher-Order Derivatives
- Solution
- Integrals of Vector-Valued Functions
- Solution
- Quick Check 4
- Solution
- Solution
- Section 14.2 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 14.3 Motion in Space
- Position, Velocity, Speed, Acceleration
- Quick Check 1
- Solution
- Solution
- Quick Check 2
- Straight-Line and Circular Motion
- Solution
- Quick Check 3
- Two-Dimensional Motion in a Gravitational Field
- Finding Velocity and Position from Acceleration
- Solution
- Quick Check 4
- Range, Time of Flight, Maximum Height
- Quick Check 5
- Solution
- Three-Dimensional Motion
- Solution
- Section 14.3 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 14.4 Length of Curves
- Arc Length
- Quick Check 1
- Solution
- Solution
- Arc Length as a Parameter
- Quick Check 2
- The Arc Length Function
- Solution
- Quick Check 3
- Section 14.4 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 14.5 Curvature and Normal Vectors
- Curvature
- Unit Tangent Vector
- Solution
- Solution
- Quick Check 1
- An Alternative Curvature Formula
- Quick Check 2
- Solution
- Solution
- Principal Unit Normal Vector
- Quick Check 3
- Solution
- Quick Check 4
- Components of the Acceleration
- Solution
- Solution
- Quick Check 5
- The Binormal Vector and Torsion
- Quick Check 6
- Quick Check 7
- Solution
- Solution
- Section 14.5 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- Chapter 14 Review Exercises
- Chapter 14 Guided Projects
- 15 Functions of Several Variables
- Chapter Preview
- 15.1 Graphs and Level Curves
- Functions of Two Variables
- Solution
- Quick Check 1
- Graphs of Functions of Two Variables
- Quick Check 2
- Solution
- Quick Check 3
- Level Curves
- Quick Check 4
- Quick Check 5
- Solution
- Quick Check 6
- Solution
- Applications of Functions of Two Variables
- Solution
- Quick Check 7
- Solution
- Quick Check 8
- Functions of More Than Two Variables
- Solution
- Quick Check 9
- Graphs of Functions of More Than Two Variables
- Section 15.1 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 15.2 Limits and Continuity
- Limit of a Function of Two Variables
- Solution
- Quick Check 1
- Limits at Boundary Points
- Quick Check 2
- Quick Check 3
- Solution
- Solution
- Quick Check 4
- Continuity of Functions of Two Variables
- Solution
- Composite Functions
- Quick Check 5
- Solution
- Functions of Three Variables
- Solution
- Section 15.2 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 15.3 Partial Derivatives
- Derivatives with Two Variables
- Notation
- Calculating Partial Derivatives
- Solution
- Solution
- Quick Check 1
- Solution
- Higher-Order Partial Derivatives
- Quick Check 2
- Solution
- Quick Check 3
- Equality of Mixed Partial Derivatives
- Functions of Three Variables
- Solution
- Quick Check 4
- Applications of Partial Derivatives
- Solution
- Quick Check 5
- Differentiability
- Solution
- Section 15.3 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 15.4 The Chain Rule
- The Chain Rule with One Independent Variable
- Quick Check 1
- Solution
- The Chain Rule with Several Independent Variables
- Quick Check 2
- Solution
- Solution
- Quick Check 3
- Solution
- Implicit Differentiation
- Solution
- Quick Check 4
- Solution
- Solution
- Section 15.4 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 15.5 Directional Derivatives and the Gradient
- Directional Derivatives
- Quick Check 1
- Quick Check 2
- Solution
- Quick Check 3
- The Gradient Vector
- Solution
- Solution
- Interpretations of the Gradient
- Solution
- Solution
- The Gradient and Level Curves
- Quick Check 4
- Solution
- Solution
- Quick Check 5
- The Gradient in Three Dimensions
- Quick Check 6
- Solution
- Section 15.5 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 15.6 Tangent Planes and Linear Approximation
- Tangent Planes
- Quick Check 1
- Tangent Planes for
- Solution
- Tangent Planes for
- Solution
- Linear Approximation
- Solution
- Quick Check 2
- Differentials and Change
- Quick Check 3
- Solution
- Solution
- Quick Check 4
- Solution
- Section 15.6 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 15.7 Maximum/Minimum Problems
- Local Maximum/Minimum Values
- Quick Check 1
- Solution
- Second Derivative Test
- Quick Check 2
- Quick Check 3
- Solution
- Solution
- Solution
- Absolute Maximum and Minimum Values
- Solution
- Solution
- Solution
- Open and/or Unbounded Regions
- Solution
- Quick Check 4
- Solution
- Section 15.7 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 15.8 Lagrange Multipliers
- The Basic Idea
- Lagrange Multipliers with Two Independent Variables
- Quick Check 1
- Solution
- Quick Check 2
- Lagrange Multipliers with Three Independent Variables
- Solution
- Quick Check 3
- Economic Models
- Solution
- Quick Check 4
- Section 15.8 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- Chapter 15 Review Exercises
- Chapter 15 Guided Projects
- 16 Multiple Integration
- Chapter Preview
- 16.1 Double Integrals over Rectangular Regions
- Volumes of Solids
- Quick Check 1
- Iterated Integrals
- Solution
- Solution
- Quick Check 2
- Solution
- Quick Check 3
- Solution
- Average Value
- Solution
- Section 16.1 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 16.2 Double Integrals over General Regions
- General Regions of Integration
- Iterated Integrals
- Solution
- Quick Check 1
- Change of Perspective
- Solution
- Quick Check 2
- Choosing and Changing the Order of Integration
- Solution
- Solution
- Quick Check 3
- Regions Between Two Surfaces
- Solution
- Decomposition of Regions
- Finding Area by Double Integrals
- Solution
- Quick Check 4
- Section 16.2 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 16.3 Double Integrals in Polar Coordinates
- Moving from Rectangular to Polar Coordinates
- Quick Check 1
- Solution
- Quick Check 2
- Solution
- Quick Check 3
- Solution
- More General Polar Regions
- Solution
- Areas of Regions
- Solution
- Quick Check 4
- Average Value over a Planar Polar Region
- Solution
- Section 16.3 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 16.4 Triple Integrals
- Triple Integrals in Rectangular Coordinates
- Quick Check 1
- Finding Limits of Integration
- Solution
- Quick Check 2
- Solution
- Quick Check 3
- Solution
- Changing the Order of Integration
- Solution
- Average Value of a Function of Three Variables
- Solution
- Quick Check 4
- Section 16.4 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 16.5 Triple Integrals in Cylindrical and Spherical Coordinates
- Cylindrical Coordinates
- Solution
- Quick Check 1
- Integration in Cylindrical Coordinates
- Finding Limits of Integration
- Solution
- Quick Check 2
- Solution
- Solution
- Spherical Coordinates
- Quick Check 3
- Solution
- Integration in Spherical Coordinates
- Finding Limits of Integration
- Solution
- Solution
- Section 16.5 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 16.6 Integrals for Mass Calculations
- Sets of Individual Objects
- Quick Check 1
- Quick Check 2
- Several Objects on a Line
- Solution
- Continuous Objects in One Dimension
- Quick Check 3
- Solution
- Two-Dimensional Objects
- Quick Check 4
- Solution
- Solution
- Three-Dimensional Objects
- Quick Check 5
- Solution
- Solution
- Section 16.6 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 16.7 Change of Variables in Multiple Integrals
- Recap of Change of Variables
- Transformations in the Plane
- Solution
- Quick Check 1
- Quick Check 2
- Solution
- Solution
- Quick Check 3
- Solution
- Quick Check 4
- Solution
- Change of Variables in Triple Integrals
- Solution
- Quick Check 5
- Strategies for Choosing New Variables
- Section 16.7 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- Chapter 16 Review Exercises
- Chapter 16 Guided Projects
- 17 Vector Calculus
- Chapter Preview
- 17.1 Vector Fields
- Vector Fields in Two Dimensions
- Solution
- Quick Check 1
- Radial Vector Fields in
- Solution
- Quick Check 2
- Vector Fields in Three Dimensions
- Solution
- Gradient Fields and Potential Functions
- Quick Check 3
- Solution
- Equipotential Curves and Surfaces
- Solution
- Section 17.1 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 17.2 Line Integrals
- Scalar Line Integrals in the Plane
- Evaluating Line Integrals
- Quick Check 1
- Solution
- Quick Check 2
- Line Integrals in
- Solution
- Solution
- Quick Check 3
- Line Integrals of Vector Fields
- Solution
- Work Integrals
- Quick Check 4
- Solution
- Circulation and Flux of a Vector Field
- Circulation
- Solution
- Solution
- Flux of Two-Dimensional Vector Fields
- Quick Check 5
- Solution
- Section 17.2 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 17.3 Conservative Vector Fields
- Types of Curves and Regions
- Quick Check 1
- Test for Conservative Vector Fields
- Solution
- Finding Potential Functions
- Quick Check 2
- Solution
- Quick Check 3
- Fundamental Theorem for Line Integrals and Path Independence
- Solution
- Solution
- Quick Check 4
- Line Integrals on Closed Curves
- Solution
- Summary of the Properties of Conservative Vector Fields
- Section 17.3 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 17.4 Green’s Theorem
- Circulation Form of Green’s Theorem
- Quick Check 1
- Solution
- Calculating Area by Green’s Theorem
- Solution
- Flux Form of Green’s Theorem
- Quick Check 2
- Solution
- Solution
- Circulation and Flux on More General Regions
- Solution
- Solution
- Stream Functions
- Quick Check 3
- Proof of Green’s Theorem on Special Regions
- Quick Check 4
- Section 17.4 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 17.5 Divergence and Curl
- The Divergence
- Solution
- Quick Check 1
- Divergence of a Radial Vector Field
- Solution
- Solution
- Quick Check 2
- The Curl
- Curl of a General Rotation Vector Field
- Quick Check 3
- Solution
- Working with Divergence and Curl
- Quick Check 4
- Solution
- Summary of Properties of Conservative Vector Fields
- Section 17.5 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 17.6 Surface Integrals
- Parameterized Surfaces
- Cylinders
- Quick Check 1
- Cones
- Quick Check 2
- Spheres
- Quick Check 3
- Solution
- Surface Integrals of Scalar-Valued Functions
- Solution
- Solution
- Solution
- Surface Integrals on Explicitly Defined Surfaces
- Solution
- Quick Check 4
- Solution
- Quick Check 5
- Surface Integrals of Vector Fields
- Flux Integrals
- Solution
- Solution
- Quick Check 6
- Section 17.6 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 17.7 Stokes’ Theorem
- Stokes’ Theorem
- Quick Check 1
- Solution
- Solution
- Solution
- Quick Check 2
- Interpreting the Curl
- Solution
- Quick Check 3
- Proof of Stokes’ Theorem
- Two Final Notes on Stokes’ Theorem
- Section 17.7 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- 17.8 Divergence Theorem
- Divergence Theorem
- Quick Check 1
- Solution
- Solution
- Solution
- Quick Check 2
- Interpretation of the Divergence Theorem Using Mass Transport
- Quick Check 3
- Proof of the Divergence Theorem
- Divergence Theorem for Hollow Regions
- Solution
- Gauss’ Law
- A Final Perspective
- Section 17.8 Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Quick Check Answers
- Chapter 17 Review Exercises
- Chapter 17 Guided Projects
- A Appendix
- B Appendix
- Algebra
- Solution
- Sets of Real Numbers
- Solution
- Absolute Value
- Solution
- Cartesian Coordinate System
- Distance Formula and Circles
- Solution
- Equations of Lines
- Solution
- Parallel and Perpendicular Lines
- Solution
- Solution
- Appendix B Exercises
- Getting Started
- Practice Exercises
- Explorations and Challenges
- Answers
- Appendix B
- Exercises, pp. B-7–B-8
- C Appendix
- Complex Numbers
- Complex Arithmetic
- Solution
- Solution
- Euler’s Formula
- Solution
- Solution
- Polar Form of Complex Numbers
- Solution
- Appendix C Exercises
- Practice Exercises
- Explorations and Challenges
- Answers
- Appendix C
- Exercises, p. C-6
- Answers
- Chapter 1
- Section 1.1 Exercises, pp. 9–13
- Section 1.2 Exercises, pp. 22–27
- Section 1.3 Exercises, pp. 35–39
- Section 1.4 Exercises, pp. 48–51
- Chapter 1 Review Exercises, pp. 51–55
- Chapter 2
- Section 2.1 Exercises, pp. 61–62
- Section 2.2 Exercises, pp. 67–71
- Section 2.3 Exercises, pp. 79–82
- Section 2.4 Exercises, pp. 88–91
- Section 2.5 Exercises, pp. 100–102
- Section 2.6 Exercises, pp. 112–115
- Section 2.7 Exercises, pp. 124–128
- Chapter 2 Review Exercises, pp. 128–130
- Chapter 3
- Section 3.1 Exercises, pp. 137–140
- Section 3.2 Exercises, pp. 148–152
- Section 3.3 Exercises, pp. 159–162
- Section 3.4 Exercises, pp. 168–170
- Section 3.5 Exercises, pp. 175–178
- Section 3.6 Exercises, pp. 186–191
- Section 3.7 Exercises, pp. 196–200
- Section 3.8 Exercises, pp. 205–208
- Section 3.9 Exercises, pp. 215–218
- Section 3.10 Exercises, pp. 225–227
- Section 3.11 Exercises, pp. 231–236
- Chapter 3 Review Exercises, pp. 236–240
- Chapter 4
- Section 4.1 Exercises, pp. 247–250
- Section 4.2 Exercises, pp. 254–257
- Section 4.3 Exercises, pp. 267–270
- Section 4.4 Exercises, pp. 277–280
- Section 4.5 Exercises, pp. 284–291
- Section 4.6 Exercises, pp. 298–300
- Section 4.7 Exercises, pp. 310–312
- Section 4.8 Exercises, pp. 318–321
- Section 4.9 Exercises, pp. 331–334
- Chapter 4 Review Exercises, pp. 334–337
- Chapter 5
- Section 5.1 Exercises, pp. 347–352
- Section 5.2 Exercises, pp. 364–367
- Section 5.3 Exercises, pp. 377–381
- Section 5.4 Exercises, pp. 385–387
- Section 5.5 Exercises, pp. 395–398
- Chapter 5 Review Exercises, pp. 398–402
- Chapter 6
- Section 6.1 Exercises, pp. 410–416
- Section 6.2 Exercises, pp. 420–425
- Section 6.3 Exercises, pp. 434–439
- Section 6.4 Exercises, pp. 447–451
- Section 6.5 Exercises, pp. 455–457
- Section 6.6 Exercises, pp. 463–465
- Section 6.7 Exercises, pp. 473–477
- Chapter 6 Review Exercises, pp. 478–482
- Chapter 7
- Section 7.1 Exercises, pp. 490–492
- Section 7.2 Exercises, pp. 499–501
- Section 7.3 Exercises, pp. 513–517
- Chapter 7 Review Exercises, pp. 518–519
- Chapter 8
- Section 8.1 Exercises, pp. 523–525
- Section 8.2 Exercises, pp. 529–532
- Section 8.3 Exercises, pp. 536–538
- Section 8.4 Exercises, pp. 543–546
- Section 8.5 Exercises, pp. 554–556
- Section 8.6 Exercises, pp. 560–562
- Section 8.7 Exercises, pp. 565–567
- Section 8.8 Exercises, pp. 578–582
- Section 8.9 Exercises, pp. 590–593
- Chapter 8 Review Exercises, pp. 593–596
- Chapter 9
- Section 9.1 Exercises, pp. 604–606
- Section 9.2 Exercises, pp. 611–614
- Section 9.3 Exercises, pp. 618–620
- Section 9.4 Exercises, pp. 625–627
- Section 9.5 Exercises, pp. 634–636
- Chapter 9 Review Exercises, pp. 636–638
- Chapter 10
- Section 10.1 Exercises, pp. 647–649
- Section 10.2 Exercises, pp. 659–662
- Section 10.3 Exercises, pp. 668–671
- Section 10.4 Exercises, pp. 680–683
- Section 10.5 Exercises, pp. 687–688
- Section 10.6 Exercises, pp. 694–696
- Section 10.7 Exercises, pp. 699–700
- Section 10.8 Exercises, pp. 703–704
- Chapter 10 Review Exercises, pp. 704–707
- Chapter 11
- Section 11.1 Exercises, pp. 718–721
- Section 11.2 Exercises, pp. 729–730
- Section 11.3 Exercises, pp. 740–742
- Section 11.4 Exercises, pp. 748–750
- Chapter 11 Review Exercises, pp. 750–752
- Chapter 12
- Section 12.1 Exercises, pp. 763–767
- Section 12.2 Exercises, pp. 775 779
- Section 12.3 Exercises, pp. 786–788
- Section 12.4 Exercises, pp. 797–800
- Chapter 12 Review Exercises, pp. 800–803
- Chapter 13
- Section 13.1 Exercises, pp. 813–816
- Section 13.2 Exercises, pp. 823–827
- Section 13.3 Exercises, pp. 833–837
- Section 13.4 Exercises, pp. 842–844
- Section 13.5 Exercises, pp. 852–855
- Section 13.6 Exercises, pp. 863–865
- Chapter 13 Review Exercises, pp. 865–867
- Chapter 14
- Section 14.1 Exercises, pp. 873–875
- Section 14.2 Exercises, pp. 881–883
- Section 14.3 Exercises, pp. 892–896
- Section 14.4 Exercises, pp. 900–902
- Section 14.5 Exercises, pp. 913–915
- Chapter 14 Review Exercises, pp. 916–918
- Chapter 15
- Section 15.1 Exercises, pp. 927–930
- Section 15.2 Exercises, pp. 937–939
- Section 15.3 Exercises, pp. 948–951
- Section 15.4 Exercises, pp. 957–961
- Section 15.5 Exercises, pp. 970–973
- Section 15.6 Exercises, pp. 980–983
- Section 15.7 Exercises, pp. 993–996
- Section 15.8 Exercises, pp. 1002–1004
- Chapter 15 Review Exercises, pp. 1005–1007
- Chapter 16
- Section 16.1 Exercises, pp. 1015–1017
- Section 16.2 Exercises, pp. 1024–1027
- Section 16.3 Exercises, pp. 1033–1036
- Section 16.4 Exercises, pp. 1043–1047
- Section 16.5 Exercises, pp. 1059–1063
- Section 16.6 Exercises, pp. 1070–1072
- Section 16.7 Exercises, pp. 1082–1084
- Chapter 16 Review Exercises, pp. 1084–1088
- Chapter 17
- Section 17.1 Exercises, pp. 1096–1098
- Section 17.2 Exercises, pp. 1110–1114
- Section 17.3 Exercises, pp. 1121–1123
- Section 17.4 Exercises, pp. 1133–1136
- Section 17.5 Exercises, pp. 1143–1146
- Section 17.6 Exercises, pp. 1159–1161
- Section 17.7 Exercises, pp. 1169–1171
- Section 17.8 Exercises, pp. 1179–1182
- Chapter 17 Review Exercises, pp. 1182–1184
- Index
- A
- B
- C
- D
- E
- F
- G
- H
- I
- J
- K
- L
- M
- N
- O
- P
- Q
- R
- S
- T
- U
- V
- W
- X
- Y
- Z
- Index of Applications
- Economics and Business
- Engineering and Physical Sciences
- General
- Life Sciences
- Social and Behavioral Sciences
- Table of Integrals
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