This is completed downloadable of Test Bank for Calculus Early Transcendentals: Briggs Cochran
Product Details:
- ISBN-10 : 0134763645
- ISBN-13 : 978-0134763644
- Author: Briggs Cochran
NOTE: Before purchasing, check with your instructor to ensure you select the correct ISBN. Several versions of the MyLab™ and Mastering™ platforms exist for each title, and registrations are not transferable. To register for and use MyLab or Mastering, you may also need a Course ID, which your instructor will provide. Used books, rentals, and purchases made outside of Pearson If purchasing or renting from companies other than Pearson, the access codes for the MyLab or Mastering platform may not be included, may be incorrect, or may be previously redeemed. Check with the seller before completing your purchase. Available for fall 2020 classes The DIGITAL UPDATE gives you revised content and resources that keep your course current For 3- to 4-semester courses covering single-variable and multivariable calculus, taken by students of mathematics, engineering, natural sciences, or economics. This package includes 18-week access card for MyLab Math. The most successful new calculus text in the last two decades The much-anticipated 3rd Edition of Briggs’ Calculus: Early Transcendentals 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. For the 3rd Edition, the authors synthesized feedback on the text and MyLab™ Math content from over 140 instructors. This thorough and extensive review process, paired with the authors’ own teaching experiences, helped create a text that is designed for today’s calculus instructors and students. Personalize learning with MyLab Math By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. 0136207685 / 9780136207689 CALCULUS, EARLY TRANSCENDENTALS PLUS MYLAB MATH WITH PEARSON ETEXT – 18-WEEK ACCESS CARD PACKAGE, 3/e
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
People Also Search:
calculus early transcendentals briggs cochran
calculus early transcendentals briggs cochran download scribd
calculus early transcendentals briggs cochran test bank download pdf