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ISBN-10 ‏ : ‎ 0134437772
ISBN-13 ‏ : ‎ 978-0134437774
Author: Larry Goldstein (Author), David Lay (Author), David Schneider (Author), Nakhle Asmar (Author)

Calculus & Its Applications builds intuition with key concepts of calculus before the analytical material. For example, the authors explain the derivative geometrically before they present limits, and they introduce the definite integral intuitively via the notion of net change before they discuss Riemann sums. The strategic organization of topics makes it easy to adjust the level of theoretical material covered. The significant applications introduced early in the course serve to motivate students and make the mathematics more accessible. Another unique aspect of the text is its intuitive use of differential equations to model a variety of phenomena in Chapter 5, which addresses applications of exponential and logarithmic functions.

Table of Content:

Chapter 0 Functions
0.1 Functions and Their Graphs
Real Numbers
Solution
Solution
Functions
Solution
Solution
Solution
More about the Domain of a Function
Solution
Graphs of Functions
Solution
Solution
Solution
Solution
Check Your Understanding 0.1
Exercises 0.1
Technology Exercises
Solutions to Check Your Understanding 0.1
0.2 Some Important Functions
Linear Functions
Solution
Solution
Solution
Solution
Piecewise-Defined Functions
Solution
Quadratic Functions
Polynomial and Rational Functions
Power Functions
Absolute Value Functions
Check Your Understanding 0.2
Exercises 0.2
Technology Exercises
Solutions to Check Your Understanding 0.2
0.3 The Algebra of Functions
Operations on Functions
Solution
Solution
Solution
Solution
Composition of Functions
Solution
Solution
Solution
Check Your Understanding 0.3
Exercises 0.3
Technology Exercises
Shifting a Graph
Solutions to Check Your Understanding 0.3
0.4 Zeros of Functions—The Quadratic Formula and Factoring
The Quadratic Formula
Solution
Solution
Solution
Factoring
Solution
Solution
Solution
Solution
Solution
Solution
Check Your Understanding 0.4
Exercises 0.4
Technology Exercises
Solutions to Check Your Understanding 0.4
0.5 Exponents and Power Functions
Solution
Compound Interest
Solution
Solution
Solution
Solution
Solution
Check Your Understanding 0.5
Exercises 0.5
Technology Exercises
Solutions to Check Your Understanding 0.5
0.6 Functions and Graphs in Applications
Geometric Problems
Solution
Business Problems
Solution
Solution
Functions and Graphs
Solution
Solution
Solution
Check Your Understanding 0.6
Exercises 0.6
Technology Exercises
Solutions to Check Your Understanding 0.6
Chapter 0 Summary
Chapter 0 Fundamental Concept Check Exercises
Chapter 0 Review Exercises
Chapter 1 The Derivative
1.1 The Slope of a Straight Line
Fixed and Marginal Costs
Solution
Interpreting the Slope and y-Intercept
Solution
Depreciation of Equipment
Solution
Calculations Involving Slope of a Line
Finding the Slope and y-Intercept
Solution
Sketching a Line Given a Point and a Slope
Solution
Slope of Line through Two Points
Solution
Equation of Line Given a Point and a Slope
Solution
Equation of Line through Two Points
Solution
Equation of Line Parallel to a Given Line
Solution
The Slope as a Rate of Change
Temperature in a City
Solution
Check Your Understanding 1.1
Exercises 1.1
Technology Exercises
Solutions to Check Your Understanding 1.1
1.2 The Slope of a Curve at a Point
Slope of a Graph
Solution
Slope of a Graph as a Rate of Change
Slope as a Rate of Change
Solution
Slope of a Graph
Solution
Slope Formulas
Using a Slope Formula
Solution
Check Your Understanding 1.2
Exercises 1.2
Technology Exercises
Solutions to Check Your Understanding 1.2
1.3 The Derivative and Limits
Examples of Derivatives: The Power Rule
Applying the Power Rule
Solution
Geometric Meaning of the Derivative and Equation of the Tangent Line
Evaluating the Derivative at One Point
Solution
Finding an Equation of the Tangent Line at a Given Point
Solution
Finding the Equation of the Tangent Line at a Given x
Solution
Equation of the Tangent Line at a Given Point
Solution
Using the Derivative to Solve Tangent Problems
Solution
Notation
Limits and the Secant-Line Calculation of the Derivative
Verification of the Power Rule for r = 2
Solution
Check Your Understanding 1.3
Exercises 1.3
Technology Exercises
Solutions to Check Your Understanding 1.3
1.4 Limits and the Derivative
Computing a Limit Using a Table of Values
Solution
Computing Limits Using Graphs
Solution
Two Basic Limits
Solution
Using Properties of Limits
Solution
Factoring Techniques
Solution
Limit Definition of the Derivative
Computing a Derivative from the Limit Definition
Solution
Computing Derivative from the Definition
Solution
Derivative of a Rational Function
Solution
Derivative of a Function with a Radical
Solution
1.5 Differentiability and Continuity
Hauling Cost
Solution
Manufacturing Cost
Solution
Continuity at a Point
Solution
Check Your Understanding 1.5
Exercises 1.5
Solutions to Check Your Understanding 1.5
1.6 Some Rules for Differentiation
Appendix Proofs of the Constant-Multiple and Sum Rules
1.7 More about Derivatives
Differentiating with Respect to a Specific Variable
Solution
The Derivative as a Rate of Change
Declining Sales
Solution
The Marginal Concept in Economics
Marginal Cost
Solution
Predicting Profits
Solution
Check Your Understanding 1.7
Exercises 1.7
Technology Exercises
Solutions to Check Your Understanding 1.7
1.8 The Derivative as a Rate of Change
Average Rates of Change
Solution
Comparing the Average and Instantaneous Rates
Solution
Rates of Change of a Population Model
Solution
Velocity and Acceleration
Velocity and Average Velocities
Solution
Position, Velocity, and Acceleration
Solution
Approximating the Change in a Function
Approximating a Production Function
Solution
Marginal Cost
Solution
Units for Rate of Change
Check Your Understanding 1.8
Exercises 1.8
Technology Exercises
Solutions to Check Your Understanding 1.8
Chapter 1 Summary
Chapter 1 Fundamental Concept Check Exercises
Chapter 1 Review Exercises
Chapter 2 Applications of the Derivative
2.1 Describing Graphs of Functions
Extreme Points
Solution
Changing Slope
Solution
Concavity
Solution
Intercepts, Undefined Points, and Asymptotes
Check Your Understanding 2.1
Exercises 2.1
Technology Exercises
Solutions to Check Your Understanding 2.1
2.2 The First- and Second-Derivative Rules
Solution
Solution
Connections between the Graphs of f(x) and f'(x)
Solution
Solution
Check Your Understanding 2.2
Exercises 2.2
Technology Exercises
Solutions to Check Your Understanding 2.2
2.3 The First- and Second-Derivative Tests and Curve Sketching
Locating Relative Extreme Points
Solution
Solution
Using Concavity to Determine Extreme Points
Solution
Solution
Locating Inflection Points
Solution
Solution
Check Your Understanding 2.3
Exercises 2.3
Technology Exercises
Solutions to Check Your Understanding 2.3
2.4 Curve Sketching (Conclusion)
Solution
Solution
Solution
A Graph with Asymptotes
Solution
Summary of Curve-Sketching Techniques
Check Your Understanding 2.4
Exercises 2.4
Technology Exercises
Solutions to Check Your Understanding 2.4
2.5 Optimization Problems
Solution
Solution
Solution
Solution
Solution
Check Your Understanding 2.5
Exercises 2.5
Technology Exercises
Solutions to Check Your Understanding 2.5
2.6 Further Optimization Problems
Inventory Control
Solution
Solution
Solution
Solution
Check Your Understanding 2.6
Exercises 2.6
Technology Exercises
Solutions to Check Your Understanding 2.6
2.7 Applications of Derivatives to Business and Economics
Cost Functions
Solution
Revenue Functions
Solution
Solution
Profit Functions
Solution
Solution
Setting Production Levels
Check Your Understanding 2.7
Exercises 2.7
Solutions to Check Your Understanding 2.7
Chapter 2 Summary
Chapter 2 Fundamental Concept Check Exercises
Chapter 2 Review Exercises
Chapter 3 Techniques of Differentiation
3.1 The Product and Quotient Rules
Verifying the Product Rule
Solution
Finding the Derivative of a Product
Solution
The Product Rule
Solution
Differentiating and Simplifying
Solution
The Quotient Rule
Using the Quotient Rule
Solution
Simplifying after the Quotient Rule
Solution
Simplifying after the Quotient Rule
Solution
Appendix: Verification of the Product and Quotient Rules
Verification of the Product Rule
Verification of the Quotient Rule
Check Your Understanding 3.1
Exercises 3.1
Technology Exercises
Solutions to Check Your Understanding 3.1
3.2 The Chain Rule
Composition of Functions
Composition of Functions
Solution
Decomposing Composite Functions
Solution
Chain Rule
The General Power Rule as a Chain Rule
Solution
Derivative of a Function That Is Not Specified
Solution
The Chain Rule
Solution
Marginal Revenue and Time Rate of Change
Solution
Time Rate of Change of Revenue
Solution
Appendix: Verification of the Chain Rule
Check Your Understanding 3.2
Exercises 3.2
Solutions to Check Your Understanding 3.2
3.3 Implicit Differentiation and Related Rates
Implicit Differentiation
Finding the Slope Using Implicit Differentiation
Solution
Related Rates
A Point Moving along a Graph
Solution
Check Your Understanding 3.3
Exercises 3.3
Solutions to Check Your Understanding 3.3
Chapter 3 Summary
Chapter 3 Fundamental Concept Check Exercises
Chapter 3 Review Exercises
Chapter 4 The Exponential and Natural Logarithm Functions
4.1 Exponential Functions
Laws of Exponents
Using the Laws of Exponents
Solution
Exponential Functions
Solving Equations with Exponentials
Solution
Check Your Understanding 4.1
Exercises 4.1
Technology Exercises
Solutions to Check Your Understanding 4.1
4.2 The Exponential Function ex
Derivative of an Exponential Calculate
Solution
Applying the Laws of Exponents with ex
Solution
Tangent Line to an Exponential Graph
Solution
Derivatives Involving ex
Solution
Differentiating an Exponential
Solution
Graph of an Exponential
Solution
4.3 Differentiation of Exponential Functions
Derivative of Functions of the Form eg(x)
Solution
Quotient Rule with Exponential Functions
Solution
Combined Returns from Two Investments
Solution
Check Your Understanding 4.3
Exercises 4.3
Technology Exercises
Solutions to Check Your Understanding 4.3
4.4 The Natural Logarithm Function
Using Properties of Exponential and Logarithm Functions
Solution
Solving Equations with Exponentials
Solution
Solving Equations with Logarithms
Solution
Other Exponential and Logarithm Functions
An Investment Portfolio
Solution
Check Your Understanding 4.4
Exercises 4.4
Technology Exercises
Solutions to Check Your Understanding 4.4
4.5 The Derivative of ln X
Derivatives Involving In x
Solution
Derivatives of Functions of the Form y=ln⁡[g(x)]
Solution
Analyzing a Function Involving ln x
Solution
Derivative of ln |x|
Solution
Check Your Understanding 4.5
Exercises 4.5
Technology Exercises
Solutions to Check Your Understanding 4.5
4.6 Properties of the Natural Logarithm Function
Simplifying Expressions with Logarithms
Solution
Simplifying Expressions with Logarithms
Solution
Using Properties of the Logarithms
Solution
Differentiating after Simplifying
Solution
Logarithmic Differentiation
Logarithmic Differentiation
Solution
Check Your Understanding 4.6
Exercises 4.6
Solutions to Check Your Understanding 4.6
Chapter 4 Summary
Chapter 4 Fundamental Concept Check Exercise
Chapter 4 Review Exercises
Chapter 5 Applications of the Exponential and Natural Logarithm Functions
5.1 Exponential Growth and Decay
Exponential Growth
Solving a Differential Equation
Solution
Exponential Growth of a Fruit Flies Population
Solution
A Differential Equation with Initial Condition
Solution
Exponential Growth
Solution
Determining the Growth Constant
Solution
Working with a Differential Equation
Solution
Exponential Decay
Exponential Decay
Solution
Half-Life and Decay Constant
Solution
Radiocarbon Dating
Carbon Dating
Solution
The Time Constant
Check Your Understanding 5.1
Exercises 5.1
Solutions to Check Your Understanding 5.1
5.2 Compound Interest
Continuous Compounding
Continuous Compound Interest
Solution
Appreciation of a Painting
Solution
Ordinary Versus Continuous Compounding
Negative Interest Rates
Negative Interest Rate
Solution
Present Value
Present Value
Solution
A Limit Formula for e
Check Your Understanding 5.2
Exercises 5.2
Technology Exercises
Solutions to Check Your Understanding 5.2
5.3 Applications of the Natural Logarithm Function to Economics
Log Derivative and Relative Rate of Change
Solution
Gross Domestic Product
Solution
Constant Relative Rate of Change
Solution
Elasticity of Demand
Elasticity of Demand
Solution
Elasticity, Price and Revenue
Elasticity of Demand
Solution
Check Your Understanding 5.3
Exercises 5.3
Technology Exercises
Solutions to Check Your Understanding 5.3
5.4 Further Exponential Models
Terminal Velocity
Velocity of a Skydiver
Solution
The Learning Curve
Diffusion of Information by Mass Media
Diffusion of Information
Solution
Intravenous Infusion of Glucose
Logistic Growth
Logistic Growth
Solution
An Epidemic Model
Spread of an Epidemic
Solution
Check Your Understanding 5.4
Exercises 5.4
Technology Exercises
Solutions to Check Your Understanding 5.4
Chapter 5 Summary
Chapter 5 Fundamental Concept Check Exercises
Chapter 5 Review Exercises
Chapter 6 The Definite Integral
6.1 Antidifferentiation
Determining the Height of a Rocket from Its Velocity
Solution (Part 1)
A Power Function
Solution
An Exponential Function
Solution
6.2 The Definite Integral and Net Change of a Function
Computing a Definite Integral
Solution
Definite Integral of an Exponential
Solution
Properties of the Definite Integral
The Definite Integral as a Net Change of a Function
Net Change in Position
Solution
Marginal Revenue Analysis
Solution
Net Increase in Federal Health Expenditures
Solution
Check Your Understanding 6.2
Exercises 6.2
Solution to Check Your Understanding 6.2
6.3 The Definite Integral and Area under a Graph
Verifying Theorem I
Solution
Area under the Graph of a Function
Solution
Area under a Cubic
Solution
Riemann Sums
Approximating the Area of a Waterfront Lot
Solution
A Riemann Sum Approximation of an Area
Solution
Improving a Riemann Sum Approximation
Solution
Check Your Understanding 6.3
Exercises 6.3
Technology Exercises
Solutions to Check Your Understanding 6.3
6.4 Areas in the xy-Plane
Area Bounded by a Curve and the x-Axis
Solution
Area Bounded by a Curve and the x-Axis
Solution
Area between Two Curves
Area between Two Curves
Solution
Area between Two Curves
Solution
Area between Two Curves
Solution
Area between Two Curves and Points of Intersection
Solution
Area between Two Curves and Points of Intersection
Solution
Areas in Applications
Marginal Profit
Solution
Displacement versus Distance Traveled
Solution
Launch of an Online Transportation Network
Solution
Areas in the Theory of Calculus: The Area Function
Check Your Understanding 6.4
Exercises 6.4
Technology Exercises
Solutions to Check Your Understanding 6.4
6.5 Applications of the Definite Integral
Using an Integral to Approximate a Sum
Solution
The Average Value of a Function
Average Value
Solution
Average World Population
Solution
Consumers’ Surplus
Consumers’ Surplus
Solution
Future Value of an Income Stream
Future Value of an Income Stream
Solution
Solids of Revolution
Volume of a Solid
Solution
Volume of a Cone
Solution
Check Your Understanding 6.5
Exercises 6.5
Technology Exercises
Solutions to Check Your Understanding 6.5
Chapter 6 Summary
Chapter 6 Fundamental Concept Check Exercises
Chapter 6 Review Exercises
Chapter 7 Functions of Several Variables
7.1 Examples of Functions of Several Variables
A Function with Two Variables
Solution
Application to Architectural Design
Heat-Loss Function
Solution
Production Functions in Economics
Production in a Firm
Solution
Level Curves
Level Curves
Solution
Check Your Understanding 7.1
Exercises 7.1
Solutions to Check Your Understanding 7.1
7.2 Partial Derivatives
Computing Partial Derivatives
Solution
Computing Partial Derivatives
Solution
Differentiation Rules and Partial Derivatives
Solution
Evaluating Partial Derivatives
Solution
Geometric Interpretation of Partial Derivatives
Partial Derivatives and Rates of Change
Interpreting Partial Derivatives
Solution
Partial Derivatives
Solution
Heat-Loss Function
Solution
Marginal Productivity of Capital
Solution
Partial Derivatives of Higher Order
Partial Derivatives of Higher Order
Solution
Check Your Understanding 7.2
Exercises 7.2
Solutions to Check Your Understanding 7.2
7.3 Maxima and Minima of  Functions of Several Variables
First Derivative Test
Locating a Minimum Point
Solution
Profit Function of Two Variables
Solution
Heat Loss
Solution
Second-Derivative Test
Application of the Second-Derivative Test
Solution
Applying the Second-Derivative Test
Solution
Check Your Understanding 7.3
Exercises 7.3
Solutions to Check Your Understanding 7.3
7.4 Lagrange Multipliers and Constrained Optimization
Problem
Lagrange Multipliers
Solution
Lagrange Multipliers
Solution
Maximizing Production
Solution
Lagrange Multipliers in Three Variables
Lagrange Multipliers in Three Variables
Solution
Check Your Understanding 7.4
Exercises 7.4
Solutions to Check Your Understanding 7.4
7.5  The Method of Least Squares
Problem of Fitting a Straight Line to Data
Problem
Least-Squares Error
Solution
Car-Accident-Related Deaths in the U.S.
Solution
Check Your Understanding 7.5
Exercises 7.5
Solutions to Check Your Understanding 7.5
7.6 Double Integrals
A Double Integral
Solution
A Double Integral
Solution
Volume Using a Double Integral
Solution
Double Integral over a Region
Solution
Check Your Understanding 7.6
Exercises 7.6
Solutions to Check Your Understanding 7.6
Chapter 7 Summary
Chapter 7 Fundamental Concept Check Exercises
Chapter 7 Review Exercises
Chapter 8 The Trigonometric Functions
8.1 Radian Measure of Angles
Converting Degrees to Radians
Solution
Measuring Angles in Radians
Solution
Check Your Understanding 8.1
Exercises 8.1
Solutions to Check Your Understanding 8.1
8.2 The Sine and the Cosine
Solving a Right Triangle
Solution
Values of the Cosine Function
Solution
Properties of the Sine and Cosine Functions
Graphs of sin t and cos t
Check Your Understanding 8.2
Exercises 8.2
Technology Exercises
Solutions to Check Your Understanding 8.2
8.3 Differentiation and Integration of sin t and cos t
Derivatives with the Sine Function
Solution
Derivatives with the Cosine Function
Solution
Differentiating Sine and Cosine Functions
Solution
Maximizing a Volume
Solution
Integrals of Sine Functions
Solution
Area under a Sine Curve
Solution
A Predators-and-Prey Model
Solution
Informal Justification of the Differentiation Rules for sin t and cos t
Check Your Understanding 8.3
Exercises 8.3
Solutions to Check Your Understanding 8.3
8.4 The Tangent and Other Trigonometric Functions
Determining the Height of a Building
Solution
The Derivative of tan t
Derivatives of Tangent Functions
Solution
The Graph of tan t
Check Your Understanding 8.4
Exercises 8.4
Solutions to Check Your Understanding 8.4
Chapter 8 Summary
Chapter 8 Fundamental Concept Check Exercises
Chapter 8 Review Exercises
Chapter 9 Techniques of Integration
9.1 Integration by Substitution
Integration by Substitution
First Solution
Second Solution of Example 1
Substitution with an Exponential
Solution
Substitution with a Radical
Solution
Substitution with a Logarithm
Solution
Substitution with an Exponential
Solution
Substitution with Fractional Powers
Solution
Integral of a Rational Function
Solution
Substitution with Trigonometric Functions
Solution
Check Your Understanding 9.1
Exercises 9.1
Solutions to Check Your Understanding 9.1
9.2 Integration by Parts
Integration by Parts
Solution
Integration by Parts
Solution
Product of x and an Exponential Function
Solution
Product of x and a Trigonometric Function
Solution
Product of a Power of x and a Logarithm
Solution
Applying Integration by Parts Twice
Solution
A Logarithmic Function
Solution
Check Your Understanding 9.2
Exercises 9.2
Solutions to Check Your Understanding 9.2
9.3 Evaluation of Definite Integrals
A Definite Integral with Substitution
First Solution
Second Solution
Integration by Parts in Definite Integrals
Definite Integral by Parts
Solution
Definite Integral by Parts
Solution
Check Your Understanding 9.3
Exercises 9.3
Solutions to Check Your Understanding 9.3
9.4 Approximation of Definite Integrals
The Midpoint Rule
Solution
The Trapezoidal Rule
Solution
Measuring Cardiac Output
Solution
Distribution of IQs
Solution
Geometric Interpretation of the Approximation Rules
Error Analysis
Error Analysis
Solution
Check Your Understanding 9.4
Exercises 9.4
Technology Exercises
Solutions to Check Your Understanding 9.4
9.5 Some Applications of the Integral
Present Value of an Income Stream
Solution
Present Value of an Income Stream
Solution
A Demographic Model
Solution
Check Your Understanding 9.5
Exercises 9.5
Solutions to Check Your Understanding 9.5
9.6 Improper Integrals
A Convergent Improper Integral
Solution
A Convergent Improper Integral
Solution
A Divergent Improper Integral
Solution
A Convergent Improper Integral
Solution
Check Your Understanding 9.6
Exercises 9.6
Solutions to Check Your Understanding 9.6
Chapter 9 Summary
Chapter 9 Fundamental Concept Check Exercises
Chapter 9 Review Exercises
Chapter 10 Differential Equations
10.1 Solutions of Differential Equations
Verifying a Solution
Solution
Verifying a Solution
Solution
Initial Value Problems
Solution
Constant Solutions
Solution
Modeling with Differential Equations
Newton’s Law of Cooling
Solution
Newton’s Law of Cooling
Solution
Geometric Meaning of a Differential Equation: Slope Fields
Slope Field
Solution
Using a Slope Field to Analyze a Solution
Solution
Check Your Understanding 10.1
Exercises 10.1
Technology Exercises
Solutions to Check Your Understanding 10.1
10.2 Separation of Variables
Separation of Variables
Solution
Separation of Variables
Solution
Separation of Variables
Solution
Initial Value Problem
Solution
Initial Value Problem
Solution
Check Your Understanding 10.2
Exercises 10.2
Solutions to Check Your Understanding 10.2
10.3 First-Order Linear Differential Equations
A First-Order Differential Equation
Solution
A First-Order Differential Equation
Solution
Initial-Value Problem
Solution
Check Your Understanding 10.3
Exercises 10.3
Technology Exercises
Solutions to Check Your Understanding 10.3
10.4 Applications of First-Order Linear Differential Equations
A Retirement Account
Solution
Paying Off a Car Loan
Solution
A Population Model with Emigration
Solution
Newton’s Law of Cooling
Solution
Newton’s Law of Cooling
Solution
Check Your Understanding 10.4
Exercises 10.4
Technology Exercises
Solution to Check Your Understanding 10.5
10.5 Graphing Solutions of Differential Equations
An Autonomous Differential Equation
Solution
Graphing a Solution
Solution
Constant Solutions and Graphing
Solution
Concavity of a Solution Curve
Solution
Check Your Understanding 10.5
Exercises 10.5
Technology Exercises
Solutions to Check Your Understanding 10.5
10.6 Applications of Differential Equations
Setting up a Differential Equation
Solution
Fish Population
Solution
Savings Account with Withdrawals
Solution
A One-Compartment Mixing Process
Solution
Check Your Understanding 10.6
Exercises 10.6
Solutions to Check Your Understanding 10.6
10.7 Numerical Solution of Differential Equations
Euler’s Method
Solution
Check Your Understanding 10.7
Exercises 10.7
Technology Exercises
Solutions to Check Your Understanding 10.7
Chapter 10 Summary
Chapter 10 Fundamental Concept Check Exercises
Chapter 10 Review Exercises
Chapter 11 Taylor Polynomials and Infinite Series
11.1 Taylor Polynomials
A Polynomial Approximation
Solution
Taylor Polynomial Approximation of ex
Solution
A Taylor Polynomial Approximation
Solution
Using Taylor Polynomials to Approximate an Integral
Solution
Taylor Polynomials at x=a
Centering a Taylor Polynomial
Solution
Accuracy of the Approximation
Using the Remainder Formula
Solution
Check Your Understanding 11.1
Exercises 11.1
Technology Exercises
Solution to Check Your Understanding 11.1
11.2 The Newton–Raphson Algorithm
Approximation Using Newton–Raphson
Solution
Iterating the Newton–Raphson Algorithm
Solution
Approximating Zeros of a Polynomial
Solution
Approximating Solutions
Solution
Internal Rate of Return
Solution
Monthly Interest Rate of a Loan
Solution
Check Your Understanding 11.2
Exercises 11.2
Technology Exercises
Solutions to Check Your Understanding 11.2
11.3 Infinite Series
Geometric Series
Solution
A Rational Number as a Geometric Series
Solution
The Multiplier Effect in Economics
Solution
Elimination of a Drug
Solution
Sigma Notation
Geometric Series and Sigma Notation
Solution
Check Your Understanding 11.3
Exercises 11.3
Technology Exercises
Solutions to Check Your Understanding 11.3
11.4 Series with Positive Terms
Applying the Integral Test
Solution
Applying the Integral Test
Solution
A Comparison Test
Solution
Check Your Understanding 11.4
Exercises 11.4
Solutions to Check Your Understanding 11.4
11.5 Taylor Series
A Taylor Series Centered at 0
Solution
A Taylor Series Centered at 0
Solution
Operations on Taylor Series
Differentiation and Integration Term by Term
Solution
Evaluating a Taylor Series
Solution
New Taylor Series from Known Ones
Solution
New Taylor Series from Known Ones
Solution
Definite Integrals
Integration Term by Term
Solution
Convergence of Power Series
Taylor Series at x=a
Check Your Understanding 11.5
Exercises 11.5
Solutions to Check Your Understanding 11.5
Chapter 11 Summary
Chapter 11 Fundamental Concept Check Exercises
Chapter 11 Review Exercises
Chapter 12 Probability and Calculus
12.1 Discrete Random Variables
Expected Value and Variance
Solution
Expected Value and Variance
Solution
Decision Making Based on Expected Value
Solution
Check Your Understanding 12.1
Exercises 12.1
Solutions to Check Your Understanding 12.1
12.2 Continuous Random Variables
Probability Density
Solution
Determining a Probability Density
Solution
A Beta Probability Density
Solution
Age of a Cell
Solution
Random Selection
Solution
Working with a Probability Density
Solution
Check Your Understanding 12.2
Exercises 12.2
Solutions to Check Your Understanding 12.2
12.3 Expected Value and Variance
Cumulative Distribution, Expected Value, and Variance
Solution
Average Age of a Cell Population
Solution
Random Selection in a Circle
Solution
Proportion of Students Using a Library
Solution
Check Your Understanding 12.3
Exercises 12.3
Solutions to Check Your Understanding 12.3
12.4 Exponential and Normal Random Variables
Exponential Density Functions
Exponential Density
Solution
Time between Phone Calls
Solution
Normal Density Functions
A Standard Normal Random Variable
Solution
Length of a Metal Flange
Solution
Check Your Understanding 12.4
Exercises 12.4
Technology Exercises
Solutions to Check Your Understanding 12.4
12.5 Poisson and Geometric Random Variables
Poisson Random Variables
A Poisson Distribution
Solution
Computing Probabilities with a Poisson Distribution
Solution
Modeling with a Poisson Distribution
Solution
Geometric Random Variables
A Geometric Distribution in Quality Control
Solution
Expected Number of Defective Toys
Solution
Check Your Understanding 12.5
Exercises 12.5
Technology Exercises
Solutions to Check Your Understanding 12.5
Chapter 12 Summary
Chapter 12 Fundamental Concept Check Exercises
Chapter 12 Review Exercises
Appendix Areas under the Standard Normal Curve
Learning Objectives
Chapter 0: Functions
0.1 Functions and Their Graphs
0.2 Some Important Functions
0.3 The Algebra of Functions
0.4 Zeros of Functions—The Quadratic Formula and Factoring
0.5 Exponents and Power Functions
0.6 Functions and Graphs in Applications
Chapter 1: The Derivative
1.1 The Slope of a Straight Line
1.2 The Slope of a Curve at a Point
1.3 The Derivative and Limits
1.4 Limits and the Derivative
1.5 Differentiability and Continuity
1.6 Some Rules for Differentiation
1.7 More about Derivatives
1.8 The Derivative as a Rate of Change
Chapter 2: Applications of the Derivative
2.1 Describing Graphs of Functions
2.2 The First- and Second-Derivative Rules
2.3 The First- and Second-Derivative Tests and Curve Sketching
2.4 Curve Sketching (Conclusion)
2.5 Optimization Problems
2.6 Further Optimization Problems
2.7 Applications of Derivatives to Business and Economics
Chapter 3: Techniques of Differentiation
3.1 The Product and Quotient Rules
3.2 The Chain Rule and the General Power Rule
3.3 Implicit Differentiation and Related Rates
Chapter 4: The Exponential and Natural Logarithm Functions
4.1 Exponential Functions
4.2 The Exponential Function ex
4.3 Differentiation of Exponential Functions
4.4 The Natural Logarithm Function
4.5 The Derivative of ln x
4.6 Properties of the Natural Logarithm Function
Chapter 5: Applications of the Exponential and Natural Logarithm Functions
5.1 Exponential Growth and Decay
5.2 Compound Interest
5.3 Applications of the Natural Logarithm Function to Economics
5.4 Further Exponential Models
Chapter 6: The Definite Integral
6.1 Antidifferentiation
6.2 The Definite Integral and Net Change of a Function
6.3 The Definite Integral and Area under a Graph
6.4 Areas in the xy–Plane
6.5 Applications of the Definite Integral
Chapter 7: Functions of Several Variables
7.1 Examples of Functions of Several Variables
7.2 Partial Derivatives
7.3 Maxima and Minima of Functions of Several Variables
7.4 Lagrange Multipliers and Constrained Optimization
7.5 The Method of Least Squares
7.6 Double Integrals
Chapter 8: The Trigonometric Functions
8.1 Radian Measure of Angles
8.2 The Sine and the Cosine
8.3 Differentiation and Integration of sin t and cos t
8.4 The Tangent and Other Trigonometric Functions
Chapter 9: Techniques of Integration
9.1 Integration by Substitution
9.2 Integration by Parts
9.3 Evaluation of Definite Integrals
9.4 Approximation of Definite Integrals
9.5 Some Applications of the Integral
9.6 Improper Integrals
Chapter 10: Differential Equations
10.1 Solutions of Differential Equations
10.2 Separation of Variables
10.3 First-Order Linear Differential Equations
10.4 Applications of First-Order Linear Differential Equations
10.5 Graphing Solutions of Differential Equations
10.6 Applications of Differential Equations
10.7 Numerical Solution of Differential Equations
Chapter 11: Taylor Polynomials and Infinite Series
11.1 Taylor Polynomials
11.2 The Newton–Raphson Algorithm
11.3 Infinite Series
11.4 Series with Positive Terms
11.5 Taylor Series
Chapter 12: Probability and Calculus
12.1 Discrete Random Variables
12.2 Continuous Random Variables
12.3 Expected Value and Variance
12.4 Exponential and Normal Random Variables
12.5 Poisson and Geometric Random Variables
Sources
Selected Answers
Prerequisite Skills Diagnostic Test
Exercises 0.1, page 9
Exercises 0.2, page 18
Exercises 0.3, page 23
Exercises 0.4, page 31
Exercises 0.5, page 39
Exercises 0.6, page 47
Chapter 0: Chapter Review Exercises, page 54
Chapter 1
Exercises 1.1, page 63
Exercises 1.2, page 69
Exercises 1.3, page 79
Exercises 1.4, page 89
Exercises 1.5, page 96
Exercises 1.6, page 102
Exercises 1.7, page 110
Exercises 1.8, page 119
Chapter 1 : Review Exercises, page 129
Chapter 2
Exercises 2.1, page 138
Exercises 2.2, page 145
Exercises 2.3, page 156
Exercises 2.4, page 162
Exercises 2.5, page 168
Exercises 2.6, page 175
Exercises 2.7, page 183
Chapter 2: Chapter Review Exercises, page 190
Chapter 3
Exercises 3.1, page 199
Exercises 3.2, page 206
Exercises 3.3, page 215
Chapter 3: Review Exercises, page 219
Chapter 4
Exercises 4.1, page 225
Exercises 4.2, page 231
Exercises 4.3, page 235
Exercises 4.4, page 240
Exercises 4.5, page 244
Exercises 4.6, page 248
Chapter 4 : Review Exercises, page 252
Chapter 5
Exercises 5.1, page 262
Exercises 5.2, page 269
Exercises 5.3, page 277
Exercises 5.4, page 286
Chapter 5: Review Exercises, page 289
Chapter 6
Exercises 6.1, page 299
Exercises 6.2, page 307
Exercises 6.3, page 317
Exercises 6.4, page 329
Exercises 6.5, page 338
Chapter 6: Review Exercises, page 344
Chapter 7
Exercises 7.1, page 352
Exercises 7.2, page 361
Exercises 7.3, page 368
Exercises 7.4, page 376
Exercises 7.5, page 383
Exercises 7.6, page 388
Chapter 7: Review Exercises, page 392
Chapter 8
Exercises 8.1, page 397
Exercises 8.2, page 402
Exercises 8.3, page 409
Exercises 8.4, page 414
Chapter 8: Review Exercises, page 418
Chapter 9
Exercises 9.1, page 426
Exercises 9.2, page 430
Exercises 9.3, page 434
Exercises 9.4, page 441
Exercises 9.5, page 448
Exercises 9.6, page 452
Chapter 9: Review Exercises, page 459
Chapter 10
Exercises 10.1, page 466
Exercises 10.2, page 473
Exercises 10.3, page 478
Exercises 10.4, page 483
Exercises 10.5, page 492
Exercises 10.6, page 498
Exercises 10.7, page 504
Chapter 10: Review Exercises, page 510
Chapter 11
Exercises 11.1, page 518
Exercises 11.2, page 524
Exercises 11.3, page 532
Exercises 11.4, page 538
Exercises 11.5, page 545
Chapter 11: Review Exercises, page 549
Chapter 12
Exercises 12.1, page 557
Exercises 12.2, page 564
Exercises 12.3, page 569
Exercises 12.4, page 577
Exercises 12.5, page 584
Chapter 12: Review Exercises, page 588
Index of Applications
Business and Economics
Health and Life Sciences
Physical Science
Social Sciences
General Interest
Index
A
B
C
D
E
F
G
H
I
J
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
Useful Algebraic Facts
Useful Geometric Formulas
Useful Differentiation Facts
Useful Integration Facts
MyMathLab®: Support You Need, When You Need It
Review Prerequisite Skills
Tutorial Videos
Interactive Figures

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