Efnisyfirlit

• Introduction
  • What You'll Find
  • Beyond the Book
    • What you'll find online
    • How to register
  • Where to Go for Additional Help
• Part I: The Questions
  • Chapter 1: Algebra Review
    • The Problems You'll Work On
    • What to Watch Out For
    • Simplifying Fractions
    • Simplifying Radicals
    • Writing Exponents Using Radical Notation
    • The Horizontal Line Test
    • Find Inverses Algebraically
    • The Domain and Range of a Function and Its Inverse
    • Linear Equations
    • Quadratic Equations
    • Solving Polynomial Equations by Factoring
    • Absolute Value Equations
    • Solving Rational Equations
    • Polynomial and Rational Inequalities
    • Absolute Value Inequalities
    • Graphing Common Functions
    • Domain and Range from a Graph
    • End Behavior of Polynomials
    • Adding Polynomials
    • Subtracting Polynomials
    • Multiplying Polynomials
    • Long Division of Polynomials
  • Chapter 2: Trigonometry Review
    • The Problems You'll Work On
    • What to Watch Out For
    • Basic Trigonometry
    • Converting Degree Measure to Radian Measure
    • Converting Radian Measure to Degree Measure
    • Finding Angles in the Coordinate Plane
    • Finding Common Trigonometric Values
    • Simplifying Trigonometric Expressions
    • Solving Trigonometric Equations
    • Amplitude, Period, Phase Shift, and Midline
    • Equations of Periodic Functions
    • Inverse Trigonometric Function Basics
    • Solving Trigonometric Equations Using Inverses
  • Chapter 3: Limits and Rates of Change
    • The Problems You'll Work On
    • What to Watch Out For
    • Finding Limits from Graphs
    • Evaluating Limits
    • Applying the Squeeze Theorem
    • Evaluating Trigonometric Limits
    • Infinite Limits
    • Limits from Graphs
    • Limits at Infinity
    • Horizontal Asymptotes
    • Classifying Discontinuities
    • Continuity and Discontinuities
    • Making a Function Continuous
    • The Intermediate Value Theorem
  • Chapter 4: Derivative Basics
    • The Problems You'll Work On
    • What to Watch Out For
    • Determining Differentiability from a Graph
    • Finding the Derivative by Using the Definition
    • Finding the Value of the Derivative Using a Graph
    • Using the Power Rule to Find Derivatives
    • Finding All Points on a Graph Where Tangent Lines Have a Given Value
  • Chapter 5: The Product, Quotient, and Chain Rules
    • The Problems You'll Work On
    • What to Watch Out For
    • Using the Product Rule to Find Derivatives
    • Using the Quotient Rule to Find Derivatives
    • Using the Chain Rule to Find Derivatives
    • More Challenging Chain Rule Problems
  • Chapter 6: Exponential and Logarithmic Functions and Tangent Lines
    • The Problems You'll Work On
    • What to Watch Out For
    • Derivatives Involving Logarithmic Functions
    • Logarithmic Differentiation to Find the Derivative
    • Finding Derivatives of Functions Involving Exponential Functions
    • Finding Equations of Tangent Lines
    • Finding Equations of Normal Lines
  • Chapter 7: Implicit Differentiation
    • The Problems You'll Work On
    • What to Watch Out For
    • Using Implicit Differentiation to Find a Derivative
    • Using Implicit Differentiation to Find a Second Derivative
    • Finding Equations of Tangent Lines Using Implicit Differentiation
  • Chapter 8: Applications of Derivatives
    • The Problems You'll Work On
    • What to Watch Out For
    • Finding and Evaluating Differentials
    • Finding Linearizations
    • Using Linearizations to Estimate Values
    • Understanding Related Rates
    • Finding Maxima and Minima from Graphs
    • Using the Closed Interval Method
    • Finding Intervals of Increase and Decrease
    • Using the First Derivative Test to Find Local Maxima and Minima
    • Determining Concavity
    • Identifying Inflection Points
    • Using the Second Derivative Test to Find Local Maxima and Minima
    • Applying Rolle's Theorem
    • Using the Mean Value Theorem
    • Applying the Mean Value Theorem to Solve Problems
    • Relating Velocity and Position
    • Finding Velocity and Speed
    • Solving Optimization Problems
    • Doing Approximations Using Newton's Method
    • Approximating Roots Using Newton's Method
  • Chapter 9: Areas and Riemann Sums
    • The Problems You'll Work On
    • What to Watch Out For
    • Calculating Riemann Sums Using Left Endpoints
    • Calculating Riemann Sums Using Right Endpoints
    • Calculating Riemann Sums Using Midpoints
    • Using Limits and Riemann Sums to Find Expressions for Definite Integrals
    • Finding a Definite Integral from the Limit and Riemann Sum Form
    • Using Limits and Riemann Sums to Evaluate Definite Integrals
  • Chapter 10: The Fundamental Theorem of Calculus and the Net Change Theorem
    • The Problems You'll Work On
    • What to Watch Out For
    • Using the Fundamental Theorem of Calculus to Find Derivatives
    • Working with Basic Examples of Definite Integrals
    • Understanding Basic Indefinite Integrals
    • Understanding the Net Change Theorem
    • Finding the Displacement of a Particle Given the Velocity
    • Finding the Distance Traveled by a Particle Given the Velocity
    • Finding the Displacement of a Particle Given Acceleration
    • Finding the Distance Traveled by a Particle Given Acceleration
  • Chapter 11: Applications of Integration
    • The Problems You'll Work On
    • What to Watch Out For
    • Areas between Curves
    • Finding Volumes Using Disks and Washers
    • Finding Volume Using Cross-Sectional Slices
    • Finding Volumes Using Cylindrical Shells
    • Work Problems
    • Average Value of a Function
  • Chapter 12: Inverse Trigonometric Functions, Hyperbolic Functions, and L'Hôpital's Rule
    • The Problems You'll Work On
    • What to Watch Out For
    • Finding Derivatives Involving Inverse Trigonometric Functions
    • Finding Antiderivatives by Using Inverse Trigonometric Functions
    • Evaluating Hyperbolic Functions Using Their Definitions
    • Finding Derivatives of Hyperbolic Functions
    • Finding Antiderivatives of Hyperbolic Functions
    • Evaluating Indeterminate Forms Using L'Hôpital's Rule
  • Chapter 13: U-Substitution and Integration by Parts
    • The Problems You'll Work On
    • What to Watch Out For
    • Using u-Substitutions
    • Using Integration by Parts
  • Chapter 14: Trigonometric Integrals, Trigonometric Substitution, and Partial Fractions
    • The Problems You'll Work On
    • What to Watch Out For
    • Trigonometric Integrals
    • Trigonometric Substitutions
    • Finding Partial Fraction Decompositions (without Coefficients)
    • Finding Partial Fraction Decompositions (Including Coefficients)
    • Integrals Involving Partial Fractions
    • Rationalizing Substitutions
  • Chapter 15: Improper Integrals and More Approximating Techniques
    • The Problems You'll Work On
    • What to Watch Out For
    • Convergent and Divergent Improper Integrals
    • The Comparison Test for Integrals
    • The Trapezoid Rule
    • Simpson's Rule
• Part II: The Answers
  • Chapter 16: Answers and Explanations
• About the Author
• Cheat Sheet
• More Dummies Products
• End User License Agreement

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