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HAWKESTV

Single Variable Calculus
with Early Transcendentals

Chapter 1: A Function Primer

  1. 1.1 Functions and How We Represent Them
    1. Example 1: Functions and How We Represent Them
    2. Example 2: Functions and How We Represent Them
    3. Example 3: Functions and How We Represent Them
    4. Example 4: Functions and How We Represent Them
    5. Example 5: Functions and How We Represent Them
    6. Example 6: Functions and How We Represent Them
    7. Example 7: Functions and How We Represent Them
    8. Example 8: Functions and How We Represent Them
    9. Example 9: Functions and How We Represent Them
  2. 1.2 A Function Repertory
    1. Example 1: A Function Repertory
    2. Example 2: A Function Repertory
    3. Example 3: A Function Repertory
    4. Example 4: A Function Repertory
    5. Example 5: A Function Repertory
    6. Example 6: A Function Repertory
    7. Example 7: A Function Repertory
    8. Example 8: A Function Repertory
  3. 1.3 Transforming and Combining Functions
    1. Example 1: Transforming and Combining Functions
    2. Example 2: Transforming and Combining Functions
    3. Example 3: Transforming and Combining Functions
    4. Example 4: Transforming and Combining Functions
    5. Example 5: Transforming and Combining Functions
    6. Example 6: Transforming and Combining Functions
    7. Example 7: Transforming and Combining Functions
    8. Example 8: Transforming and Combining Functions
    9. Example 9: Transforming and Combining Functions
    10. Example 10: Transforming and Combining Functions
    11. Example 11: Transforming and Combining Functions
  4. 1.4 Inverse Functions
    1. Example 1: Inverse Functions
    2. Example 2: Inverse Functions
    3. Example 3: Inverse Functions
    4. Example 4: Inverse Functions
    5. Example 5: Inverse Functions
    6. Example 6: Inverse Functions
    7. Example 7: Inverse Functions
    8. Example 8: Inverse Functions
    9. Example 9: Inverse Functions
    10. Example 10: Inverse Functions
  5. 1.5 Calculus, Calculators, and Computer Algebra Systems

Chapter 2: Limits and the Derivative

  1. 2.1 Rates of Change and Tangents
    1. Example 1: Rates of Change and Tangents
    2. Example 2: Rates of Change and Tangents
    3. Example 3: Rates of Change and Tangents
    4. Example 4: Rates of Change and Tangents
    5. Example 5: Rates of Change and Tangents
  2. 2.2 Limits All Around the Plane
    1. Example 1: Limits All Around the Plane
    2. Example 2: Limits All Around the Plane
    3. Example 3: Limits All Around the Plane
    4. Example 4: Limits All Around the Plane
    5. Example 5: Limits All Around the Plane
    6. Example 6: Limits All Around the Plane
    7. Example 7: Limits All Around the Plane
  3. 2.3 The Mathematical Definition of Limit
    1. Example 1: The Mathematical Definition of Limit
    2. Example 2: The Mathematical Definition of Limit
    3. Example 3: The Mathematical Definition of Limit
    4. Example 4: The Mathematical Definition of Limit
    5. Example 5: The Mathematical Definition of Limit
    6. Example 6: The Mathematical Definition of Limit
    7. Example 7: The Mathematical Definition of Limit
  4. 2.4 Determining Limits of Functions
    1. Example 1: Determining Limits of Functions
    2. Example 2: Determining Limits of Functions
    3. Example 3: Determining Limits of Functions
    4. Example 4: Determining Limits of Functions
    5. Example 5: Determining Limits of Functions
    6. Example 6: Determining Limits of Functions
    7. Example 7: Determining Limits of Functions
    8. Example 8: Determining Limits of Functions
  5. 2.5 Continuity
    1. Example 1: Continuity
    2. Example 2: Continuity
    3. Example 3: Continuity
    4. Example 4: Continuity
    5. Example 5: Continuity
    6. Example 6: Continuity
    7. Example 7: Continuity
    8. Example 8: Continuity
    9. Example 9: Continuity
    10. Example 10: Continuity
    11. Example 11: Continuity
  6. 2.6 Rate of Change Revisited: The Derivative
    1. Example 1: Rate of Change Revisited: The Derivative
    2. Example 2: Rate of Change Revisited: The Derivative
    3. Example 3: Rate of Change Revisited: The Derivative
    4. Example 4: Rate of Change Revisited: The Derivative
    5. Example 5: Rate of Change Revisited: The Derivative
    6. Example 6: Rate of Change Revisited: The Derivative

Chapter 3: Differentiation

  1. 3.1 Differentiation Notation and Consequences
    1. Topics
    2. Topic 1: Alternative Notations and Higher-Order Derivatives
    3. Topic 2: Consequences of Differentiability
    4. Examples
    5. Example 1: Differentiation Notation and Consequences
    6. Example 2: Differentiation Notation and Consequences
    7. Example 3: Differentiation Notation and Consequences
    8. Example 4: Differentiation Notation and Consequences
    9. Example 5: Differentiation Notation and Consequences
    10. Example 6: Differentiation Notation and Consequences
  2. 3.2 Derivatives of Polynomials, Exponentials, Products, and Quotients
    1. Topics
    2. Topic 1: Elementary Differentiation Rules
    3. Topic 2: Differentiation of Exponential Functions
    4. Topic 3: The Product and Quotient Rules
    5. Examples
    6. Example 1 Elementary Differentiation Rules
    7. Example 2 Elementary Differentiation Rules
    8. Example 3 Elementary Differentiation Rules
    9. Example 4 Elementary Differentiation Rules
    10. Example 5 Differentiation of Exponential Functions
    11. Example 6 The Product and Quotient Rules
    12. Example 7 The Product and Quotient Rules
    13. Example 8 The Product and Quotient Rules
    14. Example 9 The Product and Quotient Rules
  3. 3.3 Derivatives of Trigonometric Functions
    1. Topics
    2. Topic 1: Two Useful Limits
    3. Topic 2: Derivatives of Sine and Cosine
    4. Topic 3: Derivatives of Other Trigonometric Functions
    5. Examples
    6. Example 1: Derivatives of Trigonometric Functions
    7. Example 2: Derivatives of Trigonometric Functions
    8. Example 3: Derivatives of Trigonometric Functions
    9. Example 4: Derivatives of Trigonometric Functions
    10. Example 5: Derivatives of Trigonometric Functions
    11. Example 6: Derivatives of Trigonometric Functions
    12. Example 7: Derivatives of Trigonometric Functions
    13. Example 8: Derivatives of Trigonometric Functions
  4. 3.4 The Chain Rule
    1. Topics
    2. Topic 1: Proof of the chain rule
    3. Topic 2: Consequences of the chain rule
    4. Examples
    5. Example 1: The Chain Rule
    6. Example 2: The Chain Rule
    7. Example 3: The Chain Rule
    8. Example 4: The Chain Rule
    9. Example 5: The Chain Rule
    10. Example 6: The Chain Rule
    11. Example 7: The Chain Rule
  5. 3.5 Implicit Differentiation
    1. Topics
    2. Topic 1: Derivatives of implicitly defined functions
    3. Examples
    4. Example 1 Derivatives of Implicitly Defined Functions
    5. Example 2 Derivatives of Implicitly Defined Functions
    6. Example 3 Derivatives of Implicitly Defined Functions
    7. Example 4 Derivatives of Implicitly Defined Functions
    8. Example 5 Higher-Order Derivatives
    9. Example 6 Higher-Order Derivatives
  6. 3.6 Derivatives of Inverse Functions
    1. Topics
    2. Topic 1: The derivative rule for inverse functions
    3. Examples
    4. Example 1: Derivatives of Inverse Functions
    5. Example 2: Derivatives of Inverse Functions
    6. Example 3: Derivatives of Inverse Functions
    7. Example 4: Derivatives of Inverse Functions
    8. Example 5: Derivatives of Inverse Functions
    9. Example 6: Derivatives of Inverse Functions
    10. Example 7: Derivatives of Inverse Functions
    11. Example 8: Derivatives of Inverse Functions
    12. Example 9: Derivatives of Inverse Functions
  7. 3.7 Rates of Change in Use
    1. Example 1: Rates of Change in Use
    2. Example 2: Rates of Change in Use
    3. Example 3: Rates of Change in Use
    4. Example 4: Rates of Change in Use
    5. Example 5: Rates of Change in Use
  8. 3.8 Related Rates
    1. Example 1 Constructing and Solving Related Rates Equations
    2. Example 2 Constructing and Solving Related Rates Equations
    3. Example 3 Constructing and Solving Related Rates Equations
    4. Example 4 Constructing and Solving Related Rates Equations
    5. Example 5 Constructing and Solving Related Rates Equations
  9. 3.9 Linearization and Differentials
    1. Example 2: Linearization and Differentials
    2. Example 3: Linearization and Differentials
    3. Example 4: Linearization and Differentials

Chapter 4: Applications of Differentiation

  1. 4.1 Extreme Values of Functions
    1. Example 1: Extreme Values of Functions
    2. Example 2: Extreme Values of Functions
    3. Example 3: Extreme Values of Functions
    4. Example 4: Extreme Values of Functions
    5. Example 5: Extreme Values of Functions
    6. Example 6: Extreme Values of Functions
  2. 4.2 The Mean Value Theorem
    1. Example 1: The Mean Value Theorem
    2. Example 2: The Mean Value Theorem
    3. Example 3: The Mean Value Theorem
    4. Example 4: The Mean Value Theorem
    5. Example 5: The Mean Value Theorem
    6. Example 6: The Mean Value Theorem
  3. 4.3 The First and Second Derivative Tests
    1. Example 1: The First and Second Derivative Tests
    2. Example 2: The First and Second Derivative Tests
    3. Example 3: The First and Second Derivative Tests
    4. Example 4: The First and Second Derivative Tests
  4. 4.4 Lôpital's Rule
    1. Example 1: L'Hôpital's Rule
    2. Example 2: L'Hôpital's Rule
    3. Example 3: L'Hôpital's Rule
    4. Example 4: L'Hôpital's Rule
    5. Example 5: L'Hôpital's Rule
    6. Example 6: L'Hôpital's Rule
    7. Example 7: L'Hôpital's Rule
    8. Example 8: L'Hôpital's Rule
    9. Example 9: L'Hôpital's Rule
  5. 4.5 Calculus and Curve Sketching
    1. Example 1: Calculus and Curve Sketching
    2. Example 2: Calculus and Curve Sketching
    3. Example 3: Calculus and Curve Sketching
    4. Example 4: Calculus and Curve Sketching
    5. Example 5: Calculus and Curve Sketching
    6. Example 6: Calculus and Curve Sketching
    7. Example 7: Calculus and Curve Sketching
  6. 4.6 Optimization Problems
    1. Example 1: Optimization Problems
    2. Example 2: Optimization Problems
    3. Example 3: Optimization Problems
    4. Example 4: Optimization Problems
    5. Example 5: Optimization Problems
    6. Example 6: Optimization Problems
  7. 4.7 Antiderivatives
    1. Topics
    2. Topic 1: Finding Antiderivatives
    3. Topic 2: Antiderivatives in Use
    4. Examples
    5. Example 1 Finding Antiderivatives
    6. Example 2 Finding Antiderivatives
    7. Example 3 Finding Antiderivatives
    8. Example 4 Antiderivatives in Use
    9. Example 5 Antiderivatives in Use
    10. Example 6 Antiderivatives in Use

Chapter 5: Integration

  1. 5.1 Area, Distance, and Riemann Sums
    1. Example 1: Area, Distance, and Riemann Sums
    2. Example 2: Area, Distance, and Riemann Sums
    3. Example 3: Area, Distance, and Riemann Sums
    4. Example 4: Area, Distance, and Riemann Sums
  2. 5.2 The Definite Integral
    1. Example 1: The Definite Integral
    2. Example 2: The Definite Integral
    3. Example 3: The Definite Integral
    4. Example 4: The Definite Integral
    5. Example 5: The Definite Integral
    6. Example 6: The Definite Integral
  3. 5.3 The Fundamental Theorem of Calculus
    1. Example 1: The Fundamental Theorem of Calculus
    2. Example 2: The Fundamental Theorem of Calculus
    3. Example 3: The Fundamental Theorem of Calculus
    4. Example 4: The Fundamental Theorem of Calculus
    5. Example 5: The Fundamental Theorem of Calculus
    6. Example 6: The Fundamental Theorem of Calculus
    7. Example 7: The Fundamental Theorem of Calculus
  4. 5.4 Indefinite Integrals and the Substitution Rule
    1. Example 1: Indefinite Integrals and the Substitution Rule
    2. Example 2: Indefinite Integrals and the Substitution Rule
    3. Example 3: Indefinite Integrals and the Substitution Rule
    4. Example 4: Indefinite Integrals and the Substitution Rule
  5. 5.5 The Substitution Rule and Definite Integration
    1. Example 1: The Substitution Rule and Definite Integration
    2. Example 2: The Substitution Rule and Definite Integration
    3. Example 3: The Substitution Rule and Definite Integration
    4. Example 4: The Substitution Rule and Definite Integration

Chapter 6: Applications of the Definite Integral

  1. 6.1 Finding Volumes Using Slices
    1. Example 1: Finding Volumes Using Slices
    2. Example 2: Finding Volumes Using Slices
    3. Example 3: Finding Volumes Using Slices
    4. Example 4: Finding Volumes Using Slices
    5. Example 5: Finding Volumes Using Slices
    6. Example 6: Finding Volumes Using Slices
    7. Example 7: Finding Volumes Using Slices
    8. Example 8: Finding Volumes Using Slices
    9. Example 9: Finding Volumes Using Slices
  2. 6.2 Finding Volumes Using Cylindrical Shells
    1. Example 1: Finding Volumes Using Cylindrical Shells
    2. Example 2: Finding Volumes Using Cylindrical Shells
    3. Example 3: Finding Volumes Using Cylindrical Shells
    4. Example 4: Finding Volumes Using Cylindrical Shells
  3. 6.3 Arc Length and Surface Area
    1. Example 1: Arc Length and Surface Area
    2. Example 2: Arc Length and Surface Area
    3. Example 3: Arc Length and Surface Area
    4. Example 4: Arc Length and Surface Area
  4. 6.4 Moments and Centers of Mass
    1. Example 1: Moments and Centers of Mass
    2. Example 2: Moments and Centers of Mass
    3. Example 3: Moments and Centers of Mass
    4. Example 4: Moments and Centers of Mass
    5. Example 5: Moments and Centers of Mass
    6. Example 6: Moments and Centers of Mass
    7. Example 7: Moments and Centers of Mass
  5. 6.5 Force, Work, and Pressure
    1. Example 1: Force, Work, and Pressure
    2. Example 2: Force, Work, and Pressure
    3. Example 3: Force, Work, and Pressure
    4. Example 4: Force, Work, and Pressure
    5. Example 5: Force, Work, and Pressure
    6. Example 6: Force, Work, and Pressure
    7. Example 7: Force, Work, and Pressure
    8. Example 8: Force, Work, and Pressure
  6. 6.6 Hyperbolic Functions
    1. Example 1: Hyperbolic Functions
    2. Example 2: Hyperbolic Functions
    3. Example 3: Hyperbolic Functions
    4. Example 4: Hyperbolic Functions

Chapter 7: Techniques of Integration

  1. 7.1 Integration by Parts
    1. Example 1: Integration by Parts
    2. Example 2: Integration by Parts
    3. Example 3: Integration by Parts
    4. Example 4: Integration by Parts
    5. Example 5: Integration by Parts
    6. Example 6: Integration by Parts
    7. Example 7: Integration by Parts
    8. Example 8: Integration by Parts
  2. 7.2 The Partial Fractions Method
    1. Example 1: The Partial Fractions Method
    2. Example 2: The Partial Fractions Method
    3. Example 3: The Partial Fractions Method
    4. Example 4: The Partial Fractions Method
    5. Example 5: The Partial Fractions Method
    6. Example 6: The Partial Fractions Method
    7. Example 7: The Partial Fractions Method
  3. 7.3 Trigonometric Integrals
    1. Example 1: Trigonometric Integrals
    2. Example 2: Trigonometric Integrals
    3. Example 3: Trigonometric Integrals
    4. Example 4: Trigonometric Integrals
    5. Example 5: Trigonometric Integrals
    6. Example 6: Trigonometric Integrals
    7. Example 7: Trigonometric Integrals
    8. Example 8: Trigonometric Integrals
  4. 7.4 Trigonometric Substitutions
    1. Example 1: Trigonometric Substitutions
    2. Example 2: Trigonometric Substitutions
    3. Example 3: Trigonometric Substitutions
    4. Example 4: Trigonometric Substitutions
    5. Example 5: Trigonometric Substitutions
    6. Example 6: Trigonometric Substitutions
  5. 7.5 Integration Summary and Integration Using Computer Algebra Systems
    1. Example 1: Integration Summary and Integration Using Computer Algebra Systems
    2. Example 2: Integration Summary and Integration Using Computer Algebra Systems
  6. 7.6 Numerical Integration
    1. Example 1: Numerical Integration
    2. Example 2: Numerical Integration
    3. Example 3: Numerical Integration
    4. Example 4: Numerical Integration
    5. Example 5: Numerical Integration
    6. Example 6: Numerical Integration
  7. 7.7 Improper Integrals
    1. Example 1: Improper Integrals
    2. Example 2: Improper Integrals
    3. Example 3: Improper Integrals
    4. Example 4: Improper Integrals
    5. Example 5: Improper Integrals
    6. Example 6: Improper Integrals
    7. Example 7: Improper Integrals
    8. Example 8: Improper Integrals
    9. Example 9: Improper Integrals

Chapter 8: Differential Equations

  1. 8.1 Separable Differential Equations
    1. Example 1: Separable Differential Equations
    2. Example 2: Separable Differential Equations
    3. Example 3: Separable Differential Equations
    4. Example 4: Separable Differential Equations
    5. Example 5: Separable Differential Equations
  2. 8.2 First-Order Linear Differential Equations
    1. Example 1: First-Order Linear Differential Equations
    2. Example 2: First-Order Linear Differential Equations
    3. Example 3: First-Order Linear Differential Equations
    4. Example 4: First-Order Linear Differential Equations
    5. Example 5: First-Order Linear Differential Equations
  3. 8.3 Autonomous Differential Equations and Slope Fields
    1. Example 1: Autonomous Differential Equations and Slope Fields
    2. Example 2: Autonomous Differential Equations and Slope Fields
    3. Example 3: Autonomous Differential Equations and Slope Fields
    4. Example 4: Autonomous Differential Equations and Slope Fields
    5. Example 5: Autonomous Differential Equations and Slope Fields
  4. 8.4 Second-Order Differential Equations
    1. Example 1: Second-Order Linear Differential Equations
    2. Example 2: Second-Order Linear Differential Equations
    3. Example 3: Second-Order Linear Differential Equations
    4. Example 4: Second-Order Linear Differential Equations
    5. Example 5: Second-Order Linear Differential Equations
    6. Example 6: Second-Order Linear Differential Equations

Chapter 9: Parametric Equations and Polar Coordinates

  1. 9.1 Parametric Equations
    1. Example 1: Parametric Equations
    2. Example 2: Parametric Equations
    3. Example 3: Parametric Equations
    4. Example 4: Parametric Equations
  2. 9.2 Calculus and Parametric Equations
    1. Example 1: Calculus and Parametric Equations
    2. Example 2: Calculus and Parametric Equations
    3. Example 3: Calculus and Parametric Equations
    4. Example 4: Calculus and Parametric Equations
    5. Example 5: Calculus and Parametric Equations
    6. Example 6: Calculus and Parametric Equations
    7. Example 7: Calculus and Parametric Equations
    8. Example 8: Calculus and Parametric Equations
  3. 9.3 Polar Coordinates
    1. Example 1: Polar Coordinates
    2. Example 2: Polar Coordinates
    3. Example 3: Polar Coordinates
    4. Example 4: Polar Coordinates
    5. Example 5: Polar Coordinates
    6. Example 6: Polar Coordinates
    7. Example 7: Polar Coordinates
    8. Example 8: Polar Coordinates
  4. 9.4 Calculus in Polar Coordinates
    1. Example 1: Calculus in Polar Coordinates
    2. Example 2: Calculus in Polar Coordinates
    3. Example 3: Calculus in Polar Coordinates
    4. Example 4: Calculus in Polar Coordinates
    5. Example 5: Calculus in Polar Coordinates
  5. 9.5 Conic Sections in Cartesian Coordinates
    1. Example 1: Conic Sections in Cartesian Coordinates
    2. Example 2: Conic Sections in Cartesian Coordinates
    3. Example 3: Conic Sections in Cartesian Coordinates
    4. Example 4: Conic Sections in Cartesian Coordinates
    5. Example 5: Conic Sections in Cartesian Coordinates
    6. Example 6: Conic Sections in Cartesian Coordinates
    7. Example 7: Conic Sections in Cartesian Coordinates
    8. Example 8: Conic Sections in Cartesian Coordinates
  6. 9.6 Conic Sections in Polar Coordinates
    1. Example 1: Conic Sections in Polar Coordinates
    2. Example 2: Conic Sections in Polar Coordinates
    3. Example 3: Conic Sections in Polar Coordinates
    4. Example 4: Conic Sections in Polar Coordinates
    5. Example 5: Conic Sections in Polar Coordinates

Chapter 10: Sequences and Series

  1. 10.1 Sequences
    1. Example 1: Sequences
    2. Example 2: Sequences
    3. Example 3: Sequences
    4. Example 4: Sequences
    5. Example 5: Sequences
    6. Example 6: Sequences
    7. Example 7: Sequences
    8. Example 8: Sequences
  2. 10.2 Infinite Series
    1. Example 1: Infinite Series
    2. Example 2: Infinite Series
    3. Example 3: Infinite Series
    4. Example 4: Infinite Series
    5. Example 5: Infinite Series
    6. Example 6: Infinite Series
    7. Example 7: Infinite Series
    8. Example 8: Infinite Series
  3. 10.3 The Integral Test
    1. Example 1: The Integral Test
    2. Example 2: The Integral Test
    3. Example 3: The Integral Test
    4. Example 4: The Integral Test
  4. 10.4 Comparison Tests
    1. Example 1: Comparison Tests
    2. Example 2: Comparison Tests
    3. Example 3: Comparison Tests
  5. 10.5 The Ratio and Root Tests
    1. Example 1: The Ratio and Root Tests
    2. Example 2: The Ratio and Root Tests
    3. Example 3: The Ratio and Root Tests
  6. 10.6 Absolute and Conditional Convergence
    1. Example 1: Absolute and Conditional Convergence
    2. Example 2: Absolute and Conditional Convergence
    3. Example 3: Absolute and Conditional Convergence
  7. 10.7 Power Series
    1. Example 1: Power Series
    2. Example 2: Power Series
    3. Example 3: Power Series
    4. Example 4: Power Series
    5. Example 5: Power Series
    6. Example 6: Power Series
  8. 10.8 Taylor and Maclaurin Series
    1. Example 1: Taylor and Maclaurin Series
    2. Example 2: Taylor and Maclaurin Series
    3. Example 3: Taylor and Maclaurin Series
    4. Example 4: Taylor and Maclaurin Series
    5. Example 5: Taylor and Maclaurin Series
    6. Example 6: Taylor and Maclaurin Series
    7. Example 7: Taylor and Maclaurin Series
    8. Example 8: Taylor and Maclaurin Series
    9. Example 9: Taylor and Maclaurin Series
    10. Example 10: Taylor and Maclaurin Series
  9. 10.9 Further Applications of Series
    1. Example 1: Further Applications of Series
    2. Example 2: Further Applications of Series
    3. Example 3: Further Applications of Series
    4. Example 4: Further Applications of Series
    5. Example 5: Further Applications of Series