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Single Variable Calculus with Early Transcendentals
Single Variable Calculus with Early Transcendentals
Chapter 1: A Function Primer
1.1
Functions and How We Represent Them
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
1.2
A Function Repertory
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
1.3
Transforming and Combining Functions
Examples
Example 1
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11
1.4
Inverse Functions
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
1.5
Calculus, Calculators, and Computer Algebra Systems
Chapter 2: Limits and the Derivative
2.1
Rates of Change and Tangents
Examples
Example 3
2.2
Limits All Around the Plane
Examples
Example 3
Example 4
Example 6
2.3
The Mathematical Definition of Limit
Examples
Example 2
Example 3
Example 5
Example 6
Example 7
2.4
Determining Limits of Functions
Examples
Example 1
Example 3
Example 6
Example 7
Example 8
2.5
Continuity
Examples
Example 1
Example 2
Example 5
Example 6
Example 7
Example 8
Example 10
Example 11
2.6
Rate of Change Revisited: The Derivative
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Chapter 3: Differentiation
3.1
Differentiation Notation and Consequences
3.2
Derivatives of Polynomials, Exponentials, Products, and Quotients
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
3.3
Derivatives of Trigonometric Functions
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
3.4
The Chain Rule
Examples
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Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
3.5
Implicit Differentiation
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
3.6
Derivatives of Inverse Functions
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
3.7
Rates of Change in Use
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
3.8
Related Rates
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
3.9
Linearization and Differentials
Examples
Example 2
Example 3
Example 4
Chapter 4: Applications of Differentiation
4.1
Extreme Values of Functions
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
4.2
The Mean Value Theorem
Examples
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Example 2
Example 3
Example 4
Example 5
Example 6
4.3
The First and Second Derivative Tests
Examples
Example 1
Example 2
Example 3
Example 4
4.4
L'Hôpital's Rule
Examples
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Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
4.5
Calculus and Curve Sketching
Examples
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Example 2
Example 3
Example 4
Example 5
4.6
Optimization Problems
Examples
Example 1
4.7
Antiderivatives
Examples
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Example 2
Example 3
Example 4
Example 5
Example 6
Chapter 5: Integration
5.1
Area, Distance, and Riemann Sums
Examples
Example 1
Example 2
Example 4
5.2
The Definite Integral
Examples
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Example 2
Example 3
Example 6
5.3
The Fundamental Theorem of Calculus
Examples
Example 1
Example 2
Example 3
Example 5
Example 6
5.4
Indefinite Integrals and the Substitution Rule
Examples
Example 1
Example 2
Example 3
Example 4
5.5
The Substitution Rule and Definite Integration
Examples
Example 1
Example 2
Example 3
Chapter 6: Applications of the Definite Integral
6.1
Finding Volumes Using Slices
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
6.2
Finding Volumes Using Cylindrical Shells
Examples
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Example 2
Example 3
Example 4
6.3
Arc Length and Surface Area
Examples
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Example 2
Example 3
Example 4
6.4
Moments and Centers of Mass
Examples
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Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
6.5
Force, Work, and Pressure
Examples
Example 1
Example 3
Example 4
Example 5
Example 6
Example 7
6.6
Hyperbolic Functions
Examples
Example 4
Chapter 7: Techniques of Integration
7.1
Integration by Parts
Examples
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Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
7.2
The Partial Fractions Method
Examples
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Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
7.3
Trigonometric Integrals
Examples
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Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
7.4
Trigonometric Substitutions
Examples
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Example 2
Example 3
Example 4
Example 5
Example 6
7.5
Integration Summary and Integration Using Computer Algebra Systems
Examples
Example 1
Example 2
7.6
Numerical Integration
Examples
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Example 2
Example 3
Example 4
Example 5
Example 6
7.7
Improper Integrals
Examples
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Example 2
Example 3
Example 5
Example 6
Example 7
Example 8
Example 9
Chapter 8: Differential Equations
8.1
Separable Differential Equations
Examples
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Example 2
Example 3
Example 4
Example 5
8.2
First-Order Linear Differential Equations
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
8.3
Autonomous Differential Equations and Slope Fields
Examples
Example 2
Example 3
Example 4
8.4
Second-Order Linear Differential Equations
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Chapter 9: Parametric Equations and Polar Coordinates
9.1
Parametric Equations
Examples
Example 1
Example 2
9.2
Calculus and Parametric Equations
Examples
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Example 2
Example 3
Example 5
Example 6
Example 8
9.3
Polar Coordinates
Examples
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Example 2
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
9.4
Calculus in Polar Coordinates
Examples
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Example 2
Example 3
Example 4
9.5
Conic Sections in Cartesian Coordinates
Examples
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Example 3
Example 4
Example 5
Example 6
Example 7
9.6
Conic Sections in Polar Coordinates
Examples
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Example 2
Example 3
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Example 5
Chapter 10: Sequences and Series
10.1
Sequences
Examples
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Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
10.2
Infinite Series
Examples
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Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
10.3
The Integral Test
Examples
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Example 4
10.4
Comparison Tests
Examples
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Example 2
Example 3
10.5
The Ratio and Root Tests
Examples
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Example 2
Example 3
10.6
Absolute and Conditional Convergence
Examples
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Example 2
Example 3
10.7
Power Series
Examples
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Example 3
Example 4
Example 5
Example 6
10.8
Taylor and Maclaurin Series
Examples
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Example 2
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
10.9
Further Applications of Series
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Example 2
Example 3
Example 5
