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Calculus: Early Transcendentals 6th Edition
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Chapter 1
Chapter 1: FUNCTIONS AND MODELS
Section 1
Section 1: Four Ways to Represent a Function
Problem 1.1
Problem 1.2
Problem 1.3
Problem 1.10
Problem 1.11
Problem 1.12
Problem 1.13
Problem 1.14
Problem 1.15
Problem 1.16
Problem 1.17
Problem 1.19
Problem 1.20
Problem 1.21
Problem 1.22
Problem 1.23
Problem 1.24
Problem 1.25
Problem 1.26
Problem 1.27
Problem 1.28
Problem 1.29
Problem 1.30
Section 2
Section 2: Mathematical Models: A Catalog of Essential Functions
Section 3
Section 3: New Functions from Old Functions
Section 4
Section 4: Graphing Calculators and Computers
Section 5
Section 5: Exponential Functions
Section 6
Section 6: Inverse Functions and Logarithms
Section 7
Section 7: Review
Chapter 2
Chapter 2: LIMITS AND DERIVATIVES
Section 1
Section 1: The Tangent and Velocity Problems
Section 2
Section 2: The Limit of a Function
Section 3
Section 3: Calculating Limits Using the Limit Laws
Section 4
Section 4: The Precise Definition of a Limit
Section 5
Section 5: Continuity
Section 6
Section 6: Limits at Infinity; Horizontal Asymptotes
Section 7
Section 7: Derivatives and Rates of Change
Section 8
Section 8: The Derivative as a Function
Chapter 3
Chapter 3: DIFFERENTIATION RULES
Section 1
Section 1: Derivatives of Polynomials and Exponential Functions
Section 2
Section 2: The Product and Quotient Rules
Section 3
Section 3: Derivatives of Trigonometric Functions
Section 4
Section 4: The Chain Rule
Section 5
Section 5: Implicit Differentiation
Section 6
Section 6: Derivatives of Logarithmic Functions
Section 7
Section 7: Rates of Change in the Natural and Social Sciences
Section 8
Section 8: Exponential Growth and Decay
Section 9
Section 9: Related Rates
Section 10
Section 10: Linear Approximations and Differentials
Section 11
Section 11: Hyperbolic Functions
Chapter 4
Chapter 4: APPLICATIONS OF DIFFERENTIATION
Section 1
Section 1: Maximum and Minimum Values
Section 2
Section 2: The Mean Value Theorem
Section 3
Section 3: How Derivatives Affect the Shape of a Graph
Section 4
Section 4: Indeterminate Forms and L'Hospital's Rule
Section 5
Section 5: Summary of Curve Sketching
Section 6
Section 6: Graphing with Calculus andCalculators
Section 7
Section 7: Optimization Problems
Section 8
Section 8: Newton's Method
Section 9
Section 9: Antiderivatives
Chapter 5
Chapter 5: INTEGRALS
Section 1
Section 1: Areas and Distances
Section 2
Section 2: The Definite Integral
Section 3
Section 3: The Fundamental Theorem of Calculus
Section 4
Section 4: Indefinite Integrals and the Net Change Theorem
Section 5
Section 5: The Substitution Rule
Chapter 6
Chapter 6: INTEGRALS
Section 1
Section 1: Areas between Curves
Section 2
Section 2: Volumes
Section 3
Section 3: Volumes by Cylindrical Shells
Section 4
Section 4: Work
Section 5
Section 5: Average Value of a Function
Chapter 7
Chapter 7: TECHNIQUES OF INTEGRATION
Section 1
Section 1: Integration by Parts
Section 2
Section 2: Trigonometric Integrals
Section 3
Section 3: Trigonometric Substitution
Section 4
Section 4: Integration of Rational Functions by Partial Fractions
Section 5
Section 5: Strategy for Integration
Section 6
Section 6: Integration Using Tables and Computer Algebra Systems
Section 7
Section 7: Approximate Integration
Section 8
Section 8: Improper Integrals
Chapter 8
Chapter 8: FURTHER APPLICATIONS OF INTEGRATION
Section 1
Section 1: Arc Length
Section 2
Section 2: Area of a Surface of Revolution
Section 3
Section 3: Applications to Physics and Engineering
Section 4
Section 4: Applications to Economics and Biology
Section 5
Section 5: Probability
Chapter 9
Chapter 9: DIFFERENTIAL EQUATIONS
Section 1
Section 1: Modeling with Differential Equations
Section 2
Section 2: Direction Fields and Euler's Method
Section 3
Section 3: Separable Equations
Section 4
Section 4: Models for Population Growth
Section 5
Section 5: Linear Equations
Section 6
Section 6: Predator-Prey Systems
Chapter 10
Chapter 10: PARAMETRIC EQUATIONS AND POLAR COORDINATES
Section 1
Section 1: Curves Defined by Parametric Equations
Section 2
Section 2: Calculus with Parametric Curves
Section 3
Section 3: Polar Coordinates
Section 4
Section 4: Areas and Lengths in Polar Coordinates
Section 5
Section 5: Conic Sections
Section 6
Section 6: Conic Sections in Polar Coordinates
Section 7
Section 7: Review
Chapter 11
Chapter 11: INFINITE SEQUENCES AND SERIES
Section 1
Section 1: Sequences
Section 2
Section 2: Series
Section 3
Section 3: The Integral Test and Estimates of Sums
Section 4
Section 4: The Comparison Tests
Section 5
Section 5: Alternating Series
Section 6
Section 6: Absolute Convergence and the Ratio and Root Tests
Section 7
Section 7: Strategy for Testing Series
Section 8
Section 8: Power Series
Section 9
Section 9: Representations of Functions as Power Series
Section 10
Section 10: Taylor and Maclaurin Series
Section 11
Section 11: Applications of Taylor Polynomials
Section 13
Section 13: Review
Chapter 12
Chapter 12: VECTORS AND THE GEOMETRY OF SPACE
Section 1
Section 1: Three-Dimensional Coordinate Systems
Section 2
Section 2: Vectors
Section 3
Section 3: The Dot Product
Section 4
Section 4: The Cross Product
Section 5
Section 5: Equations of Lines and Planes
Section 6
Section 6: Cylinders and Quadric Surfaces
Chapter 13
Chapter 13: VECTOR FUNCTIONS
Section 1
Section 1: Vector Functions and Space Curves
Section 2
Section 2: Derivatives and Integrals of Vector Functions
Section 3
Section 3: Arc Length and Curvature
Section 4
Section 4: Motion in Space: Velocity and Acceleration
Chapter 14
Chapter 14: PARTIAL DERIVATIVES
Section 1
Section 1: Functions of Several Variables
Section 2
Section 2: Limits and Continuity
Section 3
Section 3: Partial Derivatives
Section 4
Section 4: Tangent Planes and Linear Approximations
Section 5
Section 5: The Chain Rule
Section 6
Section 6: Directional Derivatives and the Gradient Vector
Section 7
Section 7: Maximum and Minimum Values
Section 8
Section 8: Lagrange Multipliers
Chapter 15
Chapter 15: MULTIPLE INTEGRALS
Section 1
Section 1: Double Integrals over Rectangles
Section 2
Section 2: Iterated Integrals
Section 3
Section 3: Double Integrals over General Regions
Section 4
Section 4: Double Integrals in Polar Coordinates
Section 5
Section 5: Applications of Double Integrals
Section 6
Section 6: Triple Integrals
Section 7
Section 7: Triple Integrals in Cylindrical Coordinates
Section 8
Section 8: Triple Integrals in Spherical Coordinates
Section 9
Section 9: Change of Variables in Multiple Integrals
Chapter 16
Chapter 16: VECTOR CALCULUS
Section 1
Section 1: Vector Fields
Section 2
Section 2: Line Integrals
Section 3
Section 3: The Fundamental Theorem for Line Integrals
Section 4
Section 4: Green's Theorem
Section 5
Section 5: Curl and Divergence
Section 6
Section 6: Parametric Surfaces and Their Areas
Section 7
Section 7: Surface Integrals
Section 8
Section 8: Stokes' Theorem
Section 9
Section 9: The Divergence Theorem
Section 10
Section 10: Summary
Chapter 17
Chapter 17: SECOND-ORDER DIFFERENTIAL EQUATIONS
Section 1
Section 1: Second-Order Linear Equations
Section 2
Section 2: Nonhomogeneous Linear Equations
Section 3
Section 3: Applications of Second-Order Differential Equations
Section 4
Section 4: Series Solutions
Section 5
Section 5: Review
Problem 1.27
Report
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Calculus: Early Transcendentals 6th Edition
Chapter 1
Section 1
Problem 1.27
Find the domain of the function.
$$f(x)=\displaystyle \frac{x}{3x-1}$$
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