On this webpage you will find my solutions to Chapters 12-17 of the eighth edition of "Calculus: Early Transcendentals" by James Stewart. Solutions to Chapters 1-5 are here, and solutions to Chapters 6-11 are here. Here is a link to the book's page on amazon.com. If you find my work useful, please consider making a donation. Thank you.
- Chapter 1: Functions and Models
- Section 1.1: Four Ways to Represent a Function
- Section 1.2: Mathematical Models: A Catalog of Essential Functions
- Section 1.3: New Functions from Old Functions
- Section 1.4: Exponential Functions
- Section 1.5: Inverse Functions and Logarithms
- Chapter 2: Limits and Differentiation
- Section 2.1: The Tangent and Velocity Problems
- Section 2.2: The Limit of a Function
- Section 2.3: Calculating Limits Using the Limit Laws
- Section 2.4: The Precise Definition of a Limit
- Section 2.5: Continuity
- Section 2.6: Limits at Infinity; Horizontal Asymptotes
- Section 2.7: Derivatives and Rates of Change
- Section 2.8: The Derivative as a Function
- Chapter 3: Differentiation Rules
- Section 3.1: Derivatives of Polynomials and Exponential Functions
- Section 3.2: The Product and Quotient Rules
- Section 3.3: Derivatives of Trigonometric Functions
- Section 3.4: The Chain Rule
- Section 3.5: Implicit Differentiation
- Section 3.6: Derivatives of Logarithmic Functions
- Section 3.7: Rates of Change in the Natural and Social Sciences
- Section 3.8: Exponential Growth and Decay
- Section 3.9: Related Rates
- Section 3.10: Linear Approximations and Differentials
- Section 3.11: Hyperbolic Functions
- Chapter 4: Applications of Differentiation
- Section 4.1: Maximum and Minimum Values
- Section 4.2: The Mean Value Theorem
- Section 4.3: How Derivatives Affect the Shape of a Graph
- Section 4.4: Indeterminate Forms and l'Hospital's Rule
- Section 4.5: Summary of Curve Sketching
- Section 4.6: Graphing with Calculus and Calculators
- Section 4.7: Optimization Problems
- Section 4.8: Newton's Method
- Section 4.9: Antiderivatives
- Chapter 5: Integrals
- Section 5.1: Areas and Distances
- Section 5.2: The Definite Integral
- Section 5.3: The Fundamental Theorem of Calculus
- Section 5.4: Indefinite Integrals and the Net Change Theorem
- Section 5.5: The Substitution Rule
- Chapter 6: Applications of Integration
- Section 6.1: Areas Between Curves
- Section 6.2: Volumes
- Section 6.3: Volumes by Cylindrical Shells
- Section 6.4: Work
- Section 6.5: Average Value of a Function
- Chapter 7: Techniques of Integration
- Section 7.1: Integration by Parts
- Section 7.2: Trigonometric Integrals
- Section 7.3: Trigonometric Substitution
- Section 7.4: Integration of Rational Functions by Partial Fractions
- Section 7.5: Strategy for Integration
- Section 7.6: Integration Using Tables and Computer Algebra Systems
- Section 7.7: Approximate Integration
- Section 7.8: Improper Integrals
- Chapter 8: Further Applications of Integration
- Section 8.1: Arc Length
- Section 8.2: Area of a Surface of Revolution
- Section 8.3: Applications to Physics and Engineering
- Section 8.4: Applications to Economics and Biology
- Section 8.5: Probability
- Chapter 9: Differential Equations
- Section 9.1: Modeling with Differential Equations
- Section 9.2: Direction Fields and Euler's Method
- Section 9.3: Separable Equations
- Section 9.4: Models for Population Growth
- Section 9.5: Linear Equations
- Section 9.6: Predator-Prey Systems
- Chapter 10: Parametric Equations and Polar Coordinates
- Section 10.1: Curves Defined by Parametric Equations
- Section 10.2: Calculus with Parametric Curves
- Section 10.3: Polar Coordinates
- Section 10.4: Areas and Lengths in Polar Coordinates
- Section 10.5: Conic Sections
- Section 10.6: Conic Sections in Polar Coordinates
- Chapter 11: Infinite Series
- Section 11.1: Sequences
- Section 11.2: Series
- Section 11.3: The Integral Test and Estimates of Sums
- Section 11.4: The Comparison Tests
- Section 11.5: Alternating Series
- Section 11.6: Absolute Convergence and the Ratio and Root Tests
- Section 11.7: Strategy for Testing Series
- Section 11.8: Power Series
- Section 11.9: Representations of Functions as Power Series
- Section 11.10: Taylor and Maclaurin Series
- Section 11.11: Applications of Taylor Polynomials
- Chapter 12: Vectors and the Geometry of Space
- Section 12.1: Three-Dimensional Coordinate Systems
- Section 12.2: Vectors
- Section 12.3: The Dot Product
- Section 12.4: The Cross Product
- Section 12.5: Equations of Lines and Planes
- Section 12.6: Cylinders and Quadric Surfaces
- Chapter 13: Vector Functions
- Section 13.1: Vector Functions and Space Curves
- Section 13.2: Derivatives and Integrals of Vector Functions
- Section 13.3: Arc Length and Curvature
- Section 13.4: Motion in Space: Velocity and Acceleration
- Chapter 14: Partial Derivatives
- Section 14.1: Functions of Several Variables
- Section 14.2: Limits and Continuity
- Section 14.3: Partial Derivatives
- Section 14.4: Tangent Planes and Linear Approximations
- Section 14.5: The Chain Rule
- Section 14.6: Directional Derivatives and the Gradient Vector
- Section 14.7: Maximum and Minimum Values
- Section 14.8: Lagrange Multipliers
- Chapter 15: Multiple Integrals
- Section 15.1: Double Integrals over Rectangles
- Section 15.2: Double Integrals over General Regions
- Section 15.3: Double Integrals in Polar Coordinates
- Section 15.4: Applications of Double Integrals
- Section 15.5: Surface Area
- Section 15.6: Triple Integrals
- Section 15.7: Triple Integrals in Cylindrical Coordinates
- Section 15.8: Triple Integrals in Spherical Coordinates
- Section 15.9: Change of Variables in Multiple Integrals
- Chapter 16: Vector Calculus
- Section 16.1: Vector Fields
- Section 16.2: Line Integrals
- Section 16.3: The Fundamental Theorem for Line Integrals
- Section 16.4: Green's Theorem
- Section 16.5: Curl and Divergence
- Section 16.6: Parametric Surfaces and Their Areas
- Section 16.7: Surface Integrals
- Section 16.8: Stokes' Theorem
- Section 16.9: The Divergence Theorem
- Chapter 17: Second-Order Differential Equations
- Section 17.1: Second-Order Linear Equations
- Section 17.2: Nonhomogeneous Linear Equations
- Section 17.3: Applications of Second-Order Differential Equations
- Section 17.4: Series Solutions
| Section 12.1 |
Section 12.2 |
Section 12.3 |
| Exercise 1 |
Exercise 1 |
Exercise 1 |
Exercise 26 |
Exercise 51 |
| Exercise 2 |
Exercise 2 |
Exercise 2 |
Exercise 27 |
Exercise 52 |
| Exercise 3 |
Exercise 3 |
Exercise 3 |
Exercise 28 |
Exercise 53 |
| Exercise 4 |
Exercise 4 |
Exercise 4 |
Exercise 29 |
Exercise 54 |
| Exercise 5 |
Exercise 5 |
Exercise 5 |
Exercise 30 |
Exercise 55 |
| Exercise 6 |
Exercise 6 |
Exercise 6 |
Exercise 31 |
Exercise 56 |
| Exercise 7 |
Exercise 7 |
Exercise 7 |
Exercise 32 |
Exercise 57 |
| Exercise 8 |
Exercise 8 |
Exercise 8 |
Exercise 33 |
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| Exercise 9 |
Exercise 9 |
Exercise 9 |
Exercise 34 |
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| Exercise 10 |
Exercise 10 |
Exercise 10 |
Exercise 35 |
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| Exercise 11 |
Exercise 11 |
Exercise 11 |
Exercise 36 |
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| Exercise 12 |
Exercise 12 |
Exercise 12 |
Exercise 37 |
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| Exercise 13 |
Exercise 13 |
Exercise 13 |
Exercise 38 |
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| Exercise 14 |
Exercise 14 |
Exercise 14 |
Exercise 39 |
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| Exercise 15 |
Exercise 15 |
Exercise 15 |
Exercise 40 |
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| Exercise 16 |
Exercise 16 |
Exercise 16 |
Exercise 41 |
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| Exercise 17 |
Exercise 17 |
Exercise 17 |
Exercise 42 |
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| Exercise 18 |
Exercise 18 |
Exercise 18 |
Exercise 43 |
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| Exercise 19 |
Exercise 19 |
Exercise 19 |
Exercise 44 |
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| Exercise 20 |
Exercise 20 |
Exercise 20 |
Exercise 45 |
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| Exercise 21 |
Exercise 21 |
Exercise 21 |
Exercise 46 |
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| Exercise 22 |
Exercise 22 |
Exercise 22 |
Exercise 47 |
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Exercise 23 |
Exercise 23 |
Exercise 48 |
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Exercise 24 |
Exercise 24 |
Exercise 49 |
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Exercise 25 |
Exercise 50 |
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