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Solutions A Answers to Odd Exercises

Chapter 1 Limits

Section 1.1 An Introduction To Limits

Exercises 1.1.3 Exercises

Section 1.2 Epsilon-Delta Definition of a Limit

Exercises Exercises

Section 1.3 Finding Limits Analytically

Exercises Exercises

Section 1.4 One-Sided Limits

Exercises Exercises
Problems

Section 1.5 Continuity

Exercises Exercises

Section 1.6 Limits Involving Infinity

Exercises 1.6.4 Exercises

Chapter 2 Derivatives

Section 2.1 Instantaneous Rates of Change: The Derivative

Exercises 2.1.3 Exercises

Section 2.2 Interpretations of the Derivative

Exercises 2.2.5 Exercises

Section 2.3 Basic Differentiation Rules

Exercises 2.3.3 Exercises

Section 2.4 The Product and Quotient Rules

Exercises Exercises

Section 2.5 The Chain Rule

Exercises Exercises

Section 2.6 Implicit Differentiation

Exercises 2.6.4 Exercises

Section 2.7 Derivatives of Inverse Functions

Exercises Exercises

Chapter 3 The Graphical Behavior of Functions

Section 3.1 Extreme Values

Exercises Exercises

Section 3.2 The Mean Value Theorem

Exercises Exercises

Section 3.3 Increasing and Decreasing Functions

Exercises Exercises

Section 3.4 Concavity and the Second Derivative

Exercises 3.4.3 Exercises
Problems

Section 3.5 Curve Sketching

Exercises Exercises

Chapter 4 Applications of the Derivative

Section 4.1 Newton's Method

Exercises Exercises

Section 4.2 Related Rates

Exercises Exercises

Section 4.3 Optimization

Exercises Exercises

Section 4.4 Differentials

Exercises Exercises

Chapter 5 Integration

Section 5.1 Antiderivatives and Indefinite Integration

Exercises Exercises

Section 5.2 The Definite Integral

Exercises Exercises

Section 5.3 Riemann Sums

Exercises 5.3.4 Exercises

Section 5.4 The Fundamental Theorem of Calculus

Exercises 5.4.6 Exercises

Section 5.5 Numerical Integration

Exercises 5.5.6 Exercises

Chapter 6 Techniques of Antidifferentiation

Section 6.1 Substitution

Exercises 6.1.5 Exercises
Problems

Section 6.2 Integration by Parts

Exercises Exercises

Section 6.3 Trigonometric Integrals

Exercises 6.3.4 Exercises

Section 6.4 Trigonometric Substitution

Exercises Exercises

Section 6.5 Partial Fraction Decomposition

Exercises Exercises

Section 6.6 Hyperbolic Functions

Exercises 6.6.3 Exercises

Section 6.7 L'Hospital's Rule

Exercises 6.7.4 Exercises

Section 6.8 Improper Integration

Exercises 6.8.4 Exercises

Chapter 7 Applications of Integration

Section 7.1 Area Between Curves

Exercises Exercises

Section 7.2 Volume by Cross-Sectional Area; Disk and Washer Methods

Exercises Exercises

Section 7.3 The Shell Method

Exercises Exercises

Section 7.4 Arc Length and Surface Area

Exercises 7.4.3 Exercises

Section 7.5 Work

Exercises 7.5.4 Exercises

Section 7.6 Fluid Forces

Exercises Exercises

Chapter 8 Differential Equations

Section 8.1 Graphical and Numerical Solutions to Differential Equations

Exercises 8.1.4 Exercises

Section 8.2 Separable Differential Equations

Exercises 8.2.2 Exercises

Section 8.3 First Order Linear Differential Equations

Exercises 8.3.2 Exercises

Section 8.4 Modeling with Differential Equations

Exercises 8.4.3 Exercises

Chapter 9 Sequences and Series

Section 9.1 Sequences

Exercises Exercises

Section 9.2 Infinite Series

Exercises 9.2.4 Exercises

Section 9.3 Integral and Comparison Tests

Exercises 9.3.4 Exercises

Section 9.4 Ratio and Root Tests

Exercises 9.4.3 Exercises

Section 9.5 Alternating Series and Absolute Convergence

Exercises Exercises

Section 9.6 Power Series

Exercises Exercises

Section 9.7 Taylor Polynomials

Exercises Exercises

Section 9.8 Taylor Series

Exercises Exercises

Chapter 10 Curves in the Plane

Section 10.1 Conic Sections

Exercises 10.1.4 Exercises

Section 10.2 Parametric Equations

Exercises 10.2.4 Exercises
Problems

Section 10.3 Calculus and Parametric Equations

Exercises 10.3.4 Exercises

Section 10.4 Introduction to Polar Coordinates

Exercises 10.4.4 Exercises
Problems

Section 10.5 Calculus and Polar Functions

Exercises 10.5.5 Exercises

Chapter 11 Vectors

Section 11.1 Introduction to Cartesian Coordinates in Space

Exercises 11.1.7 Exercises

Section 11.2 An Introduction to Vectors

Exercises Exercises

Section 11.3 The Dot Product

Exercises 11.3.2 Exercises

Section 11.4 The Cross Product

Exercises 11.4.3 Exercises

Section 11.5 Lines

Exercises 11.5.4 Exercises

Section 11.6 Planes

Exercises 11.6.2 Exercises

Chapter 12 Vector Valued Functions

Section 12.1 Vector-Valued Functions

Exercises 12.1.4 Exercises

Section 12.2 Calculus and Vector-Valued Functions

Exercises 12.2.5 Exercises

Section 12.3 The Calculus of Motion

Exercises 12.3.3 Exercises

Section 12.4 Unit Tangent and Normal Vectors

Exercises 12.4.4 Exercises

Section 12.5 The Arc Length Parameter and Curvature

Exercises 12.5.4 Exercises

Chapter 13 Functions of Several Variables

Section 13.1 Introduction to Multivariable Functions

Exercises 13.1.5 Exercises

Section 13.2 Limits and Continuity of Multivariable Functions

Exercises 13.2.5 Exercises

Section 13.3 Partial Derivatives

Exercises 13.3.7 Exercises

Section 13.4 Differentiability and the Total Differential

Exercises 13.4.6 Exercises

Section 13.5 The Multivariable Chain Rule

Exercises 13.5.3 Exercises

Section 13.6 Directional Derivatives

Exercises 13.6.3 Exercises

Section 13.7 Tangent Lines, Normal Lines, and Tangent Planes

Exercises 13.7.5 Exercises

Section 13.8 Extreme Values

Exercises 13.8.3 Exercises

Chapter 14 Multiple Integration

Section 14.1 Iterated Integrals and Area

Exercises 14.1.4 Exercises

Section 14.2 Double Integration and Volume

Exercises Exercises

Section 14.3 Double Integration with Polar Coordinates

Exercises Exercises

Section 14.4 Center of Mass

Exercises 14.4.3 Exercises

Section 14.5 Surface Area

Exercises Exercises

Section 14.6 Volume Between Surfaces and Triple Integration

Exercises 14.6.4 Exercises

Section 14.7 Triple Integration with Cylindrical and Spherical Coordinates

Exercises 14.7.3 Exercises

Chapter 15 Vector Analysis

Section 15.1 Introduction to Line Integrals

Exercises 15.1.4 Exercises

Section 15.2 Vector Fields

Exercises 15.2.3 Exercises

Section 15.3 Line Integrals over Vector Fields

Exercises 15.3.4 Exercises

Section 15.4 Flow, Flux, Green's Theorem and the Divergence Theorem

Exercises 15.4.4 Exercises

Section 15.5 Parametrized Surfaces and Surface Area

Exercises 15.5.3 Exercises

Section 15.6 Surface Integrals

Exercises 15.6.3 Exercises

Section 15.7 The Divergence Theorem and Stokes' Theorem

Exercises 15.7.4 Exercises