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Appendix A Answers to Odd Exercises

1 Limits
1.1 An Introduction To Limits
1.1.3 Exercises

1.2 Epsilon-Delta Definition of a Limit

Exercises

1.3 Finding Limits Analytically

Exercises

1.4 One-Sided Limits

Exercises

Problems

1.5 Continuity

Exercises

1.6 Limits Involving Infinity
1.6.4 Exercises

2 Derivatives
2.1 Instantaneous Rates of Change: The Derivative
2.1.3 Exercises

Terms and Concepts

2.2 Interpretations of the Derivative
2.2.5 Exercises

2.3 Basic Differentiation Rules
2.3.3 Exercises

2.4 The Product and Quotient Rules

Exercises

2.5 The Chain Rule

Exercises

2.6 Implicit Differentiation
2.6.4 Exercises

Terms and Concepts

2.7 Derivatives of Inverse Functions

Exercises

3 The Graphical Behavior of Functions
3.1 Extreme Values

Exercises

3.2 The Mean Value Theorem

Exercises

3.3 Increasing and Decreasing Functions

Exercises

3.4 Concavity and the Second Derivative
3.4.3 Exercises

Problems

3.5 Curve Sketching

Exercises

4 Applications of the Derivative
4.1 Newton's Method

Exercises

4.2 Related Rates

Exercises

4.3 Optimization

Exercises

4.4 Differentials

Exercises

5 Integration
5.1 Antiderivatives and Indefinite Integration

Exercises

5.2 The Definite Integral

Exercises

5.3 Riemann Sums
5.3.4 Exercises

5.4 The Fundamental Theorem of Calculus
5.4.6 Exercises

Terms and Concepts

5.5 Numerical Integration
5.5.6 Exercises

6 Techniques of Antidifferentiation
6.1 Substitution
6.1.5 Exercises

Terms and Concepts

Problems

6.2 Integration by Parts

Exercises

6.3 Trigonometric Integrals
6.3.4 Exercises

6.4 Trigonometric Substitution

Exercises

6.5 Partial Fraction Decomposition

Exercises

6.6 Hyperbolic Functions
6.6.3 Exercises

6.7 L'Hospital's Rule
6.7.4 Exercises

6.8 Improper Integration
6.8.4 Exercises

7 Applications of Integration
7.1 Area Between Curves

Exercises

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

Exercises

7.3 The Shell Method

Exercises

7.4 Arc Length and Surface Area
7.4.3 Exercises

7.5 Work
7.5.4 Exercises

7.6 Fluid Forces

Exercises

8 Differential Equations
8.1 Graphical and Numerical Solutions to Differential Equations
8.1.4 Exercises

8.2 Separable Differential Equations
8.2.2 Exercises

8.3 First Order Linear Differential Equations
8.3.2 Exercises

8.4 Modeling with Differential Equations
8.4.3 Exercises

9 Sequences and Series
9.1 Sequences

Exercises

9.2 Infinite Series
9.2.4 Exercises

9.3 Integral and Comparison Tests
9.3.4 Exercises

9.4 Ratio and Root Tests
9.4.3 Exercises

9.5 Alternating Series and Absolute Convergence

Exercises

9.6 Power Series

Exercises

9.7 Taylor Polynomials

Exercises

9.8 Taylor Series

Exercises

10 Curves in the Plane
10.1 Conic Sections
10.1.4 Exercises

10.2 Parametric Equations
10.2.4 Exercises

Problems

10.3 Calculus and Parametric Equations
10.3.4 Exercises

10.4 Introduction to Polar Coordinates
10.4.4 Exercises

Problems

10.5 Calculus and Polar Functions
10.5.5 Exercises

11 Vectors
11.1 Introduction to Cartesian Coordinates in Space
11.1.7 Exercises

11.2 An Introduction to Vectors

Exercises

11.3 The Dot Product
11.3.2 Exercises

11.4 The Cross Product
11.4.3 Exercises

11.5 Lines
11.5.4 Exercises

11.6 Planes
11.6.2 Exercises

Terms and Concepts

12 Vector Valued Functions
12.1 Vector-Valued Functions
12.1.4 Exercises

12.2 Calculus and Vector-Valued Functions
12.2.5 Exercises

12.3 The Calculus of Motion
12.3.3 Exercises

12.4 Unit Tangent and Normal Vectors
12.4.4 Exercises

12.5 The Arc Length Parameter and Curvature
12.5.4 Exercises

13 Functions of Several Variables
13.1 Introduction to Multivariable Functions
13.1.5 Exercises

13.2 Limits and Continuity of Multivariable Functions
13.2.5 Exercises

13.3 Partial Derivatives
13.3.7 Exercises

13.4 Differentiability and the Total Differential
13.4.6 Exercises

13.5 The Multivariable Chain Rule
13.5.3 Exercises

13.6 Directional Derivatives
13.6.3 Exercises

13.7 Tangent Lines, Normal Lines, and Tangent Planes
13.7.5 Exercises

13.8 Extreme Values
13.8.3 Exercises

14 Multiple Integration
14.1 Iterated Integrals and Area
14.1.4 Exercises

14.2 Double Integration and Volume

Exercises

14.3 Double Integration with Polar Coordinates

Exercises

14.4 Center of Mass
14.4.3 Exercises

14.5 Surface Area

Exercises

14.6 Volume Between Surfaces and Triple Integration
14.6.4 Exercises

14.7 Triple Integration with Cylindrical and Spherical Coordinates
14.7.3 Exercises

15 Vector Analysis
15.1 Introduction to Line Integrals
15.1.4 Exercises

15.2 Vector Fields
15.2.3 Exercises

15.3 Line Integrals over Vector Fields
15.3.4 Exercises

15.4 Flow, Flux, Green's Theorem and the Divergence Theorem
15.4.4 Exercises

15.5 Parametrized Surfaces and Surface Area
15.5.3 Exercises

Terms and Concepts

15.6 Surface Integrals
15.6.3 Exercises

15.7 The Divergence Theorem and Stokes' Theorem
15.7.4 Exercises