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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

Terms and Concepts

1.1.3.3.

Problems

1.1.3.7.

1.1.3.9.

1.1.3.11.

1.1.3.13.

1.1.3.15.

1.1.3.17.

1.1.3.19.

1.1.3.21.

1.1.3.23.

1.1.3.25.

1.1.3.27.

Section 1.2 Epsilon-Delta Definition of a Limit

Exercises Exercises

Terms and Concepts

1.2.3.

Section 1.3 Finding Limits Analytically

Exercises Exercises

Problems

1.3.7.

1.3.9.

1.3.11.

1.3.13.

1.3.15.

1.3.17.

1.3.19.

1.3.21.

1.3.23.

1.3.25.

1.3.27.

1.3.29.

1.3.31.

1.3.33.

1.3.35.

1.3.37.

1.3.39.

1.3.41.

Section 1.4 One-Sided Limits

Exercises Exercises

Terms and Concepts

1.4.3.

Problems

1.4.5.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5 Answer 6

1.4.7.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5 Answer 6

1.4.9.

Answer 1 Answer 2 Answer 3 Answer 4

1.4.11.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5 Answer 6 Answer 7 Answer 8

1.4.13.

Answer 1 Answer 2 Answer 3 Answer 4

1.4.15.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5 Answer 6 Answer 7 Answer 8

1.4.17.

Answer 1 Answer 2 Answer 3 Answer 4

1.4.19.

Answer 1 Answer 2 Answer 3 Answer 4

1.4.21.

Answer 1 Answer 2 Answer 3 Answer 4

Review

1.4.23.

1.4.25.

Section 1.5 Continuity

Exercises Exercises

Terms and Concepts

1.5.5.

1.5.7.

1.5.9.

Problems

1.5.11.

1.5.13.

1.5.15.

1.5.17.

Answer 1 Answer 2 Answer 3

1.5.19.

Answer 1 Answer 2

1.5.21.

Answer 1 Answer 2

1.5.23.

1.5.25.

1.5.27.

1.5.29.

1.5.31.

1.5.33.

1.5.39.

1.5.41.

Review

1.5.43.

Answer 1 Answer 2 Answer 3 Answer 4

Section 1.6 Limits Involving Infinity

Exercises 1.6.4 Exercises

Terms and Concepts

1.6.4.1.

1.6.4.3.

1.6.4.5.

Problems

1.6.4.9.

Answer 1 Answer 2

1.6.4.11.

Answer 1 Answer 2 Answer 3 Answer 4

1.6.4.13.

Answer 1 Answer 2

1.6.4.15.

Answer 1 Answer 2 Answer 3

1.6.4.17.

Answer 1 Answer 2 Answer 3

1.6.4.19.

1.6.4.21.

1.6.4.23.

1.6.4.25.

1.6.4.27.

Review

1.6.4.31.

Chapter 2 Derivatives

Section 2.1 Instantaneous Rates of Change: The Derivative

Exercises 2.1.3 Exercises

Terms and Concepts

2.1.3.1.

Problems

2.1.3.7.

2.1.3.9.

2.1.3.11.

2.1.3.13.

2.1.3.15.

Answer 1 Answer 2

2.1.3.17.

Answer 1 Answer 2

2.1.3.19.

Answer 1 Answer 2

2.1.3.21.

Answer 1 Answer 2

2.1.3.23.

2.1.3.25.

2.1.3.27.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5 Answer 6 Answer 7

2.1.3.33.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5 Answer 6

2.1.3.35.

Review

2.1.3.37.

2.1.3.39.

Answer 1 Answer 2 Answer 3 Answer 4

Section 2.2 Interpretations of the Derivative

Exercises 2.2.5 Exercises

Terms and Concepts

2.2.5.1.

2.2.5.3.

Problems

2.2.5.5.

2.2.5.7.

2.2.5.9.

2.2.5.11.

2.2.5.15.

2.2.5.17.

Review

2.2.5.19.

2.2.5.21.

Section 2.3 Basic Differentiation Rules

Exercises 2.3.3 Exercises

Terms and Concepts

2.3.3.1.

2.3.3.3.

2.3.3.7.

2.3.3.9.

Answer 1 Answer 2

Problems

2.3.3.11.

2.3.3.13.

2.3.3.15.

2.3.3.17.

2.3.3.19.

2.3.3.21.

2.3.3.23.

2.3.3.25.

2.3.3.27.

Answer 1 Answer 2 Answer 3 Answer 4

2.3.3.29.

Answer 1 Answer 2 Answer 3 Answer 4

2.3.3.31.

Answer 1 Answer 2 Answer 3 Answer 4

2.3.3.33.

Answer 1 Answer 2

2.3.3.35.

Answer 1 Answer 2

2.3.3.37.

Answer 1 Answer 2

Review

2.3.3.39.

Section 2.4 The Product and Quotient Rules

Exercises Exercises

Terms and Concepts

2.4.1.

2.4.3.

2.4.5.

Problems

2.4.15.

2.4.17.

2.4.19.

2.4.21.

2.4.23.

2.4.25.

2.4.27.

2.4.29.

2.4.31.

2.4.33.

2.4.35.

2.4.37.

Answer 1 Answer 2

2.4.39.

Answer 1 Answer 2

2.4.41.

2.4.43.

2.4.45.

2.4.47.

Review

2.4.49.

2.4.51.

Section 2.5 The Chain Rule

Exercises Exercises

Terms and Concepts

2.5.1.

2.5.3.

2.5.5.

Problems

2.5.7.

2.5.9.

2.5.11.

2.5.13.

2.5.15.

2.5.17.

2.5.19.

2.5.21.

2.5.23.

2.5.25.

2.5.27.

2.5.29.

2.5.31.

2.5.33.

2.5.35.

2.5.37.

Answer 1 Answer 2

2.5.39.

Answer 1 Answer 2

2.5.41.

Review

2.5.43.

Section 2.6 Implicit Differentiation

Exercises 2.6.4 Exercises

Terms and Concepts

2.6.4.3.

Problems

2.6.4.5.

2.6.4.7.

2.6.4.9.

2.6.4.11.

2.6.4.13.

2.6.4.15.

2.6.4.17.

2.6.4.19.

2.6.4.21.

2.6.4.23.

2.6.4.25.

2.6.4.27.

Answer 1 Answer 2

2.6.4.29.

Answer 1 Answer 2

2.6.4.31.

Answer 1 Answer 2

2.6.4.33.

2.6.4.35.

2.6.4.37.

Answer 1 Answer 2

2.6.4.39.

Answer 1 Answer 2

2.6.4.41.

Answer 1 Answer 2

Section 2.7 Derivatives of Inverse Functions

Exercises Exercises

Terms and Concepts

2.7.1.

Problems

2.7.9.

2.7.11.

2.7.13.

2.7.15.

2.7.17.

2.7.19.

2.7.21.

2.7.23.

2.7.29.

Review

2.7.31.

Chapter 3 The Graphical Behavior of Functions

Section 3.1 Extreme Values

Exercises Exercises

Terms and Concepts

3.1.5.

Problems

3.1.7.

Answer 1 Answer 2 Answer 3 Answer 4

3.1.9.

3.1.11.

Answer 1 Answer 2

3.1.13.

Answer 1 Answer 2

3.1.15.

3.1.17.

Answer 1 Answer 2

3.1.19.

Answer 1 Answer 2

3.1.21.

Answer 1 Answer 2

3.1.23.

Answer 1 Answer 2

3.1.25.

Answer 1 Answer 2

Review

3.1.27.

3.1.29.

Section 3.2 The Mean Value Theorem

Exercises Exercises

Problems

3.2.3.

3.2.5.

3.2.7.

3.2.9.

3.2.11.

3.2.13.

3.2.15.

3.2.17.

3.2.19.

Review

3.2.21.

Answer 1 Answer 2

Section 3.3 Increasing and Decreasing Functions

Exercises Exercises

Terms and Concepts

3.3.3.

3.3.5.

Problems

3.3.15.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5 Answer 6

3.3.17.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5 Answer 6

3.3.19.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5 Answer 6

3.3.21.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5 Answer 6

3.3.23.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5 Answer 6

Review

3.3.25.

Section 3.4 Concavity and the Second Derivative

Exercises 3.4.3 Exercises

Terms and Concepts

3.4.3.1.

3.4.3.3.

Problems

3.4.3.15.

Answer 1 Answer 2 Answer 3

3.4.3.17.

Answer 1 Answer 2 Answer 3

3.4.3.19.

Answer 1 Answer 2 Answer 3

3.4.3.21.

Answer 1 Answer 2 Answer 3

3.4.3.23.

Answer 1 Answer 2 Answer 3

3.4.3.25.

Answer 1 Answer 2 Answer 3

3.4.3.27.

Answer 1 Answer 2 Answer 3

3.4.3.29.

Answer 1 Answer 2 Answer 3

3.4.3.31.

Answer 1 Answer 2 Answer 3

3.4.3.33.

Answer 1 Answer 2 Answer 3

3.4.3.35.

Answer 1 Answer 2 Answer 3

3.4.3.37.

Answer 1 Answer 2 Answer 3

3.4.3.39.

Answer 1 Answer 2 Answer 3

3.4.3.41.

Answer 1 Answer 2 Answer 3

3.4.3.43.

Answer 1 Answer 2

3.4.3.45.

Answer 1 Answer 2

3.4.3.47.

Answer 1 Answer 2

3.4.3.49.

Answer 1 Answer 2

3.4.3.51.

Answer 1 Answer 2

3.4.3.53.

Answer 1 Answer 2

3.4.3.55.

Answer 1 Answer 2

Section 3.5 Curve Sketching

Exercises Exercises

3.5.3.

3.5.5.

Chapter 4 Applications of the Derivative

Section 4.1 Newton's Method

Exercises Exercises

Terms and Concepts

4.1.1.

Problems

4.1.3.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5

4.1.5.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5

4.1.7.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5

4.1.9.

4.1.11.

4.1.13.

4.1.15.

Section 4.2 Related Rates

Exercises Exercises

Terms and Concepts

4.2.1.

Problems

4.2.3.

Answer 1 Answer 2 Answer 3

4.2.5.

4.2.11.

Answer 1 Answer 2 Answer 3 Answer 4

4.2.13.

Answer 1 Answer 2 Answer 3 Answer 4

4.2.15.

Section 4.3 Optimization

Exercises Exercises

Terms and Concepts

4.3.1.

Problems

4.3.3.

4.3.5.

4.3.7.

4.3.9.

Answer 1 Answer 2

4.3.11.

Answer 1 Answer 2

4.3.13.

4.3.15.

Answer 1 Answer 2

4.3.17.

Section 4.4 Differentials

Exercises Exercises

Terms and Concepts

4.4.1.

4.4.3.

Problems

4.4.7.

4.4.9.

4.4.11.

4.4.13.

4.4.15.

4.4.17.

4.4.19.

4.4.21.

4.4.23.

4.4.25.

4.4.27.

4.4.29.

4.4.31.

4.4.33.

4.4.35.

Answer 1 Answer 2 Answer 3

4.4.37.

Answer 1 Answer 2 Answer 3

4.4.39.

Chapter 5 Integration

Section 5.1 Antiderivatives and Indefinite Integration

Exercises Exercises

Terms and Concepts

5.1.7.

Problems

5.1.9.

5.1.11.

5.1.13.

5.1.15.

5.1.17.

5.1.19.

5.1.21.

5.1.23.

5.1.25.

5.1.27.

5.1.29.

5.1.31.

5.1.33.

5.1.35.

5.1.37.

5.1.39.

Review

5.1.41.

Section 5.2 The Definite Integral

Exercises Exercises

Terms and Concepts

5.2.3.

Problems

5.2.5.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5 Answer 6

5.2.7.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5 Answer 6

5.2.9.

Answer 1 Answer 2 Answer 3 Answer 4

5.2.11.

Answer 1 Answer 2 Answer 3 Answer 4

5.2.13.

Answer 1 Answer 2 Answer 3 Answer 4

5.2.15.

Answer 1 Answer 2 Answer 3

5.2.17.

Answer 1 Answer 2 Answer 3 Answer 4

5.2.19.

5.2.21.

5.2.23.

5.2.25.

Review

5.2.27.

5.2.29.

Section 5.3 Riemann Sums

Exercises 5.3.4 Exercises

Terms and Concepts

5.3.4.1.

5.3.4.3.

Problems

5.3.4.5.

Answer 1 Answer 2

5.3.4.7.

Answer 1 Answer 2

5.3.4.9.

Answer 1 Answer 2

5.3.4.11.

Answer 1 Answer 2

5.3.4.13.

5.3.4.15.

5.3.4.17.

5.3.4.19.

5.3.4.21.

5.3.4.23.

5.3.4.25.

5.3.4.27.

5.3.4.35.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5

5.3.4.37.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5

5.3.4.39.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5

Review

5.3.4.41.

5.3.4.43.

5.3.4.45.

Section 5.4 The Fundamental Theorem of Calculus

Exercises 5.4.6 Exercises

5.4.6.3.

5.4.6.5.

5.4.6.7.

5.4.6.9.

5.4.6.11.

5.4.6.13.

5.4.6.15.

5.4.6.17.

5.4.6.19.

5.4.6.21.

5.4.6.23.

5.4.6.25.

5.4.6.27.

5.4.6.31.

5.4.6.33.

5.4.6.35.

5.4.6.37.

5.4.6.39.

5.4.6.41.

5.4.6.43.

5.4.6.45.

5.4.6.47.

5.4.6.49.

5.4.6.51.

5.4.6.53.

5.4.6.55.

5.4.6.57.

Section 5.5 Numerical Integration

Exercises 5.5.6 Exercises

5.5.6.1.

5.5.6.5.

Answer 1 Answer 2 Answer 3

5.5.6.7.

Answer 1 Answer 2 Answer 3

5.5.6.9.

Answer 1 Answer 2 Answer 3

5.5.6.11.

Answer 1 Answer 2 Answer 3

5.5.6.13.

Answer 1 Answer 2

5.5.6.15.

Answer 1 Answer 2

5.5.6.17.

Answer 1 Answer 2

5.5.6.19.

Answer 1 Answer 2

5.5.6.21.

Answer 1 Answer 2

5.5.6.23.

Answer 1 Answer 2

Chapter 6 Techniques of Antidifferentiation

Section 6.1 Substitution

Exercises 6.1.5 Exercises

6.1.5.3.

6.1.5.5.

6.1.5.7.

6.1.5.9.

6.1.5.11.

6.1.5.13.

6.1.5.15.

6.1.5.17.

6.1.5.19.

6.1.5.21.

6.1.5.23.

6.1.5.25.

6.1.5.27.

6.1.5.29.

6.1.5.31.

6.1.5.33.

6.1.5.35.

6.1.5.37.

6.1.5.39.

6.1.5.41.

6.1.5.43.

6.1.5.45.

6.1.5.47.

6.1.5.49.

6.1.5.51.

6.1.5.53.

6.1.5.55.

6.1.5.57.

6.1.5.59.

6.1.5.61.

6.1.5.63.

6.1.5.65.

6.1.5.67.

6.1.5.69.

6.1.5.71.

6.1.5.73.

6.1.5.75.

6.1.5.77.

6.1.5.79.

6.1.5.81.

6.1.5.83.

6.1.5.85.

Section 6.2 Integration by Parts

Exercises Exercises

6.2.1.

6.2.5.

6.2.7.

6.2.9.

6.2.11.

6.2.13.

6.2.15.

6.2.17.

6.2.19.

6.2.21.

6.2.23.

6.2.25.

6.2.27.

6.2.29.

6.2.31.

6.2.33.

6.2.35.

6.2.37.

6.2.39.

6.2.41.

6.2.43.

6.2.45.

6.2.47.

6.2.49.

Section 6.3 Trigonometric Integrals

Exercises 6.3.4 Exercises

6.3.4.1.

6.3.4.3.

6.3.4.5.

6.3.4.7.

6.3.4.9.

6.3.4.11.

6.3.4.13.

6.3.4.15.

6.3.4.17.

6.3.4.19.

6.3.4.21.

6.3.4.23.

6.3.4.25.

6.3.4.27.

6.3.4.29.

6.3.4.31.

6.3.4.33.

Section 6.4 Trigonometric Substitution

Exercises Exercises

6.4.5.

6.4.7.

6.4.9.

6.4.11.

6.4.13.

6.4.15.

6.4.17.

6.4.19.

6.4.21.

6.4.23.

6.4.25.

6.4.27.

6.4.29.

6.4.31.

Section 6.5 Partial Fraction Decomposition

Exercises Exercises

6.5.7.

6.5.9.

6.5.11.

6.5.13.

6.5.15.

6.5.17.

6.5.19.

6.5.21.

6.5.23.

6.5.25.

6.5.27.

6.5.29.

Section 6.6 Hyperbolic Functions

Exercises 6.6.3 Exercises

6.6.3.11.

6.6.3.13.

6.6.3.15.

6.6.3.17.

6.6.3.19.

6.6.3.21.

6.6.3.23.

6.6.3.25.

6.6.3.27.

6.6.3.29.

6.6.3.31.

6.6.3.33.

6.6.3.35.

6.6.3.37.

6.6.3.39.

6.6.3.41.

6.6.3.43.

6.6.3.45.

6.6.3.47.

Section 6.7 L'Hospital's Rule

Exercises 6.7.4 Exercises

6.7.4.3.

6.7.4.9.

6.7.4.11.

6.7.4.13.

6.7.4.15.

6.7.4.17.

6.7.4.19.

6.7.4.21.

6.7.4.23.

6.7.4.25.

6.7.4.27.

6.7.4.29.

6.7.4.31.

6.7.4.33.

6.7.4.35.

6.7.4.37.

6.7.4.39.

6.7.4.41.

6.7.4.43.

6.7.4.45.

6.7.4.47.

6.7.4.49.

6.7.4.51.

6.7.4.53.

Section 6.8 Improper Integration

Exercises 6.8.4 Exercises

6.8.4.5.

6.8.4.7.

6.8.4.9.

6.8.4.11.

6.8.4.13.

6.8.4.15.

6.8.4.17.

6.8.4.19.

6.8.4.21.

6.8.4.23.

6.8.4.25.

6.8.4.27.

6.8.4.29.

6.8.4.31.

6.8.4.33.

6.8.4.35.

Answer 1 Answer 2 Answer 3

6.8.4.37.

Answer 1 Answer 2 Answer 3

6.8.4.39.

Answer 1 Answer 2 Answer 3

6.8.4.41.

Answer 1 Answer 2 Answer 3

6.8.4.43.

Answer 1 Answer 2 Answer 3

Chapter 7 Applications of Integration

Section 7.1 Area Between Curves

Exercises Exercises

7.1.1.

7.1.5.

7.1.7.

7.1.9.

7.1.11.

7.1.13.

7.1.15.

7.1.17.

7.1.19.

7.1.21.

7.1.23.

7.1.25.

7.1.27.

7.1.29.

7.1.31.

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

Exercises Exercises

7.2.1.

7.2.5.

7.2.7.

7.2.9.

7.2.11.

7.2.19.

7.2.21.

Section 7.3 The Shell Method

Exercises Exercises

7.3.1.

7.3.3.

7.3.5.

7.3.7.

7.3.9.

7.3.11.

Section 7.5 Work

Exercises 7.5.4 Exercises

7.5.4.1.

7.5.4.3.

7.5.4.5.

7.5.4.7.

7.5.4.9.

7.5.4.11.

7.5.4.13.

7.5.4.15.

7.5.4.17.

7.5.4.19.

7.5.4.21.

7.5.4.23.

7.5.4.25.

7.5.4.27.

Section 7.6 Fluid Forces

Exercises Exercises

7.6.1.

7.6.3.

7.6.5.

7.6.7.

7.6.9.

7.6.11.

7.6.13.

7.6.15.

7.6.17.

7.6.19.

Chapter 8 Sequences and Series

Section 8.1 Sequences

Exercises Exercises

8.1.1.

8.1.3.

8.1.5.

8.1.7.

8.1.9.

8.1.11.

8.1.13.

8.1.15.

8.1.17.

8.1.19.

8.1.21.

8.1.23.

8.1.25.

8.1.27.

8.1.29.

8.1.31.

8.1.33.

8.1.35.

8.1.37.

Section 8.2 Infinite Series

Exercises 8.2.4 Exercises

8.2.4.1.

8.2.4.5.

Section 8.3 Integral and Comparison Tests

Exercises 8.3.4 Exercises

8.3.4.1.

8.3.4.5.

8.3.4.7.

8.3.4.9.

8.3.4.11.

Section 8.4 Ratio and Root Tests

Exercises 8.4.3 Exercises

8.4.3.1.

8.4.3.3.

8.4.3.5.

8.4.3.7.

8.4.3.9.

8.4.3.11.

8.4.3.13.

8.4.3.15.

8.4.3.17.

8.4.3.19.

8.4.3.21.

8.4.3.23.

Section 8.5 Alternating Series and Absolute Convergence

Exercises Exercises

8.5.3.

Section 8.7 Taylor Polynomials

Exercises Exercises

8.7.3.

8.7.5.

8.7.7.

8.7.9.

8.7.11.

8.7.13.

8.7.15.

8.7.17.

8.7.19.

8.7.31.

Chapter 9 Curves in the Plane

Section 9.1 Conic Sections

Exercises 9.1.4 Exercises

9.1.4.19.

9.1.4.29.

9.1.4.31.

9.1.4.45.

Section 9.2 Parametric Equations

Exercises 9.2.4 Exercises

9.2.4.1.

9.2.4.3.

9.2.4.5.

9.2.4.7.

9.2.4.9.

9.2.4.11.

9.2.4.13.

9.2.4.15.

9.2.4.17.

9.2.4.21.

9.2.4.25.

9.2.4.35.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5

9.2.4.37.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5

9.2.4.39.

Answer 1 Answer 2

9.2.4.51.

Section 9.3 Calculus and Parametric Equations

Exercises 9.3.4 Exercises

9.3.4.1.

9.3.4.3.

9.3.4.15.

Answer 1 Answer 2

9.3.4.21.

Answer 1 Answer 2

9.3.4.27.

Answer 1 Answer 2 Answer 3

9.3.4.33.

9.3.4.35.

Section 9.4 Introduction to Polar Coordinates

Exercises 9.4.4 Exercises

9.4.4.1.

9.4.4.3.

9.4.4.5.

9.4.4.7.

9.4.4.9.

Answer 1 Answer 2 Answer 3 Answer 4

9.4.4.11.

9.4.4.13.

9.4.4.15.

9.4.4.17.

9.4.4.19.

9.4.4.21.

9.4.4.23.

9.4.4.25.

9.4.4.27.

9.4.4.29.

9.4.4.31.

9.4.4.33.

9.4.4.35.

9.4.4.39.

9.4.4.41.

9.4.4.43.

9.4.4.45.

9.4.4.47.

9.4.4.49.

9.4.4.51.

Section 9.5 Calculus and Polar Functions

Exercises 9.5.5 Exercises

9.5.5.3.

Answer 1 Answer 2 Answer 3

9.5.5.7.

Answer 1 Answer 2 Answer 3

9.5.5.9.

Answer 1 Answer 2 Answer 3

9.5.5.19.

9.5.5.21.

9.5.5.23.

9.5.5.25.

9.5.5.27.

9.5.5.29.

9.5.5.31.

9.5.5.39.

Chapter 10 Vectors

Section 10.1 Introduction to Cartesian Coordinates in Space

Exercises 10.1.7 Exercises

10.1.7.7.

Answer 1 Answer 2 Answer 3 Answer 4

10.1.7.9.

Answer 1 Answer 2

10.1.7.15.

10.1.7.17.

10.1.7.19.

10.1.7.21.

10.1.7.23.

10.1.7.25.

10.1.7.27.

10.1.7.29.

10.1.7.31.

Section 10.2 An Introduction to Vectors

Exercises Exercises

10.2.7.

Answer 1 Answer 2

10.2.9.

Answer 1 Answer 2

10.2.17.

Answer 1 Answer 2 Answer 3 Answer 4

10.2.19.

Answer 1 Answer 2 Answer 3 Answer 4

10.2.23.

10.2.25.

10.2.27.

Section 10.3 The Dot Product

Exercises 10.3.2 Exercises

10.3.2.1.

10.3.2.5.

10.3.2.7.

10.3.2.9.

10.3.2.11.

10.3.2.13.

10.3.2.15.

10.3.2.17.

Answer 1 Answer 2

10.3.2.19.

Answer 1 Answer 2

10.3.2.21.

10.3.2.23.

10.3.2.25.

10.3.2.27.

Answer 1 Answer 2

10.3.2.29.

Answer 1 Answer 2

10.3.2.31.

Answer 1 Answer 2

10.3.2.33.

10.3.2.35.

10.3.2.37.

10.3.2.39.

Section 10.4 The Cross Product

Exercises 10.4.3 Exercises

10.4.3.1.

10.4.3.3.

10.4.3.5.

10.4.3.7.

10.4.3.9.

10.4.3.11.

10.4.3.13.

10.4.3.15.

10.4.3.17.

10.4.3.19.

10.4.3.21.

10.4.3.23.

10.4.3.25.

10.4.3.27.

10.4.3.29.

10.4.3.31.

10.4.3.33.

10.4.3.35.

10.4.3.37.

10.4.3.39.

10.4.3.41.

Section 10.5 Lines

Exercises 10.5.2 Exercises

10.5.2.1.

10.5.2.3.

10.5.2.11.

Answer 1 Answer 2 Answer 3

10.5.2.15.

10.5.2.19.

10.5.2.23.

10.5.2.25.

10.5.2.27.

Section 10.6 Planes

Exercises 10.6.2 Exercises

10.6.2.1.

10.6.2.3.

10.6.2.5.

10.6.2.17.

Answer 1 Answer 2

10.6.2.19.

Answer 1 Answer 2

10.6.2.27.

10.6.2.29.

Chapter 11 Vector Valued Functions

Section 11.1 Vector-Valued Functions

Exercises 11.1.4 Exercises

11.1.4.1.

11.1.4.3.

11.1.4.15.

11.1.4.17.

11.1.4.19.

11.1.4.21.

11.1.4.25.

11.1.4.27.

11.1.4.29.

11.1.4.31.

11.1.4.33.

Section 11.2 Calculus and Vector-Valued Functions

Exercises 11.2.5 Exercises

11.2.5.1.

11.2.5.5.

11.2.5.7.

11.2.5.9.

11.2.5.11.

11.2.5.13.

11.2.5.15.

11.2.5.21.

11.2.5.23.

11.2.5.33.

11.2.5.35.

11.2.5.37.

11.2.5.39.

11.2.5.41.

11.2.5.43.

Section 11.3 The Calculus of Motion

Exercises 11.3.3 Exercises

11.3.3.7.

11.3.3.19.

Answer 1 Answer 2 Answer 3

11.3.3.39.

Answer 1 Answer 2

Section 11.4 Unit Tangent and Normal Vectors

Exercises 11.4.4 Exercises

11.4.4.1.

11.4.4.3.

11.4.4.5.

11.4.4.9.

11.4.4.13.

11.4.4.15.

Section 11.5 The Arc Length Parameter and Curvature

Exercises 11.5.3 Exercises

11.5.3.1.

11.5.3.3.

11.5.3.5.

11.5.3.15.

Answer 1 Answer 2 Answer 3 Answer 4

11.5.3.23.

11.5.3.25.

Chapter 12 Functions of Several Variables

Section 12.3 Partial Derivatives

Exercises 12.3.7 Exercises

12.3.7.3.

12.3.7.19.

Answer 1 Answer 2 Answer 3 Answer 4 Answer 5 Answer 6

Section 12.5 The Multivariable Chain Rule

Exercises 12.5.3 Exercises

12.5.3.5.

12.5.3.21.

Answer 1 Answer 2 Answer 3 Answer 4

Section 12.6 Directional Derivatives

Exercises 12.6.3 Exercises

12.6.3.3.

Section 12.7 Tangent Lines, Normal Lines, and Tangent Planes

Exercises 12.7.5 Exercises

12.7.5.3.

Section 12.8 Extreme Values

Exercises 12.8.3 Exercises

12.8.3.1.

12.8.3.3.

12.8.3.15.

Answer 1 Answer 2 Answer 3 Answer 4

Chapter 13 Multiple Integration

Section 13.1 Iterated Integrals and Area

Exercises 13.1.4 Exercises

13.1.4.3.

13.1.4.5.

13.1.4.7.

13.1.4.9.

Section 13.3 Double Integration with Polar Coordinates

Exercises Exercises

13.3.3.

13.3.5.

Section 13.5 Surface Area

Exercises Exercises

13.5.7.

13.5.9.

Section 13.6 Volume Between Surfaces and Triple Integration

Exercises 13.6.4 Exercises

13.6.4.9.

13.6.4.11.

13.6.4.13.

13.6.4.15.

Section 13.7 Triple Integration with Cylindrical and Spherical Coordinates

Exercises 13.7.3 Exercises

13.7.3.9.

13.7.3.17.

Chapter 14 Vector Analysis

Section 14.1 Introduction to Line Integrals

Exercises 14.1.4 Exercises

14.1.4.1.

14.1.4.3.

14.1.4.5.

14.1.4.7.

14.1.4.9.

14.1.4.11.

14.1.4.13.

14.1.4.15.

14.1.4.17.

14.1.4.19.

Section 14.2 Vector Fields

Exercises 14.2.3 Exercises

14.2.3.1.

14.2.3.3.

14.2.3.5.

14.2.3.7.

14.2.3.9.

14.2.3.11.

14.2.3.13.

14.2.3.15.

14.2.3.17.

Section 14.3 Line Integrals over Vector Fields

Exercises 14.3.4 Exercises

14.3.4.1.

14.3.4.3.

14.3.4.5.

14.3.4.7.

14.3.4.9.

14.3.4.11.

14.3.4.13.

14.3.4.15.

14.3.4.17.

14.3.4.19.

Section 14.4 Flow, Flux, Green's Theorem and the Divergence Theorem

Exercises 14.4.4 Exercises

14.4.4.1.

14.4.4.3.

14.4.4.5.

14.4.4.7.

14.4.4.9.

14.4.4.11.

14.4.4.13.

14.4.4.15.

14.4.4.17.

14.4.4.19.

14.4.4.21.

14.4.4.23.

Section 14.5 Parametrized Surfaces and Surface Area

Exercises 14.5.3 Exercises

14.5.3.1.

14.5.3.3.

14.5.3.5.

14.5.3.7.

14.5.3.9.

14.5.3.11.

14.5.3.13.

14.5.3.15.

14.5.3.17.

14.5.3.19.

14.5.3.21.

14.5.3.23.

Section 14.6 Surface Integrals

Exercises 14.6.3 Exercises

14.6.3.1.

14.6.3.3.

14.6.3.5.

14.6.3.7.

14.6.3.9.

14.6.3.11.

14.6.3.13.

Section 14.7 The Divergence Theorem and Stokes' Theorem

Exercises 14.7.4 Exercises

14.7.4.1.

14.7.4.3.

14.7.4.5.

14.7.4.7.

14.7.4.9.

14.7.4.11.

14.7.4.13.

14.7.4.15.

14.7.4.17.

14.7.4.19.

14.7.4.21.

14.7.4.23.