Chapter 16.5, Problem 22E

BuyFind*arrow_forward*

8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Show that any vector field of the form

**F**(*x*, *y*, *z*) = *f*(*y*, *z*) **i** + *g*(*x*, *z*) **j** + *h*(*x*, *y*) **k**

is incompressible.

To determine

**To show:** The vector field of the form

Explanation

**Given data:**

**Formula used:**

Consider the standard equation of a divergence of vector field for

Substitute

Sect-16.1 P-1ESect-16.1 P-2ESect-16.1 P-3ESect-16.1 P-4ESect-16.1 P-5ESect-16.1 P-6ESect-16.1 P-7ESect-16.1 P-8ESect-16.1 P-9ESect-16.1 P-10E

Sect-16.1 P-11ESect-16.1 P-12ESect-16.1 P-13ESect-16.1 P-14ESect-16.1 P-15ESect-16.1 P-16ESect-16.1 P-17ESect-16.1 P-18ESect-16.1 P-21ESect-16.1 P-22ESect-16.1 P-23ESect-16.1 P-24ESect-16.1 P-25ESect-16.1 P-26ESect-16.1 P-29ESect-16.1 P-30ESect-16.1 P-31ESect-16.1 P-32ESect-16.1 P-33ESect-16.1 P-34ESect-16.1 P-35ESect-16.1 P-36ESect-16.2 P-1ESect-16.2 P-2ESect-16.2 P-3ESect-16.2 P-4ESect-16.2 P-5ESect-16.2 P-6ESect-16.2 P-7ESect-16.2 P-8ESect-16.2 P-9ESect-16.2 P-10ESect-16.2 P-11ESect-16.2 P-12ESect-16.2 P-13ESect-16.2 P-14ESect-16.2 P-15ESect-16.2 P-16ESect-16.2 P-17ESect-16.2 P-18ESect-16.2 P-19ESect-16.2 P-20ESect-16.2 P-21ESect-16.2 P-22ESect-16.2 P-23ESect-16.2 P-24ESect-16.2 P-25ESect-16.2 P-26ESect-16.2 P-31ESect-16.2 P-32ESect-16.2 P-33ESect-16.2 P-34ESect-16.2 P-35ESect-16.2 P-36ESect-16.2 P-37ESect-16.2 P-38ESect-16.2 P-39ESect-16.2 P-40ESect-16.2 P-41ESect-16.2 P-42ESect-16.2 P-43ESect-16.2 P-44ESect-16.2 P-45ESect-16.2 P-46ESect-16.2 P-47ESect-16.2 P-48ESect-16.2 P-49ESect-16.2 P-50ESect-16.2 P-51ESect-16.2 P-52ESect-16.3 P-1ESect-16.3 P-2ESect-16.3 P-3ESect-16.3 P-4ESect-16.3 P-5ESect-16.3 P-6ESect-16.3 P-7ESect-16.3 P-8ESect-16.3 P-9ESect-16.3 P-10ESect-16.3 P-11ESect-16.3 P-12ESect-16.3 P-13ESect-16.3 P-14ESect-16.3 P-15ESect-16.3 P-16ESect-16.3 P-17ESect-16.3 P-18ESect-16.3 P-19ESect-16.3 P-20ESect-16.3 P-21ESect-16.3 P-22ESect-16.3 P-23ESect-16.3 P-24ESect-16.3 P-25ESect-16.3 P-26ESect-16.3 P-28ESect-16.3 P-29ESect-16.3 P-30ESect-16.3 P-31ESect-16.3 P-32ESect-16.3 P-33ESect-16.3 P-34ESect-16.3 P-35ESect-16.4 P-1ESect-16.4 P-2ESect-16.4 P-3ESect-16.4 P-4ESect-16.4 P-5ESect-16.4 P-6ESect-16.4 P-7ESect-16.4 P-8ESect-16.4 P-9ESect-16.4 P-10ESect-16.4 P-11ESect-16.4 P-12ESect-16.4 P-13ESect-16.4 P-14ESect-16.4 P-17ESect-16.4 P-18ESect-16.4 P-19ESect-16.4 P-20ESect-16.4 P-21ESect-16.4 P-22ESect-16.4 P-23ESect-16.4 P-24ESect-16.4 P-25ESect-16.4 P-26ESect-16.4 P-27ESect-16.4 P-28ESect-16.4 P-29ESect-16.4 P-30ESect-16.4 P-31ESect-16.5 P-1ESect-16.5 P-2ESect-16.5 P-3ESect-16.5 P-4ESect-16.5 P-5ESect-16.5 P-6ESect-16.5 P-7ESect-16.5 P-8ESect-16.5 P-9ESect-16.5 P-10ESect-16.5 P-11ESect-16.5 P-12ESect-16.5 P-13ESect-16.5 P-14ESect-16.5 P-15ESect-16.5 P-16ESect-16.5 P-17ESect-16.5 P-18ESect-16.5 P-19ESect-16.5 P-20ESect-16.5 P-21ESect-16.5 P-22ESect-16.5 P-23ESect-16.5 P-24ESect-16.5 P-25ESect-16.5 P-26ESect-16.5 P-27ESect-16.5 P-28ESect-16.5 P-29ESect-16.5 P-30ESect-16.5 P-31ESect-16.5 P-32ESect-16.5 P-33ESect-16.5 P-34ESect-16.5 P-35ESect-16.5 P-36ESect-16.5 P-37ESect-16.5 P-38ESect-16.5 P-39ESect-16.6 P-1ESect-16.6 P-2ESect-16.6 P-3ESect-16.6 P-4ESect-16.6 P-5ESect-16.6 P-6ESect-16.6 P-13ESect-16.6 P-14ESect-16.6 P-15ESect-16.6 P-16ESect-16.6 P-17ESect-16.6 P-18ESect-16.6 P-19ESect-16.6 P-20ESect-16.6 P-21ESect-16.6 P-22ESect-16.6 P-23ESect-16.6 P-24ESect-16.6 P-25ESect-16.6 P-26ESect-16.6 P-29ESect-16.6 P-30ESect-16.6 P-33ESect-16.6 P-34ESect-16.6 P-35ESect-16.6 P-36ESect-16.6 P-37ESect-16.6 P-38ESect-16.6 P-39ESect-16.6 P-40ESect-16.6 P-41ESect-16.6 P-42ESect-16.6 P-43ESect-16.6 P-44ESect-16.6 P-45ESect-16.6 P-46ESect-16.6 P-47ESect-16.6 P-48ESect-16.6 P-49ESect-16.6 P-50ESect-16.6 P-51ESect-16.6 P-52ESect-16.6 P-53ESect-16.6 P-54ESect-16.6 P-56ESect-16.6 P-59ESect-16.6 P-60ESect-16.6 P-61ESect-16.6 P-62ESect-16.6 P-63ESect-16.7 P-1ESect-16.7 P-2ESect-16.7 P-3ESect-16.7 P-4ESect-16.7 P-5ESect-16.7 P-6ESect-16.7 P-7ESect-16.7 P-8ESect-16.7 P-9ESect-16.7 P-10ESect-16.7 P-11ESect-16.7 P-12ESect-16.7 P-13ESect-16.7 P-14ESect-16.7 P-15ESect-16.7 P-16ESect-16.7 P-17ESect-16.7 P-18ESect-16.7 P-19ESect-16.7 P-20ESect-16.7 P-21ESect-16.7 P-22ESect-16.7 P-23ESect-16.7 P-24ESect-16.7 P-25ESect-16.7 P-26ESect-16.7 P-28ESect-16.7 P-37ESect-16.7 P-38ESect-16.7 P-39ESect-16.7 P-40ESect-16.7 P-41ESect-16.7 P-42ESect-16.7 P-43ESect-16.7 P-44ESect-16.7 P-45ESect-16.7 P-46ESect-16.7 P-47ESect-16.7 P-48ESect-16.7 P-49ESect-16.8 P-1ESect-16.8 P-2ESect-16.8 P-3ESect-16.8 P-4ESect-16.8 P-5ESect-16.8 P-6ESect-16.8 P-7ESect-16.8 P-8ESect-16.8 P-9ESect-16.8 P-10ESect-16.8 P-11ESect-16.8 P-12ESect-16.8 P-13ESect-16.8 P-14ESect-16.8 P-15ESect-16.8 P-17ESect-16.8 P-18ESect-16.8 P-19ESect-16.8 P-20ESect-16.9 P-1ESect-16.9 P-2ESect-16.9 P-3ESect-16.9 P-4ESect-16.9 P-5ESect-16.9 P-6ESect-16.9 P-7ESect-16.9 P-8ESect-16.9 P-9ESect-16.9 P-10ESect-16.9 P-11ESect-16.9 P-12ESect-16.9 P-13ESect-16.9 P-14ESect-16.9 P-17ESect-16.9 P-18ESect-16.9 P-19ESect-16.9 P-20ESect-16.9 P-23ESect-16.9 P-24ESect-16.9 P-25ESect-16.9 P-26ESect-16.9 P-27ESect-16.9 P-28ESect-16.9 P-29ESect-16.9 P-30ESect-16.9 P-31ESect-16.9 P-32ECh-16 P-1RCCCh-16 P-2RCCCh-16 P-3RCCCh-16 P-4RCCCh-16 P-5RCCCh-16 P-6RCCCh-16 P-7RCCCh-16 P-8RCCCh-16 P-9RCCCh-16 P-10RCCCh-16 P-11RCCCh-16 P-12RCCCh-16 P-13RCCCh-16 P-14RCCCh-16 P-15RCCCh-16 P-16RCCCh-16 P-1RQCh-16 P-2RQCh-16 P-3RQCh-16 P-4RQCh-16 P-5RQCh-16 P-6RQCh-16 P-7RQCh-16 P-8RQCh-16 P-9RQCh-16 P-10RQCh-16 P-11RQCh-16 P-12RQCh-16 P-13RQCh-16 P-1RECh-16 P-2RECh-16 P-3RECh-16 P-4RECh-16 P-5RECh-16 P-6RECh-16 P-7RECh-16 P-8RECh-16 P-9RECh-16 P-10RECh-16 P-11RECh-16 P-12RECh-16 P-13RECh-16 P-14RECh-16 P-15RECh-16 P-16RECh-16 P-17RECh-16 P-18RECh-16 P-19RECh-16 P-20RECh-16 P-21RECh-16 P-22RECh-16 P-23RECh-16 P-24RECh-16 P-25RECh-16 P-27RECh-16 P-28RECh-16 P-29RECh-16 P-30RECh-16 P-31RECh-16 P-32RECh-16 P-33RECh-16 P-34RECh-16 P-35RECh-16 P-36RECh-16 P-37RECh-16 P-38RECh-16 P-39RECh-16 P-40RECh-16 P-41RECh-16 P-1PCh-16 P-2PCh-16 P-3PCh-16 P-5PCh-16 P-6P

Calculus: An Applied Approach (MindTap Course List)

Applied Calculus

Calculus (MindTap Course List)

Single Variable Calculus: Early Transcendentals, Volume I

Calculus: Early Transcendental Functions

Finite Mathematics and Applied Calculus (MindTap Course List)

Precalculus: Mathematics for Calculus (Standalone Book)

Multivariable Calculus

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Essentials Of Statistics

Calculus (MindTap Course List)

Statistics for The Behavioral Sciences (MindTap Course List)

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Single Variable Calculus

Understanding Basic Statistics

Probability and Statistics for Engineering and the Sciences

Finite Mathematics

Mathematical Excursions (MindTap Course List)

Elementary Geometry For College Students, 7e

Elementary Technical Mathematics

Contemporary Mathematics for Business & Consumers

Mathematical Applications for the Management, Life, and Social Sciences

Intermediate Algebra

Calculus of a Single Variable

Calculus: Early Transcendental Functions (MindTap Course List)

Single Variable Calculus: Early Transcendentals

Trigonometry (MindTap Course List)

Elements Of Modern Algebra

Study Guide for Stewart's Multivariable Calculus, 8th

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Finite Mathematics for the Managerial, Life, and Social Sciences

Elementary Geometry for College Students