Chapter 15.7, Problem 14E

BuyFind*arrow_forward*

7th Edition

Ron Larson + 1 other

ISBN: 9781337552516

Textbook Problem

Using the Divergence Theorem In Exercises 9-18, use the Divergence Theorem to evaluate

and find the outward flux of F through the surface of the solid *S* bounded by the graphs of the equations. Use a computer algebra system to verify your results.

*S*:

To determine

**To calculate:** The value of

Explanation

**Given:**

The vector field, *S*:

**Formula used:**

The divergence theorem,

**Calculation:**

Find the divergence of vector field **F**,

For the surface bounded by *S*: *r* = 2, and height

Sect-15.1 P-1ESect-15.1 P-2ESect-15.1 P-3ESect-15.1 P-4ESect-15.1 P-5ESect-15.1 P-6ESect-15.1 P-7ESect-15.1 P-8ESect-15.1 P-9ESect-15.1 P-10E

Sect-15.1 P-11ESect-15.1 P-12ESect-15.1 P-13ESect-15.1 P-14ESect-15.1 P-15ESect-15.1 P-16ESect-15.1 P-17ESect-15.1 P-18ESect-15.1 P-19ESect-15.1 P-20ESect-15.1 P-21ESect-15.1 P-22ESect-15.1 P-23ESect-15.1 P-24ESect-15.1 P-25ESect-15.1 P-26ESect-15.1 P-27ESect-15.1 P-28ESect-15.1 P-29ESect-15.1 P-30ESect-15.1 P-31ESect-15.1 P-32ESect-15.1 P-33ESect-15.1 P-34ESect-15.1 P-35ESect-15.1 P-36ESect-15.1 P-37ESect-15.1 P-38ESect-15.1 P-39ESect-15.1 P-40ESect-15.1 P-41ESect-15.1 P-42ESect-15.1 P-43ESect-15.1 P-44ESect-15.1 P-45ESect-15.1 P-46ESect-15.1 P-47ESect-15.1 P-48ESect-15.1 P-49ESect-15.1 P-50ESect-15.1 P-51ESect-15.1 P-52ESect-15.1 P-53ESect-15.1 P-54ESect-15.1 P-55ESect-15.1 P-56ESect-15.1 P-57ESect-15.1 P-58ESect-15.1 P-59ESect-15.1 P-60ESect-15.1 P-61ESect-15.1 P-62ESect-15.1 P-63ESect-15.1 P-64ESect-15.1 P-65ESect-15.1 P-66ESect-15.1 P-67ESect-15.1 P-68ESect-15.1 P-69ESect-15.1 P-70ESect-15.1 P-71ESect-15.1 P-72ESect-15.1 P-73ESect-15.1 P-74ESect-15.1 P-75ESect-15.1 P-76ESect-15.1 P-77ESect-15.1 P-78ESect-15.2 P-1ESect-15.2 P-2ESect-15.2 P-3ESect-15.2 P-4ESect-15.2 P-5ESect-15.2 P-6ESect-15.2 P-7ESect-15.2 P-8ESect-15.2 P-9ESect-15.2 P-10ESect-15.2 P-11ESect-15.2 P-12ESect-15.2 P-13ESect-15.2 P-14ESect-15.2 P-15ESect-15.2 P-16ESect-15.2 P-17ESect-15.2 P-18ESect-15.2 P-19ESect-15.2 P-20ESect-15.2 P-21ESect-15.2 P-22ESect-15.2 P-23ESect-15.2 P-24ESect-15.2 P-25ESect-15.2 P-26ESect-15.2 P-27ESect-15.2 P-28ESect-15.2 P-29ESect-15.2 P-30ESect-15.2 P-31ESect-15.2 P-32ESect-15.2 P-33ESect-15.2 P-34ESect-15.2 P-35ESect-15.2 P-36ESect-15.2 P-37ESect-15.2 P-38ESect-15.2 P-39ESect-15.2 P-40ESect-15.2 P-41ESect-15.2 P-42ESect-15.2 P-43ESect-15.2 P-44ESect-15.2 P-45ESect-15.2 P-46ESect-15.2 P-47ESect-15.2 P-48ESect-15.2 P-49ESect-15.2 P-50ESect-15.2 P-51ESect-15.2 P-52ESect-15.2 P-53ESect-15.2 P-54ESect-15.2 P-55ESect-15.2 P-56ESect-15.2 P-57ESect-15.2 P-58ESect-15.2 P-59ESect-15.2 P-60ESect-15.2 P-61ESect-15.2 P-62ESect-15.2 P-63ESect-15.2 P-64ESect-15.2 P-65ESect-15.2 P-66ESect-15.2 P-67ESect-15.2 P-68ESect-15.2 P-69ESect-15.2 P-70ESect-15.2 P-71ESect-15.2 P-72ESect-15.2 P-73ESect-15.2 P-74ESect-15.2 P-75ESect-15.2 P-76ESect-15.2 P-77ESect-15.2 P-78ESect-15.2 P-79ESect-15.2 P-80ESect-15.2 P-81ESect-15.2 P-82ESect-15.2 P-83ESect-15.2 P-84ESect-15.2 P-85ESect-15.2 P-86ESect-15.2 P-87ESect-15.3 P-1ESect-15.3 P-2ESect-15.3 P-3ESect-15.3 P-4ESect-15.3 P-5ESect-15.3 P-6ESect-15.3 P-7ESect-15.3 P-8ESect-15.3 P-9ESect-15.3 P-10ESect-15.3 P-11ESect-15.3 P-12ESect-15.3 P-13ESect-15.3 P-14ESect-15.3 P-15ESect-15.3 P-16ESect-15.3 P-17ESect-15.3 P-18ESect-15.3 P-19ESect-15.3 P-20ESect-15.3 P-21ESect-15.3 P-22ESect-15.3 P-23ESect-15.3 P-24ESect-15.3 P-25ESect-15.3 P-26ESect-15.3 P-27ESect-15.3 P-28ESect-15.3 P-29ESect-15.3 P-30ESect-15.3 P-31ESect-15.3 P-32ESect-15.3 P-33ESect-15.3 P-34ESect-15.3 P-35ESect-15.3 P-36ESect-15.3 P-37ESect-15.3 P-38ESect-15.3 P-39ESect-15.3 P-40ESect-15.3 P-41ESect-15.3 P-42ESect-15.3 P-43ESect-15.3 P-44ESect-15.3 P-45ESect-15.3 P-46ESect-15.3 P-47ESect-15.3 P-48ESect-15.3 P-49ESect-15.4 P-1ESect-15.4 P-2ESect-15.4 P-3ESect-15.4 P-4ESect-15.4 P-5ESect-15.4 P-6ESect-15.4 P-7ESect-15.4 P-8ESect-15.4 P-9ESect-15.4 P-10ESect-15.4 P-11ESect-15.4 P-12ESect-15.4 P-13ESect-15.4 P-14ESect-15.4 P-15ESect-15.4 P-16ESect-15.4 P-17ESect-15.4 P-18ESect-15.4 P-19ESect-15.4 P-20ESect-15.4 P-21ESect-15.4 P-22ESect-15.4 P-23ESect-15.4 P-24ESect-15.4 P-25ESect-15.4 P-26ESect-15.4 P-27ESect-15.4 P-28ESect-15.4 P-29ESect-15.4 P-30ESect-15.4 P-31ESect-15.4 P-32ESect-15.4 P-33ESect-15.4 P-34ESect-15.4 P-35ESect-15.4 P-36ESect-15.4 P-37ESect-15.4 P-38ESect-15.4 P-39ESect-15.4 P-40ESect-15.4 P-41ESect-15.4 P-42ESect-15.4 P-43ESect-15.4 P-44ESect-15.4 P-45ESect-15.4 P-46ESect-15.4 P-47ESect-15.4 P-48ESect-15.4 P-49ESect-15.4 P-50ESect-15.4 P-51ESect-15.4 P-52ESect-15.4 P-53ESect-15.4 P-54ESect-15.5 P-1ESect-15.5 P-2ESect-15.5 P-3ESect-15.5 P-4ESect-15.5 P-5ESect-15.5 P-6ESect-15.5 P-7ESect-15.5 P-8ESect-15.5 P-9ESect-15.5 P-10ESect-15.5 P-11ESect-15.5 P-12ESect-15.5 P-13ESect-15.5 P-14ESect-15.5 P-15ESect-15.5 P-16ESect-15.5 P-17ESect-15.5 P-18ESect-15.5 P-19ESect-15.5 P-20ESect-15.5 P-21ESect-15.5 P-22ESect-15.5 P-23ESect-15.5 P-24ESect-15.5 P-25ESect-15.5 P-26ESect-15.5 P-27ESect-15.5 P-28ESect-15.5 P-29ESect-15.5 P-30ESect-15.5 P-31ESect-15.5 P-32ESect-15.5 P-33ESect-15.5 P-34ESect-15.5 P-35ESect-15.5 P-36ESect-15.5 P-37ESect-15.5 P-38ESect-15.5 P-39ESect-15.5 P-40ESect-15.5 P-41ESect-15.5 P-42ESect-15.5 P-43ESect-15.5 P-44ESect-15.5 P-45ESect-15.5 P-46ESect-15.5 P-47ESect-15.5 P-48ESect-15.5 P-49ESect-15.5 P-50ESect-15.5 P-51ESect-15.5 P-52ESect-15.5 P-53ESect-15.5 P-54ESect-15.5 P-55ESect-15.5 P-56ESect-15.5 P-57ESect-15.5 P-58ESect-15.6 P-1ESect-15.6 P-2ESect-15.6 P-3ESect-15.6 P-4ESect-15.6 P-5ESect-15.6 P-6ESect-15.6 P-7ESect-15.6 P-8ESect-15.6 P-9ESect-15.6 P-10ESect-15.6 P-11ESect-15.6 P-12ESect-15.6 P-13ESect-15.6 P-14ESect-15.6 P-15ESect-15.6 P-16ESect-15.6 P-17ESect-15.6 P-18ESect-15.6 P-19ESect-15.6 P-20ESect-15.6 P-21ESect-15.6 P-22ESect-15.6 P-23ESect-15.6 P-24ESect-15.6 P-25ESect-15.6 P-26ESect-15.6 P-27ESect-15.6 P-28ESect-15.6 P-29ESect-15.6 P-30ESect-15.6 P-31ESect-15.6 P-32ESect-15.6 P-33ESect-15.6 P-34ESect-15.6 P-35ESect-15.6 P-36ESect-15.6 P-37ESect-15.6 P-38ESect-15.6 P-39ESect-15.6 P-40ESect-15.6 P-41ESect-15.6 P-42ESect-15.6 P-43ESect-15.7 P-1ESect-15.7 P-2ESect-15.7 P-3ESect-15.7 P-4ESect-15.7 P-5ESect-15.7 P-6ESect-15.7 P-7ESect-15.7 P-8ESect-15.7 P-9ESect-15.7 P-10ESect-15.7 P-11ESect-15.7 P-12ESect-15.7 P-13ESect-15.7 P-14ESect-15.7 P-15ESect-15.7 P-16ESect-15.7 P-17ESect-15.7 P-18ESect-15.7 P-19ESect-15.7 P-20ESect-15.7 P-21ESect-15.7 P-22ESect-15.7 P-23ESect-15.7 P-24ESect-15.7 P-25ESect-15.7 P-26ESect-15.7 P-27ESect-15.7 P-28ESect-15.7 P-29ESect-15.7 P-30ESect-15.7 P-31ESect-15.7 P-32ESect-15.8 P-1ESect-15.8 P-2ESect-15.8 P-3ESect-15.8 P-4ESect-15.8 P-5ESect-15.8 P-6ESect-15.8 P-7ESect-15.8 P-8ESect-15.8 P-9ESect-15.8 P-10ESect-15.8 P-11ESect-15.8 P-12ESect-15.8 P-13ESect-15.8 P-14ESect-15.8 P-15ESect-15.8 P-16ESect-15.8 P-17ESect-15.8 P-18ESect-15.8 P-19ESect-15.8 P-20ESect-15.8 P-21ECh-15 P-1RECh-15 P-2RECh-15 P-3RECh-15 P-4RECh-15 P-5RECh-15 P-6RECh-15 P-7RECh-15 P-8RECh-15 P-9RECh-15 P-10RECh-15 P-11RECh-15 P-12RECh-15 P-13RECh-15 P-14RECh-15 P-15RECh-15 P-16RECh-15 P-17RECh-15 P-18RECh-15 P-19RECh-15 P-20RECh-15 P-21RECh-15 P-22RECh-15 P-23RECh-15 P-24RECh-15 P-25RECh-15 P-26RECh-15 P-27RECh-15 P-28RECh-15 P-29RECh-15 P-30RECh-15 P-31RECh-15 P-32RECh-15 P-33RECh-15 P-34RECh-15 P-35RECh-15 P-36RECh-15 P-37RECh-15 P-38RECh-15 P-39RECh-15 P-40RECh-15 P-41RECh-15 P-42RECh-15 P-43RECh-15 P-44RECh-15 P-45RECh-15 P-46RECh-15 P-47RECh-15 P-48RECh-15 P-49RECh-15 P-50RECh-15 P-51RECh-15 P-52RECh-15 P-53RECh-15 P-54RECh-15 P-55RECh-15 P-56RECh-15 P-57RECh-15 P-58RECh-15 P-59RECh-15 P-60RECh-15 P-61RECh-15 P-62RECh-15 P-63RECh-15 P-64RECh-15 P-65RECh-15 P-66RECh-15 P-67RECh-15 P-68RECh-15 P-69RECh-15 P-70RECh-15 P-71RECh-15 P-72RECh-15 P-73RECh-15 P-74RECh-15 P-75RECh-15 P-76RECh-15 P-77RECh-15 P-78RECh-15 P-79RECh-15 P-80RECh-15 P-81RECh-15 P-82RECh-15 P-83RECh-15 P-84RECh-15 P-85RECh-15 P-86RECh-15 P-1PSCh-15 P-2PSCh-15 P-3PSCh-15 P-4PSCh-15 P-5PSCh-15 P-6PSCh-15 P-7PSCh-15 P-8PSCh-15 P-9PSCh-15 P-10PSCh-15 P-11PSCh-15 P-12PS

Precalculus: Mathematics for Calculus (Standalone Book)

Calculus: Early Transcendentals

Single Variable Calculus: Early Transcendentals, Volume I

Multivariable Calculus

Finite Mathematics and Applied Calculus (MindTap Course List)

Calculus (MindTap Course List)

Calculus: An Applied Approach (MindTap Course List)

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

Essentials Of Statistics

Applied Calculus

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

Elementary Geometry For College Students, 7e

Intermediate Algebra

Mathematical Excursions (MindTap Course List)

Elementary Technical Mathematics

Mathematical Applications for the Management, Life, and Social Sciences

Calculus of a Single Variable

Single Variable Calculus: Early Transcendentals

Elements Of Modern Algebra

Trigonometry (MindTap Course List)

Contemporary Mathematics for Business & Consumers

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

Study Guide for Stewart's Multivariable Calculus, 8th

Finite Mathematics for the Managerial, Life, and Social Sciences

Elementary Geometry for College Students