   Chapter 16.5, Problem 8E

Chapter
Section
Textbook Problem

Find (a) the curl and (b) the divergence of the vector field.8. F(x, y, z) = ⟨arctan(xy), arctan(yz), arctan(zx)⟩

(a)

To determine

To find: The curl F.

Explanation

Given data:

F(x,y,z)=arctan(xy),arctan(yz),arctan(zx) .

Formula used:

Consider the standard equation of an curl F for F=P,Q,R .

curlF=|ijkxyzPQR| (1)

Substitute arctan(xy) for P , arctan(yz) for Q and arctan(zx) for R in equation (1),

curlF=|ijkxyzarctan(xy)arctan(yz)arctan(zx)|={[y(arctan(zx))z(arctan(yz))]i[x(arctan(zx))z(arctan(xy))]j+[x(arctan(yz))y(arctan(xy))]k}={[(arctan(zx))y(1)z(

(b)

To determine

To find: The divergence of the vector field.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Evaluate the integral. /6/2csctcottdt

Single Variable Calculus: Early Transcendentals, Volume I

For the following scores, find the value of each expression: X 3 2 4 2 a. X b. (X)2 c. X 2 d. (X 2)

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

In Exercises 4144, determine whether the statement is true or false. 44. 561112

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

In Exercises 17 to 22, factor completely. 4x2-16

Elementary Geometry For College Students, 7e

Find the matrix A such that A= Hint: Let A=[abcd]

Finite Mathematics for the Managerial, Life, and Social Sciences

True or false:

Study Guide for Stewart's Multivariable Calculus, 8th

If limx0sinxx=1, the angle x must be measured in: a) radians b) degrees c) it does not matter

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