   Chapter 16, Problem 3RQ

Chapter
Section
Textbook Problem

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f has continuous. partial derivatives of all orders on ℝ3, then div(curl ∇f) = 0.

To determine

Whether the statement “If f has continuous partial derivatives of all orders on 3 , then div(curl f)=0 ” is true or false.

Explanation

Given data:

div(curl f)=0 (1)

Formula used:

Write the expression for curl(f) .

curl(f)=0

Write the expression for div(0) .

div(0)=0

Consider left hand side (LHS) of equation (1).

LHS=div(curl f) (2)

Substitute 0 for curl f

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

Find the mean for the following set of scores: 2, 7, 9, 4, 5, 3, 0, 6

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

In Exercises 1-6, show the interval on a number line. 6. (, 5)

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

37.

Mathematical Applications for the Management, Life, and Social Sciences

A number c that satisfies the Mean Value Theorem for f(x) = x3 on [1, 4] is: a) 7 b) 12 c) 63 d) 63

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