   Chapter 16, Problem 10RCC

Chapter
Section
Textbook Problem

If F = P i + Q j, how do you determine whether F is conservative? What if F is a vector field on ℝ3?

To determine

Whether the field F is conservative and what if F is a vector field on 3 .

Explanation

A vector field (F) is said to be a conservative vector field, if there exist a gradient of scalar function f such that F=f .

Consider a vector field as F(x,y)=P(x,y)i+Q(x,y)j . The condition for vector field F being a conservative vector field is as follows,

Py=Qx

Here,

Py is continuous first-order partial derivative of P,

Qx is continuous first-order partial derivative of Q, and

P and Q have continuous partial derivatives

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

Expand each expression in Exercises 122. (x22x+1)2

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 43-46, find f(a + h) f(a) for each function. Simplify yoiir answer. 44. f(x)=12x+3

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

The simplified form of the derivative of y=(x+11−x2)3.

Mathematical Applications for the Management, Life, and Social Sciences 