Consider the conservative vector field 8 4 F(x, y, z) = - 2xz, - 3y²cos(3nz), 3ny sin(3nz) – x² ) 2х + у 2х + y (a) Find the potential function o of F that satisfies (2, 2, 1) = 2. (b) Use the Fundamental Theorem of Line Integrals to find the work done by F along the curve with parametrization R(t) = (2 – t, -cos(t), 3'), t € [0,1]
Consider the conservative vector field 8 4 F(x, y, z) = - 2xz, - 3y²cos(3nz), 3ny sin(3nz) – x² ) 2х + у 2х + y (a) Find the potential function o of F that satisfies (2, 2, 1) = 2. (b) Use the Fundamental Theorem of Line Integrals to find the work done by F along the curve with parametrization R(t) = (2 – t, -cos(t), 3'), t € [0,1]
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![Consider the conservative vector field
8
4
F(x,y,z) =
- 2xz,
- 3y²cos(3nz),
3ny sin(3nz) – x² )
"2х + у
2х + у
(a) Find the potential function o of F that satisfies (2, 2, 1) = 2.
(b) Use the Fundamental Theorem of Line Integrals to find the work done by F along the
curve with parametrization
R(t) = (2 – t,-cos(at), 3*),
t e [0,1]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F353d54ed-f7b8-41e7-82ee-d2b8d2f759c5%2F19637976-de51-462f-a028-b4a395eb73d5%2Fqw015vr_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the conservative vector field
8
4
F(x,y,z) =
- 2xz,
- 3y²cos(3nz),
3ny sin(3nz) – x² )
"2х + у
2х + у
(a) Find the potential function o of F that satisfies (2, 2, 1) = 2.
(b) Use the Fundamental Theorem of Line Integrals to find the work done by F along the
curve with parametrization
R(t) = (2 – t,-cos(at), 3*),
t e [0,1]
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