1) Of the following vector fields, the one that is conservative corresponds to: (See the answers in the images for question 1) 2) If f is a potential function for the vector field F = (−2y + 2xyz, −2x + x2z, x2y + 8z), then the value of f(3, −4, 1) is: A) −12 B) 14 C) −8 D) 10

1) Of the following vector fields, the one that is conservative corresponds to: (See the answers in the images for question 1) 2) If f is a potential function for the vector field F = (−2y + 2xyz, −2x + x2z, x2y + 8z), then the value of f(3, −4, 1) is: A) −12 B) 14 C) −8 D) 10

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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Question

1) Of the following vector fields, the one that is conservative corresponds to:

(See the answers in the images for question 1)

2) If f is a potential function for the vector field F = (−2y + 2xyz, −2x + x²z, x²y + 8z), then the value of f(3, −4, 1) is:

A) −12
B) 14
C) −8
D) 10

A) F(x, y, z) = (y² – !, 2xy – , )
z+y
-
B) F(z, y, z) =D (2 -1, 2ry-글, 딸)
2xy – 2,
x+y
C) F(x, y, z) = (x² – !, 2xz – !, t)
1
x+y
D) F(x, y, z) = (y² – !, 2xy – !, )
1
x+y
-
|

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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