Let F(x, y, z) = (x-1z, y¬lz, In(xy). (a) Verify that F = V ƒ, where ƒ(x, y, z) = z In(xy). (b) Evaluate F. dr, where r(t) = (e', e²" , r²) for 1 < 1 < 3. . (c) Evaluate F. dr for any path C from P = (}, 4, 2) to Q = (2, 2, 3) contained in the region x > 0, y > 0. (d) Why is it necessary to specify that the path lies in the region where x and y are positive?
Let F(x, y, z) = (x-1z, y¬lz, In(xy). (a) Verify that F = V ƒ, where ƒ(x, y, z) = z In(xy). (b) Evaluate F. dr, where r(t) = (e', e²" , r²) for 1 < 1 < 3. . (c) Evaluate F. dr for any path C from P = (}, 4, 2) to Q = (2, 2, 3) contained in the region x > 0, y > 0. (d) Why is it necessary to specify that the path lies in the region where x and y are positive?
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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![Let F(x, y, z) = (x-1z, y¬lz, In(xy).
(a) Verify that F = V ƒ, where ƒ(x, y, z) = z In(xy).
(b) Evaluate F. dr, where r(t) = (e', e²" , r²) for 1 < 1 < 3.
.
(c) Evaluate F. dr for any path C from P = (}, 4, 2) to Q =
(2, 2, 3) contained in the region x > 0, y > 0.
(d) Why is it necessary to specify that the path lies in the region where
x and y are positive?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff55a687f-3208-4b34-b089-f2d68b597146%2F8fbb948c-ae9f-4fd0-9428-4b882aa1335f%2Ftc09fd6_processed.png&w=3840&q=75)
Transcribed Image Text:Let F(x, y, z) = (x-1z, y¬lz, In(xy).
(a) Verify that F = V ƒ, where ƒ(x, y, z) = z In(xy).
(b) Evaluate F. dr, where r(t) = (e', e²" , r²) for 1 < 1 < 3.
.
(c) Evaluate F. dr for any path C from P = (}, 4, 2) to Q =
(2, 2, 3) contained in the region x > 0, y > 0.
(d) Why is it necessary to specify that the path lies in the region where
x and y are positive?
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