Let F(x, y, z) = y° z°i+ 2xyz³j+ 3xy° z²k. (a) Find the domain of F, and show that F is conservative.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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calc 3 - a through c, line integral

f(x, y, z) = L0
Let
F(x, y, z) = y z’i+ 2xyz³j+ 3xy z²k.
(a) Find the domain of F, and show that F is conservative.
(b) Find a formula for
(х, у,z)
F· dr
by parametrizing the line segment from (0, 0, 0) to (x, y, z) and evaluating the line integral of F along this line segment.
(c) Find the gradient vector field of the function f in part (a).
Transcribed Image Text:f(x, y, z) = L0 Let F(x, y, z) = y z’i+ 2xyz³j+ 3xy z²k. (a) Find the domain of F, and show that F is conservative. (b) Find a formula for (х, у,z) F· dr by parametrizing the line segment from (0, 0, 0) to (x, y, z) and evaluating the line integral of F along this line segment. (c) Find the gradient vector field of the function f in part (a).
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