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(a) Consider the vector field G = (xyz, yz, xz). Find div(G). (b) (1,2,3). Using the G from part (a), find So Let C be the straight line segment from (0,0,0) to (1,2,3), oriented towards G.dr. (c). Suppose F (f₁, f2) is a conservative vector field defined on all of the xy- plane, and f₁ and f2 are continuously differentiable. Suppose g(x) is a continuously differ- entiable function. Why is (f₁ + g(x), f2) conservative? =

(a) Consider the vector field G = (xyz, yz, xz). Find div(G). (b) (1,2,3). Using the G from part (a), find So Let C be the straight line segment from (0,0,0) to (1,2,3), oriented towards G.dr. (c). Suppose F (f₁, f2) is a conservative vector field defined on all of the xy- plane, and f₁ and f2 are continuously differentiable. Suppose g(x) is a continuously differ- entiable function. Why is (f₁ + g(x), f2) conservative? =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 5. (a) Consider the vector field G = (xyz, yz, xz). Find div(G). (b) Let C be the straight line segment from (0,0,0) to (1,2,3), oriented towards (1,2,3). Using the G from part (a), find G.dr. (c). Suppose F = (f₁, f2) is a conservative vector field defined on all of the xy- plane, and f₁ and f₂ are continuously differentiable. Suppose g(x) is a continuously differ- entiable function. Why is (f₁ + g(x), f₂) conservative?
Transcribed Image Text:Question 5. (a) Consider the vector field G = (xyz, yz, xz). Find div(G). (b) Let C be the straight line segment from (0,0,0) to (1,2,3), oriented towards (1,2,3). Using the G from part (a), find G.dr. (c). Suppose F = (f₁, f2) is a conservative vector field defined on all of the xy- plane, and f₁ and f₂ are continuously differentiable. Suppose g(x) is a continuously differ- entiable function. Why is (f₁ + g(x), f₂) conservative?
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