Why does a two-dimensional vector field with zero divergence on a region have zero outward flux across a closed curve that bounds the region? Choose the correct answer below. O A. Since dx* dy = 0, PF. = 0 by the flux form of Green's Theorem. dg O B. Since = 0. PF•nds = 0 by the flux form of Green's Theorem. dy dg OC. Since of = 0. PF•dr= 0 by the flux form of Green's Theorem. O D. Since of dg = 0. PF•dr=0 by the flux form of Green's Theorem. dx' dy
Why does a two-dimensional vector field with zero divergence on a region have zero outward flux across a closed curve that bounds the region? Choose the correct answer below. O A. Since dx* dy = 0, PF. = 0 by the flux form of Green's Theorem. dg O B. Since = 0. PF•nds = 0 by the flux form of Green's Theorem. dy dg OC. Since of = 0. PF•dr= 0 by the flux form of Green's Theorem. O D. Since of dg = 0. PF•dr=0 by the flux form of Green's Theorem. dx' dy
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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![Why does a two-dimensional vector field with zero divergence on a region have zero outward flux across a closed curve that bounds the region?
Choose the correct answer below.
df dg
O A. Since
= 0, PF•nds = 0 by the flux form of Green's Theorem.
dy
B. Since
дх
dg df
= 0,
dy
'F•nds = 0 by the flux form of Green's Theorem.
dg
OC. Since
df
F•dr = 0 by the flux form of Green's Theorem.
--%3D
dx
ду
dg
= 0,
dx' dy
O D. Since
•dr = 0 by the flux form of Green's Theorem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9eb0d6a0-7b31-4c7c-a65e-3c9db0c9eac7%2Fe2913338-fb48-4d5d-9a3d-ecaa033b1033%2Flw9oks7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Why does a two-dimensional vector field with zero divergence on a region have zero outward flux across a closed curve that bounds the region?
Choose the correct answer below.
df dg
O A. Since
= 0, PF•nds = 0 by the flux form of Green's Theorem.
dy
B. Since
дх
dg df
= 0,
dy
'F•nds = 0 by the flux form of Green's Theorem.
dg
OC. Since
df
F•dr = 0 by the flux form of Green's Theorem.
--%3D
dx
ду
dg
= 0,
dx' dy
O D. Since
•dr = 0 by the flux form of Green's Theorem.
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