3(b). FF as defined above, a misguided professor claims that for any losed curve C, F. dr = 0 because of the argument: f F-dr = f( (▼ × F) ds = [], div (curl F) dV = [₁ 0dV = 0, by using Stokes' theorem, the divergence theorem, and then part (a), for an appropriately chosen surface S and volume W. Carefully explain all the errors in this argument.
3(b). FF as defined above, a misguided professor claims that for any losed curve C, F. dr = 0 because of the argument: f F-dr = f( (▼ × F) ds = [], div (curl F) dV = [₁ 0dV = 0, by using Stokes' theorem, the divergence theorem, and then part (a), for an appropriately chosen surface S and volume W. Carefully explain all the errors in this argument.
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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![Let F: R³ R³ be any C² vector field.
3(a). Prove that the divergence of the curl of F is zero.
3(b). F F as defined above, a misguided professor claims that for any
Mosed curve C, fF.dr = 0 because of the argument:
$o
F-dr
- 11.S
( ( ▼ × F)-dS = [], div (curl F) dV = [] oav = 0,
by using Stokes theorem, the divergence theorem, and then part (a),
for an appropriately chosen surface S and volume W. Carefully explain
all the errors in this argument.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34b405ee-de8e-44e4-9e9f-2a9724b6da82%2Fdd62647e-d85d-4fb0-a05f-26fd45072a99%2Fbe3etbi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let F: R³ R³ be any C² vector field.
3(a). Prove that the divergence of the curl of F is zero.
3(b). F F as defined above, a misguided professor claims that for any
Mosed curve C, fF.dr = 0 because of the argument:
$o
F-dr
- 11.S
( ( ▼ × F)-dS = [], div (curl F) dV = [] oav = 0,
by using Stokes theorem, the divergence theorem, and then part (a),
for an appropriately chosen surface S and volume W. Carefully explain
all the errors in this argument.
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