((V x F)(x)) u = 1 lim r-0 Tr2 F. ds, he circle of radius r in R3 centered at x lying in the plane perpendicular to u. + MVT]

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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Let F be a C1-vector field on R3 and u E R³ be a unit vector. Prove that for every
x E R³,
1
lim
r→0 Tr2
((V x F)(x)) · u =
F. ds,
where C, is the circle of radius r in R3 centered at x lying in the plane perpendicular to u.
[Hint: Stokes + MVT]
Transcribed Image Text:Let F be a C1-vector field on R3 and u E R³ be a unit vector. Prove that for every x E R³, 1 lim r→0 Tr2 ((V x F)(x)) · u = F. ds, where C, is the circle of radius r in R3 centered at x lying in the plane perpendicular to u. [Hint: Stokes + MVT]
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