EBK CALCULUS
4th Edition
ISBN: 9781319055844
Author: FRANZOSA
Publisher: VST
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Question
Chapter 18.3, Problem 8E
To determine
The flux for the given function using divergence theorem.
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Use the flux form of Green's Theorem to evaluate|(6xy + 8y) dA, where R is the triangle with vertices (0,0), (1,0), and (0,1).
R
S[ 6xy + By') dA = [
R
(Simplify your lanswer.)
Evaluate the circulation of G = xyi + zj + 4yk around a square of side 4, centered at the
origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis.
Circulation =
Jo
F. dr
=
Use the Divergence Theorem to find the flux of
F(x, y, z)=z³ i-x³j+y³ k
across the sphere x² + y² + z² = a² with outward orientation.
$ = i
Chapter 18 Solutions
EBK CALCULUS
Ch. 18.1 - Prob. 1PQCh. 18.1 - Prob. 2PQCh. 18.1 - Prob. 3PQCh. 18.1 - Prob. 4PQCh. 18.1 - Prob. 5PQCh. 18.1 - Prob. 1ECh. 18.1 - Prob. 2ECh. 18.1 - Prob. 3ECh. 18.1 - Prob. 4ECh. 18.1 - Prob. 5E
Ch. 18.1 - Prob. 6ECh. 18.1 - Prob. 7ECh. 18.1 - Prob. 8ECh. 18.1 - Prob. 9ECh. 18.1 - Prob. 10ECh. 18.1 - Prob. 11ECh. 18.1 - Prob. 12ECh. 18.1 - Prob. 13ECh. 18.1 - Prob. 14ECh. 18.1 - Prob. 15ECh. 18.1 - Prob. 16ECh. 18.1 - Prob. 17ECh. 18.1 - Prob. 18ECh. 18.1 - Prob. 19ECh. 18.1 - Prob. 20ECh. 18.1 - Prob. 21ECh. 18.1 - Prob. 22ECh. 18.1 - Prob. 23ECh. 18.1 - Prob. 24ECh. 18.1 - Prob. 25ECh. 18.1 - Prob. 26ECh. 18.1 - Prob. 27ECh. 18.1 - Prob. 28ECh. 18.1 - Prob. 29ECh. 18.1 - Prob. 30ECh. 18.1 - Prob. 31ECh. 18.1 - Prob. 32ECh. 18.1 - Prob. 33ECh. 18.1 - Prob. 34ECh. 18.1 - Prob. 35ECh. 18.1 - Prob. 36ECh. 18.1 - Prob. 37ECh. 18.1 - Prob. 38ECh. 18.1 - Prob. 39ECh. 18.1 - Prob. 40ECh. 18.1 - Prob. 41ECh. 18.1 - Prob. 42ECh. 18.1 - Prob. 43ECh. 18.1 - Prob. 44ECh. 18.1 - Prob. 45ECh. 18.1 - Prob. 46ECh. 18.1 - Prob. 47ECh. 18.1 - Prob. 48ECh. 18.1 - Prob. 49ECh. 18.1 - Prob. 50ECh. 18.1 - Prob. 51ECh. 18.2 - Prob. 1PQCh. 18.2 - Prob. 2PQCh. 18.2 - Prob. 3PQCh. 18.2 - Prob. 4PQCh. 18.2 - Prob. 5PQCh. 18.2 - Prob. 1ECh. 18.2 - Prob. 2ECh. 18.2 - Prob. 3ECh. 18.2 - Prob. 4ECh. 18.2 - Prob. 5ECh. 18.2 - Prob. 6ECh. 18.2 - Prob. 7ECh. 18.2 - Prob. 8ECh. 18.2 - Prob. 9ECh. 18.2 - Prob. 10ECh. 18.2 - Prob. 11ECh. 18.2 - Prob. 12ECh. 18.2 - Prob. 13ECh. 18.2 - Prob. 14ECh. 18.2 - Prob. 15ECh. 18.2 - Prob. 16ECh. 18.2 - Prob. 17ECh. 18.2 - Prob. 18ECh. 18.2 - Prob. 19ECh. 18.2 - Prob. 20ECh. 18.2 - Prob. 21ECh. 18.2 - Prob. 22ECh. 18.2 - Prob. 23ECh. 18.2 - Prob. 24ECh. 18.2 - Prob. 25ECh. 18.2 - Prob. 26ECh. 18.2 - Prob. 27ECh. 18.2 - Prob. 28ECh. 18.2 - Prob. 29ECh. 18.2 - Prob. 30ECh. 18.2 - Prob. 31ECh. 18.2 - Prob. 32ECh. 18.2 - Prob. 33ECh. 18.2 - Prob. 34ECh. 18.2 - Prob. 35ECh. 18.2 - Prob. 36ECh. 18.2 - Prob. 37ECh. 18.2 - Prob. 38ECh. 18.3 - Prob. 1PQCh. 18.3 - Prob. 2PQCh. 18.3 - Prob. 3PQCh. 18.3 - Prob. 4PQCh. 18.3 - Prob. 5PQCh. 18.3 - Prob. 1ECh. 18.3 - Prob. 2ECh. 18.3 - Prob. 3ECh. 18.3 - Prob. 4ECh. 18.3 - Prob. 5ECh. 18.3 - Prob. 6ECh. 18.3 - Prob. 7ECh. 18.3 - Prob. 8ECh. 18.3 - Prob. 9ECh. 18.3 - Prob. 10ECh. 18.3 - Prob. 11ECh. 18.3 - Prob. 12ECh. 18.3 - Prob. 13ECh. 18.3 - Prob. 14ECh. 18.3 - Prob. 15ECh. 18.3 - Prob. 16ECh. 18.3 - Prob. 17ECh. 18.3 - Prob. 18ECh. 18.3 - Prob. 19ECh. 18.3 - Prob. 20ECh. 18.3 - Prob. 21ECh. 18.3 - Prob. 22ECh. 18.3 - Prob. 23ECh. 18.3 - Prob. 24ECh. 18.3 - Prob. 25ECh. 18.3 - Prob. 26ECh. 18.3 - Prob. 27ECh. 18.3 - Prob. 28ECh. 18.3 - Prob. 29ECh. 18.3 - Prob. 30ECh. 18.3 - Prob. 31ECh. 18.3 - Prob. 32ECh. 18.3 - Prob. 33ECh. 18.3 - Prob. 34ECh. 18.3 - Prob. 35ECh. 18.3 - Prob. 36ECh. 18.3 - Prob. 37ECh. 18.3 - Prob. 38ECh. 18.3 - Prob. 39ECh. 18.3 - Prob. 40ECh. 18.3 - Prob. 41ECh. 18.3 - Prob. 42ECh. 18.3 - Prob. 43ECh. 18.3 - Prob. 44ECh. 18 - Prob. 1CRECh. 18 - Prob. 2CRECh. 18 - Prob. 3CRECh. 18 - Prob. 4CRECh. 18 - Prob. 5CRECh. 18 - Prob. 6CRECh. 18 - Prob. 7CRECh. 18 - Prob. 8CRECh. 18 - Prob. 9CRECh. 18 - Prob. 10CRECh. 18 - Prob. 11CRECh. 18 - Prob. 12CRECh. 18 - Prob. 13CRECh. 18 - Prob. 14CRECh. 18 - Prob. 15CRECh. 18 - Prob. 16CRECh. 18 - Prob. 17CRECh. 18 - Prob. 18CRECh. 18 - Prob. 19CRECh. 18 - Prob. 20CRECh. 18 - Prob. 21CRECh. 18 - Prob. 22CRECh. 18 - Prob. 23CRECh. 18 - Prob. 24CRECh. 18 - Prob. 25CRECh. 18 - Prob. 26CRECh. 18 - Prob. 27CRECh. 18 - Prob. 28CRECh. 18 - Prob. 29CRECh. 18 - Prob. 30CRECh. 18 - Prob. 31CRECh. 18 - Prob. 32CRECh. 18 - Prob. 33CRECh. 18 - Prob. 34CRECh. 18 - Prob. 35CRECh. 18 - Prob. 36CRECh. 18 - Prob. 37CRECh. 18 - Prob. 38CRECh. 18 - Prob. 39CRECh. 18 - Prob. 40CRECh. 18 - Prob. 41CRE
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- Let F = = (x, y, z) (x² + y² + z²)3/2 Use the fact that V F = 0 when (x, y, z) following surfaces. (0,0,0) to find the flux of F through the The square with corners (1, 1, 1), (1, −1, 1), (−1, 1, 1), and (-1, -1, 1), oriented upward. Hint: Use the fact that this is a face of a cube centered at the origin.arrow_forwardEvaluate the circulation of G = xyi+zj+7yk around a square of side 9, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. Circulation = Prevs So F.dr-arrow_forward
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