= (x + y², x² - y); R = {(x, y): y² ≤ x ≤ 2 - y²}. 47. F =

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 60E
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number 47 only please part a and b

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41-48. Circulation and flux For the following vector fields, compute (a)
the circulation on, and (b) the outward flux across, the boundary of the
given region. Assume boundary curves are oriented counterclockwise.
F= (x. v): R is the half-annulus {(r, 0); 1 ≤r≤ 2,
00 S
46.
((r, 0)
3,0
0): 1 ≤ r ≤ 3,
qr-annulus
π/2}.
is the pe
ogra
< 1}.
Rinalflus
..2) tan
{(r, 0): 1 ≤ r ≤ 2,0 ≤ 0 ≤ π/4}.
47. F = (x + y², x² - y); R = {(x, y): y² ≤ x ≤ 2 - y²}.
n-annulus
Transcribed Image Text:41-48. Circulation and flux For the following vector fields, compute (a) the circulation on, and (b) the outward flux across, the boundary of the given region. Assume boundary curves are oriented counterclockwise. F= (x. v): R is the half-annulus {(r, 0); 1 ≤r≤ 2, 00 S 46. ((r, 0) 3,0 0): 1 ≤ r ≤ 3, qr-annulus π/2}. is the pe ogra < 1}. Rinalflus ..2) tan {(r, 0): 1 ≤ r ≤ 2,0 ≤ 0 ≤ π/4}. 47. F = (x + y², x² - y); R = {(x, y): y² ≤ x ≤ 2 - y²}. n-annulus
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