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Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and curve C. = (4x + ex sin y)i + (5x + ex cos y sy)j C: The right-hand loop of the lemniscate r² = cos 20 Describe the given region using polar coordinates. Choose 0-values between - and . <0< ≤rs √cos (20) (Type exact answers.) The outward flux is. (Type an integer or a simplified fraction.) The counterclockwise circulation is (Type an integer or a simplified fraction.)

Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and curve C. = (4x + ex sin y)i + (5x + ex cos y sy)j C: The right-hand loop of the lemniscate r² = cos 20 Describe the given region using polar coordinates. Choose 0-values between - and . <0< ≤rs √cos (20) (Type exact answers.) The outward flux is. (Type an integer or a simplified fraction.) The counterclockwise circulation is (Type an integer or a simplified fraction.)

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
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Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and curve C. F= (4x + ex siny)i + (5x + ex cos y sy)j C: The right-hand loop of the lemniscate r² = cos 20 Describe the given region using polar coordinates. Choose 0-values between - and . <0< ≤r≤√cos (20) (Type exact answers.) The outward flux is. (Type an integer or a simplified fraction.) The counterclockwise circulation is. (Type an integer or a simplified fraction.)
Transcribed Image Text:Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and curve C. F= (4x + ex siny)i + (5x + ex cos y sy)j C: The right-hand loop of the lemniscate r² = cos 20 Describe the given region using polar coordinates. Choose 0-values between - and . <0< ≤r≤√cos (20) (Type exact answers.) The outward flux is. (Type an integer or a simplified fraction.) The counterclockwise circulation is. (Type an integer or a simplified fraction.)
Verify the conclusion of Green's Theorem by evaluating both sides of each of the two forms of Green's Theorem for the field F = -3yi + 3xj. Take the domains of integration in each case to be the disk R: x² + y² ≤a² and its bounding circle C: r = (a cos t)i + (a sin t)j, 0≤t≤ 2π. Click the icon to view the two forms of Green's Theorem. The flux is (Type an exact answer, using as needed.) The circulation is. (Type an exact answer, using as needed.)
Transcribed Image Text:Verify the conclusion of Green's Theorem by evaluating both sides of each of the two forms of Green's Theorem for the field F = -3yi + 3xj. Take the domains of integration in each case to be the disk R: x² + y² ≤a² and its bounding circle C: r = (a cos t)i + (a sin t)j, 0≤t≤ 2π. Click the icon to view the two forms of Green's Theorem. The flux is (Type an exact answer, using as needed.) The circulation is. (Type an exact answer, using as needed.)
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ISBN:
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