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12. Let F(x, y) = esinx+cosy(cos x ,– sin y) and C = {(x, y): x² + y² < b} where b > 0. Show that F- dR = 0 Hint: Note that C is closed. Consider ø(x, y) = e$sin x+cos y. What is the relationship between o and F?

12. Let F(x, y) = esinx+cosy(cos x ,– sin y) and C = {(x, y): x² + y² < b} where b > 0. Show that F- dR = 0 Hint: Note that C is closed. Consider ø(x, y) = e$sin x+cos y. What is the relationship between o and F?

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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12. Let F (x, y) = esinx+cosy (cos x,- sin y) and C {(x, y): x² + y² < b} where b > 0. Show that F. dR = 0 Hint: Note that C is closed. Consider p(x, y) = e sin x+cos y, What is the relationship between o and F?
Transcribed Image Text:12. Let F (x, y) = esinx+cosy (cos x,- sin y) and C {(x, y): x² + y² < b} where b > 0. Show that F. dR = 0 Hint: Note that C is closed. Consider p(x, y) = e sin x+cos y, What is the relationship between o and F?
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