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conservative force field F = (P(x, y), Q(x, y)). Let (x, y) be any point in the plane. We create a function, f(x, y) = F· dr, where the curve C consists of a vertical line segment from (1, 1) to the point (1, y), and then a horizontal line segment from (1, y) to (x, y). Then, P of by applying the fundamental theorem of calculus. af = ?x Show that Q= af მყ Hint: You must use the hypothesis that ♬ has the property of path-independence.

conservative force field F = (P(x, y), Q(x, y)). Let (x, y) be any point in the plane. We create a function, f(x, y) = F· dr, where the curve C consists of a vertical line segment from (1, 1) to the point (1, y), and then a horizontal line segment from (1, y) to (x, y). Then, P of by applying the fundamental theorem of calculus. af = ?x Show that Q= af მყ Hint: You must use the hypothesis that ♬ has the property of path-independence.

Algebra & Trigonometry with Analytic Geometry
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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conservative force field F = (P(x, y), Q(x, y)). Let (x, y) be any point in the plane. We create a function, f(x, y) = F· dr, where the curve C consists of a vertical line segment from (1, 1) to the point (1, y), and then a horizontal line segment from (1, y) to (x, y). Then, P of by applying the fundamental theorem of calculus. af = ?x Show that Q= af მყ Hint: You must use the hypothesis that ♬ has the property of path-independence.
Transcribed Image Text:conservative force field F = (P(x, y), Q(x, y)). Let (x, y) be any point in the plane. We create a function, f(x, y) = F· dr, where the curve C consists of a vertical line segment from (1, 1) to the point (1, y), and then a horizontal line segment from (1, y) to (x, y). Then, P of by applying the fundamental theorem of calculus. af = ?x Show that Q= af მყ Hint: You must use the hypothesis that ♬ has the property of path-independence.
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