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Show that if the vector field F = Pi + Qj + Rk is conservative and P, Q, R have continuous first-order partial derivatives, then the following is true. ӘР aq ӘР ƏR aq aR %3D %3D ay ax az ax az ay Since F is conservative, there exists a function f such that F = Vf, that is, P, Q, and R are defined as follows. (Enter your answers in the form fy, fy, fz;) P = Q = R = Since P, Q, and R have continuous first order partial derivatives, -Select--- says that

Show that if the vector field F = Pi + Qj + Rk is conservative and P, Q, R have continuous first-order partial derivatives, then the following is true. ӘР aq ӘР ƏR aq aR %3D %3D ay ax az ax az ay Since F is conservative, there exists a function f such that F = Vf, that is, P, Q, and R are defined as follows. (Enter your answers in the form fy, fy, fz;) P = Q = R = Since P, Q, and R have continuous first order partial derivatives, -Select--- says that

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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-.........-.... ................ ........................................ ......... Let F = Vf, where f(x, y) = sin(x - 3y). Find curves C, and C, that are not closed and satisfy the equation. (a) F. dr = 0 C,: r(t) = 0 sts1 (b) F dr = 1 C2: r(t) = , Ostsi
Transcribed Image Text:-.........-.... ................ ........................................ ......... Let F = Vf, where f(x, y) = sin(x - 3y). Find curves C, and C, that are not closed and satisfy the equation. (a) F. dr = 0 C,: r(t) = 0 sts1 (b) F dr = 1 C2: r(t) = , Ostsi
Show that if the vector field F = Pi + Qj + Rk is conservative and P, Q, R have continuous first-order partial derivatives, then the following is true. ӘР aQ ƏR aQ ƏR %3D ду Əx az ax az ду Since F is conservative, there exists a function f such that F = Vf, that is, P, Q, and R are defined as follows. (Enter your answers in the form fy, fy, fz;) P = Q = R = Since P, Q, and R have continuous first order partial derivatives, ---Select--- Əp/ay = fyy = fx = aQ/əx, Əp/əz = f, = fx = ƏR/əx, and aQ/əz = fy, = fzy = ƏR/əy. V says that
Transcribed Image Text:Show that if the vector field F = Pi + Qj + Rk is conservative and P, Q, R have continuous first-order partial derivatives, then the following is true. ӘР aQ ƏR aQ ƏR %3D ду Əx az ax az ду Since F is conservative, there exists a function f such that F = Vf, that is, P, Q, and R are defined as follows. (Enter your answers in the form fy, fy, fz;) P = Q = R = Since P, Q, and R have continuous first order partial derivatives, ---Select--- Əp/ay = fyy = fx = aQ/əx, Əp/əz = f, = fx = ƏR/əx, and aQ/əz = fy, = fzy = ƏR/əy. V says that
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