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. ƏR ax ӘР aQ ax az ӘР aQ az %3D %3D ду 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, f7.) P = Q = Izy R = --Select--- Since P, Q, and R have continuous first order partial derivatives, apiaz = f.- = f.. = aR/ax. and ao/az = f.-= f.. = aR/ay. says that ƏP/ây = fxy = fyx = ôqjəx,

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. ƏR ax ӘР aQ ax az ӘР aQ az %3D %3D ду 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, f7.) P = Q = Izy R = --Select--- Since P, Q, and R have continuous first order partial derivatives, apiaz = f.- = f.. = aR/ax. and ao/az = f.-= f.. = aR/ay. says that ƏP/ây = fxy = fyx = ôqjəx,

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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below math question

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
ƏR
=
=
ду
ax
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 fx, fy, f,.)
P =
fr
ху
Q = Jzy
f,
R =
says that aP/ay = fxy = fyx = aQ/əx,
Since P, Q, and R have continuous first order partial derivatives,
ƏP/az = fxz = fzx = ƏR/Əx, and aQ/əz = fyz = fzy = ƏR/ay.
---
--Select---
ZX

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