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categoryرياضيات
schoolبكالوريوس
event_available2026-07-13
السؤال
Transcribed Image Text:
12.
-/4 points SCalc7 16.3.029.
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.
др aQ др
ду
дх Jz
aR
дх
до
Jz
aR
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, fz.)
P =
Q
R
My Notes
Since P, Q, and R have continuous first order partial derivatives, ---Select---
▾ says that ap/ay = fxy = fyx = aQ/ax, ap/dz = fxz = fzx=
=
OR/ax, and aQ/dz = fyz = fzy
=
aR/ay.
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