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. ap aQ ap aR aQ aR 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 terms of fx, f, and fz.) P E Q R = ys that . ay = fxy = fyx = aQ op = fg = fzx = aR aR ax' az ax az -, and = fvz = fzy = ay Since P, Q, and R have continuous first-order partial derivatives v ---Select--- the fundamental theorem of calculus Clairaut's theorem Need Help? Read It Watch It the net change theorem Green's theorem