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. ∂p ∂y = ∂q ∂x ∂p ∂z = ∂r ∂x ∂q ∂z = ∂r ∂y . since f is conservative, there exists a function f such that f = ∇f, that is, p, q, and r are defined as follows. (enter your answers in the form fx, fy, fz.) p = q = r = since p, q, and r have continuous first order partial derivatives, says that ∂p/∂y = fxy = fyx = ∂q/∂x, ∂p/∂z = fxz = fzx = ∂r/∂x, and ∂q/∂z = fyz = fzy = ∂r/∂y.

may i see the picture? it would a lot, xox

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

yes

step-by-step explanation:

yes