Question

@rational

Answer 1

Determine whether or not the vector field is conservative. If it is conservative, find a function f such that \[F = \nabla f\]

Answer 2

\[F(x,y,z) = e^xsin yz i+ze^xcosyz j+ye^x \cos yz\] ok so I used the determinant for curl and found that it = 0. Now I need to find a function f, which is what I'm trying to figure out

Answer 3

I'm thinking of using fundamental theorem of line integrals

Answer 4

Since it reminds me of \[\frac{ \partial P }{ \partial y } = \frac{ \partial Q }{ \partial x }\] kind of stuff

Answer 5

No need. we can eyeball the potential function

Answer 6

Interesting

Answer 7

try this potential function
\[e^x\sin(yz)\]

Answer 8

The problem was deliberately cooked up to eyeball

Answer 9

For practice you may setup a simple line integral and work the potential function

Answer 10

Yeah I think I may do that, but what you said does work