Determine whether or not the vector field is conservative. if it is, find a function f such that f = ∇f. if the vector field is not conservative, enter none. f(x, y, z) = 5y2z3 i + 10xyz3 j + 15xy2z2 k f(x, y, z) = + k

is conservative if we can find a scalar function such that . This would require

Integrate both sides of the first PDE with respect to :

(*)

Differentiate both sides of (*) with respect to :

Differentiate both sides of (*) with respect to :

So we have

and so is indeed conservative.

fwms@lil_ben06

step-by-step explanation: