We say that a vector field F is conservative on a domain D if it is defined on D and there is a scalar function o defined on D such that F = Vo on D. In the lecture, we have seen that the vector field F(x, y) = -y 12 +y?' x2 + 32 is not conservative on the domain R2 \\ {(0, 0) }. In this exercise, we will show that F is conservative on a smaller domain. (a) Find the domain D of the function (x, y) = arctan(y/x). (b) Shows that F is conservative on D (Hint: Compute Vy(x, y)). (c) Is D open? Is D connected? Give reasons for your