1. 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 x2 +y2 2 2 + 12' 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 4(x, y) = arctan(y/x). (b) Shows that F is conservative on D (Hint: Compute Ve(x, y)). (c) Is D open? Is D connected? Give reasons for your