No 5 and 6 please show all procedures
we ignore the domain D for a he circulation/fux integrals, by first transforming to double light of the hypotheses of Green's theorem. ute, what would this version of Green's theorem tell us about all foar o would this integrals? Explain why this is not an e in 6. Now let D be any simply connected domain containing (0.0), whose boundary aD satisfn of Green's theorem. Let CR be a circle of radius R, where R is large atiaties the bypothes considering the domain betueen Cr and OD, and the correct orientation on these for Grea's enough that D is inside CR By orientation on these for Gren's theorem, show 8D Using the instantaneous circulation/Aux way of thinking from above, we can say â½Vi truly conservative even at (0,0) the instantaneous circulation is 0. However, it is not truly divergence free: (0,0) is a point soure r flux. Similarly, â½U is strictly conservative on the plane without (0,0), because it has instanta circulation at (0, 0). It is however truly divergence free in the whole plane. A very deep theorem of mathematics, perhaps the first result less than 100 years old you have encountered in Calculus, says that in some sense â½U is the only vector field with this property. We will discuss this more in class if we have time.