Let $C$ be a simple closed curve in the $xy-$plane, and let $R$ be the region bounded by $C.$ Denote by $n$ the outward pointing unit normal vector of $C.$ Assume that the point $(2,2)$ is in the interior of $R.$ Consider the function $=ln((x-2{)}^2(y-2{)}^2)$ on $\frac{R^2}{\frac{?}{?}}\{(2,2)\},$ and let $F=$grad$.$

a$)$ Calculate grad$*F$ on $\frac{R^2}{\frac{?}{?}}\{(2,2)\}.$

b$)$ Calculate $o{\displaystyle \underset{C^{\text{'}}}{\overset{\phantom{}}{}}}F*n^{\text{'}}ds,$ where $C^{\text{'}}$ is the circle of a small radius $lon$ centred at $(2,2)$ orientated anti$-$clockwise, and $n^{\text{'}}$ is its outward pointing unit normal vector.

c$)$ Calculate $o{\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*nds.$ You need to justify all steps of your calculation.