Q$5($a$)($i$)$ Sketch the region in the first quadrant that is bounded by $x=4,x=y^2$ and the $x-$axis

$($ii$)$ Find the area of that region

$($b$)$ Find the values of constants $a,b,c$ and $d$ so that the function $f(z)=(2c{x}^2+a{y}^2-2xy)+j(b{x}^2-d{y}^2+2xy)$ is differentiable everywhere.

$($c$)$ Use the Root Test to determine if the series ${\displaystyle \underset{n=1}{\overset{}{}}}[ln(\frac{n^2+1}{3}){]}^n$ converges absolutely or diverges.