Let $S$ be the surface parametrized by

$G(u,v)=(2$usin$(\frac{v}{2}),2$ucos$(\frac{v}{2}),3v)$

for $0u1$ and $0v2.$

$($a$)$ Calculate the tangent vectors $T_u$ and $T_v$ and the normal vector $N(u,v)$ at $P=G(1,\frac{}{3}).$

$($b$)$ Find the equation of the tangent plane at $P.$

$($c$)$ Compute the surface area of $S.$Just option C ONLY