
Profile Curve
This is translated from my own language, so feel free to correct me if I'm using a wrong translation.
A profile curve in (x, z)plan is given by the graph of the function z = ln (x), where
x $\displaystyle \epsilon$ [1, 2]. The profile curve is rotated the angle $\displaystyle Pi$ around zaxis counterclockwise as seen from the zaxis'
positive end. This yields the rotation surface F.
Find a parametrization for the profile curve and F.

$\displaystyle
F=ln(\sqrt{x^2+y^2})
$
In cylindrical coordinates
$\displaystyle
F=ln \ r \ .
$

Still need to find r(u,v) any help here? (Thinking)

If this helps:
$\displaystyle
u=x
$
$\displaystyle
v=y
$
$\displaystyle
F=ln \sqrt{u^2+v^2}
$
where
$\displaystyle
v>=0 \ and \ 1<=\sqrt{u^2+v^2}<=2 \ .
$

I think I'm being misunderstood.
I need to find the parametrization/parametric equation for the profile curve and F.
I was given this general equation:
$\displaystyle r(u,v)=(x(u,v),y(u,v)$