Question

How do you sketch `f(x,y) = ln(x^2+y^2)`?

Answer 1

Hello,

Let `mathcal(S)` the surface of equation `z = ln(x^2+y^2)` : it's the graph of your function `f`.

Remark that `mathcal(S)` is a revolution surface, because
`f(x,y) = g(r)`
where `r = sqrt(x^2+y^2)` is the polar radius. Actually, `g(r) = ln(r^2) = 2 ln(r)`.

So, graph the curve of equation `z = 2ln(x)` in the `xOz` plane. You get :

Finally, rotate this curve around the `Oz` axis. You get `mathcal(S)` :