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

1 Answer
Feb 23, 2015

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 :

enter image source here

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

enter image source here