If f is a function of two variables, we define the graph of (r, y) in...

  

Transcribed Image Text:

If f is a function of two variables, we define the graph of (r, y) in ryz-space f(r, y). In general, such a graph will be a surface in to be the graph of the equation z = 3-space. E Xample: f x ,y) = Jx² +y?-I %3D 2. ス と=2 ス=Jy? +y? -1 ース=S3 *スン。 53 2; スミ x+ y2 -1 (Hyperboloid of 1-sheet) ス=o→*+y - | ス=o ス=3 → x*+y2= 4 Ccirele r=2) Example: f( X,y) = x² + y? r=1 a = x? +y? (paraboloid) 1 え= x Z =0 pointlo,o, 0) え =| + x² + y² = 1 %3D 1 Question. f(Xッり)%=Jx?+ y2 1. 2. 2. If f is a function of two variables, we define the graph of (r, y) in ryz-space f(r, y). In general, such a graph will be a surface in to be the graph of the equation z = 3-space. E Xample: f x ,y) = Jx² +y?-I %3D 2. ス と=2 ス=Jy? +y? -1 ース=S3 *スン。 53 2; スミ x+ y2 -1 (Hyperboloid of 1-sheet) ス=o→*+y - | ス=o ス=3 → x*+y2= 4 Ccirele r=2) Example: f( X,y) = x² + y? r=1 a = x? +y? (paraboloid) 1 え= x Z =0 pointlo,o, 0) え =| + x² + y² = 1 %3D 1 Question. f(Xッり)%=Jx?+ y2 1. 2. 2.