Describe geometrically the level surfaces of the functions

[matt_crouch]

So the question is as titled

i) f=(x^2 +y^2 +z^2) ^1/2

if I can figure out the method I can solve the other equations but I'm not really sure where to start I know that a function f(x,y,z) of a level surface well be constant so do I just find del f ?

 

[HallsofIvy]

So the question is as titled

i) f=(x^2 +y^2 +z^2) ^1/2

if I can figure out the method I can solve the other equations but I'm not really sure where to start I know that a function f(x,y,z) of a level surface well be constant so do I just find del f ?

No, this has nothing to do with the gradient. A "level surface" for any function f(x,y,z) is, as you say, the set of points (x, y, z) where f(x, y, z)= C, a constant.

Here, that gives (x^2+ y^2+ z^2)^{1/2}= C. What do you get if you square both sides?

 

[matt_crouch]

so you just square both sides so id get

x²+y²+z²= C²

where C² is just another constant

is that right?