- #1

- 297

- 6

## Homework Statement

I know that the equation ##z = f(x,y)## gives a surface while ##w = f(x, y, z) ## gives an object that has the same surface shape on top as ##z = f(x,y)## but also includes everything below it. If these statements are correct, what is the level surface of a function of three variables like ##F(x,y,z) = k ##

## Homework Equations

Tangent line for ## z = f(z, y) ## = ##z-z_0 = f_x##

## The Attempt at a Solution

To me, it seems like the level surface of a function of three variables is only a number line. Does this also apply to the level surface of a function of two variables? What about of one variable? Is a level surface the higher dimensional analogy of a level curve, which in itself is a graph of a level set? Finally how are topographical maps related?

Thank you all so much. All of the "level" stuff in calculus is so confusing. What's worse is that because of them, there isn't one single formula for finding a tangent plane....