Exploring Level Surfaces of a Multivariable Function

[M.Qayyum]

Homework Statement

Homework Equations

f(x,y,z,)=(x-2)²+y²+z²

The Attempt at a Solution

 

[tiny-tim]

Welcome to PF!

Hi M.Qayyum! Welcome to PF!

I assume you want the surfaces with f(x,y,z) = constant?

Hint: that looks pretty much like a sphere, doesn't it?

 

[M.Qayyum]

First of all thanks for welcome...
and thanks for your time...But i want to know, how to solve these questions, please explain little more.
(New to Calculus-Sorry for my Bad English)

 

[MechanicalMan]

First of all thanks for welcome...
and thanks for your time...But i want to know, how to solve these questions, please explain little more.
(New to Calculus-Sorry for my Bad English)

What is the problem statement? You can't be just given an equation and asked to solve it. Your question is too ambiguous.

 

[HallsofIvy]

In order to solve a problem, you have to have a problem! So far, you just have function! What is the problem? If it is "describe the level surfaces" of a given function, set the function equal to a constant and try to determine what the graph of that equation looks like.

f(x,y,z)= c is one equation in three variables, x, y, and z. Given values for two of those, you could (theoretically) solve for the third. So the figure is a two dimensional figure- a surface. The term "level surface" comes from the lower dimensional case: the graph of z= f(x,y) is itself a surface. If we look at f(x,y)= c, we get a one-dimensional graph, the "level curve" since every point is at the "z= c" level of the original graph.

 

[M.Qayyum]

In order to solve a problem, you have to have a problem! So far, you just have function! What is the problem? If it is "describe the level surfaces" of a given function, set the function equal to a constant and try to determine what the graph of that equation looks like.

f(x,y,z)= c is one equation in three variables, x, y, and z. Given values for two of those, you could (theoretically) solve for the third. So the figure is a two dimensional figure- a surface. The term "level surface" comes from the lower dimensional case: the graph of z= f(x,y) is itself a surface. If we look at f(x,y)= c, we get a one-dimensional graph, the "level curve" since every point is at the "z= c" level of the original graph.

Thanks for your help,that's what i was looking for...
(New to Calculus-Sorry For my Bad English)

 

[HallsofIvy]

Your English is very good- in fact, excellent compared to my (put pretty much any language here)!

 

[M.Qayyum]

it's 7 A.M in Pakistan...(Sorry for my Timing as well...ha ha ha)