- #1
M.Qayyum
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Homework Statement
Homework Equations
f(x,y,z,)=(x-2)2+y2+z2
What Are the Level Surfaces of the Function f(x,y,z) = (x-2)² + y² + z²?
- Thread starter M.Qayyum
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Homework Help Overview
The discussion revolves around identifying the level surfaces of the function f(x,y,z) = (x-2)² + y² + z². Participants are exploring the implications of setting the function equal to a constant and what that means for the geometry of the surfaces described by the function.
Discussion Character
- Exploratory, Conceptual clarification
Approaches and Questions Raised
- Some participants suggest that the level surfaces may resemble spheres, prompting questions about how to formally describe these surfaces. Others express confusion regarding the problem statement and seek clarification on how to approach the question of level surfaces.
Discussion Status
Participants are actively engaging with the problem, with some offering hints and guidance on how to interpret the function in terms of level surfaces. There is a recognition of the need for a clearer problem statement, as some participants question the ambiguity of the original inquiry.
Contextual Notes
There is an acknowledgment that the original poster is new to calculus, which may influence their understanding of the concepts being discussed. Additionally, some participants note the importance of defining the problem more clearly to facilitate better assistance.
f(x,y,z,)=(x-2)2+y2+z2
- #2
tiny-tim
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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?
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?
- #3
M.Qayyum
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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)
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)
- #4
MechanicalMan
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M.Qayyum said:
What is the problem statement? You can't be just given an equation and asked to solve it. Your question is too ambiguous.
- #5
HallsofIvy
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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.
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.
- #6
M.Qayyum
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HallsofIvy said:
Thanks for your help,that's what i was looking for...
(New to Calculus-Sorry For my Bad English)
- #7
HallsofIvy
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Your English is very good- in fact, excellent compared to my (put pretty much any language here)!
- #8
M.Qayyum
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it's 7 A.M in Pakistan...(Sorry for my Timing as well...ha ha ha)
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