The discussion revolves around finding a level surface from a two-variable function, specifically f(x,y) = 9/(x+y). Participants explore the concept of level surfaces and curves, questioning the appropriate terminology and methods for representing the function in three dimensions.
The discussion is active, with participants providing insights on the nature of level curves versus level surfaces. Some guidance has been offered regarding the plotting of functions and the interpretation of level sets, but there remains a lack of consensus on the terminology and the correct approach to the problem.
Participants note that the original problem may not require a z variable, leading to discussions about the implications of this on the representation of the function. There is also mention of the need to clarify definitions and assumptions regarding level surfaces and curves.
Painguy said:Homework Statement
given f(x,y)=9/(x+y) find a level surface.
Homework Equations
The Attempt at a Solution
g(x,y,z)=f(x,y)-z=0?
g(x,y,z)=9/(x+y) -z=0?
That answer is wrong. Apparently i must have the following:
g(x,y,z)=z(x+y)=9
How do I solve problems like these?
Another example is to find a function f(x,y,z) whose level surface f=5 is the graph of the paraboloid
g(x,y)=-x^2 -y^2
LCKurtz said:You don't need any ##z## variable. To find level surface of a function ##f(x,y)## just plot the graphs of ##f(x,y)=C## for various constants ##C##. For a two variable problem like yours, they will be curves in the ##xy## plane, not surfaces.
Painguy said:Wouldn't that be generating level curves? I guess my terminology is bad. What i am asking is how do make f(x,y) into
F(x,y,z)