The discussion centers on generating level surfaces from a two-variable function, specifically f(x,y) = 9/(x+y). The correct formulation for the level surface is g(x,y,z) = z(x+y) = 9, which indicates that z is dependent on x and y. Participants clarify that for two-variable functions, the appropriate approach is to plot level curves rather than surfaces, as level curves represent the function's behavior in the xy-plane. The transition from f(x,y) to F(x,y,z) involves creating a 3D plot where z = f(x,y).
PREREQUISITESStudents and educators in mathematics, particularly those studying multivariable calculus, as well as anyone interested in visualizing functions of two variables and their corresponding level 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)