Need help with graph and level set equation, please!!!!

Question

anonymous · Answer

Can You post the questions or a graph question?
:)

anonymous · Answer

Yes!! Consider the surface in R3 determined by the equation z sin(x + y) + x^2- 3xy + 2z = 7: Find a function g(x, y, z) such that this surface is a level set of g and ﬁnd a function f(x, y) such that this surface is the graph of f. Help please! Consider the surface in R3 determined by the equation z sin(x + y) + x^2- 3xy + 2z = 7: Find a function g(x, y, z) such that this surface is a level set of g and ﬁnd a function f(x, y) such that this surface is the graph of f.

anonymous · Answer

Yes .. i believe so..  not sure how to go about solving it though.

anonymous · Answer

no, not graph it! just Find a function g(x, y, z) such that this surface is a level set of g and ﬁnd a function f(x, y) such that this surface is the graph of f.

anonymous · Answer

im not sure

anonymous · Answer

you will get f(x,y) by made z as a constatnt

anonymous · Answer

how we cut the curve and all variables are there?

anonymous · Answer

@amistre64

amistre64 · Answer

Consider the surface in R3 determined by the equation 
               z sin(x + y) + x^2- 3xy + 2z = 7: 

Find a function g(x, y, z) such that 
        this surface is a level set of g and 

ﬁnd a function f(x, y) such that 
       this surface is the graph of f. 


f(x,y) = z is the right idea for the last part

amistre64 · Answer

.... just got an awsnap page :/

amistre64 · Answer

move nonZs to other side, factor out a z from whats left over, and divide off the extra.

amistre64 · Answer

f(x,y) is http://web.monroecc.edu/manila/webfiles/calcNSF/JavaCode/CalcPlot3D.htm

amistre64 · Answer

attachment

amistre64 · Answer

can you refresh my memory on what a level set is?

anonymous · Answer

i think not sure it's when we made z a constant

amistre64 · Answer

a slice of the graph level across the z axis ... perchance

anonymous · Answer

example x²+y²+z²=9 
if we made z a constant we will get a circle x²+y²=9-c

anonymous · Answer

we cut the sphere so we will get a circle

amistre64 · Answer

are those level curves? or level sets?

anonymous · Answer

a level set of a real-valued function f of n variables is a set of the form

that is, a set where the function takes on a given constant value c.

anonymous · Answer

so how can we make one variale constant and a have a function of three variables?

amistre64 · Answer

i dont think i have enough experience to determine the level set part

amistre64 · Answer

i would be inclined to thing that f(x,y) = z defines the level set .... but i cant be sure im reading the materials corretly

anonymous · Answer

hmm ok .. thank you