1) Given that z^3-xz-y=0, determine d^2f/dxdy
2) Given that u^2-v=3x+y and u-2v^2=x-2y, determine du/dx, dv/dx,
du/dy, and dv/dy
3) Given that u=f(x,y) and v=g(x,y), prove that there exists a
functional relationship between u and v in the form (u,v) = 0 if and
only if the Jacobian d(u,v)/d(x,y) is identically zero.

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Request for Question Clarification by livioflores-ga on 07 Dec 2002 21:13 PST

In the part 1), you may be wnt to know d^2z/dxdy

Thank you

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Clarification of Question by roadapples-ga on 07 Dec 2002 21:17 PST

Thats what I thought too. As far as I know it is d^2f, not d^2z. Can
this be solved differentiating it by making it (d/dx)(df/dy) with just
keeping the z's constant throughout? If you cant figure this part out,
it would be appreciated if I could get the other 2 solved with part 1
being solved as d^2z. But please try for d^2f. Thanks for you work!

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Request for Question Clarification by livioflores-ga on 07 Dec 2002 21:26 PST

It is very difficult to solve part one using f without knowing who is
f. We need a definition of function f, the equation defines a function
z(x,y).

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Clarification of Question by roadapples-ga on 07 Dec 2002 21:29 PST

Thats fine then. If you could solve it with d^2z along with the others
that would be great! Thanks again!

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Request for Question Clarification by livioflores-ga on 07 Dec 2002 21:47 PST

Need a little clarification with the part 3). I think that you forgot
to type a letter: there exists a functional relationship between u and
v in the form
F(u,v) = 0 or (u,v) = 0 is right? 
Can you tell me more about the meaning of this proposition?

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Clarification of Question by roadapples-ga on 07 Dec 2002 21:56 PST

Sorry about that. I tried putting the symbol in. Guess it didnt work.
Not sure the name of it, but its the symbol O with a / through it.
That goes in front of the (u,v) = 0

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Request for Question Clarification by livioflores-ga on 07 Dec 2002 23:17 PST

Sorry, I could only find the answer of the part 3) of your question.
livioflores-ga

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Clarification of Question by roadapples-ga on 07 Dec 2002 23:24 PST

Is there a way that I can repost the one question with the price at
1/3 of the price on here and make sure you get it?

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Clarification of Question by roadapples-ga on 07 Dec 2002 23:56 PST

Do not answer #3!! I reposted it. Thanks!