(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The equations:

uz - 2e^(vz) = 0

u - x^2 - y^2 = 0

v^2 - xy*log(v) - 1 = 0

define z (implicitly) as a function of (u,v) and (u,v) as a function of (x,y),

thus z as a function f (x,y)

Describe the role of the inverse and implicit function theorems in the

above statement and compute

[tex]\partial[/tex]z/[tex]\partial[/tex]x(0,e).

(Note that when x=0 and y=e, u=e^2, v=1 and z=2)

2. Relevant equations

Implicit and inverse function theorems

3. The attempt at a solution

I'm finally starting to get a grasp on the 2 theorems and their

respective proofs (I hope), but as far as explaining their role in this

concrete example I'm a little lost.

If anyone can put me on the right path, it would be greatly appreciated.

(This is for an undergrad analysis course)

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# Homework Help: Analysis (implicit and inverse func thrms)

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