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

.pdf file of assignment is here: http://www.math.washington.edu/~sullivan/3264_sp10.pdf

So, I have a few questions about the assignment.

Problem #1 I need to know how to find the 14 points.

Problem #2 When it tells me to computer ∂f/∂x amd ∂f/dy at (0,0), does that mean I just I take the limit as (x,y)-->(0,0), since obviously the two are undefined at (0,0)?

Problem #3 The two conditions for differentiability at a point are that f(x,y) is continuous at that point and that lim (h,k)-->(0,0) |f(x+h,y+k)-f(x,y)-(Ah+Bh)| / √(x^{2}+y^{2}) = 0, where A= [f(x+h,y)-f(x,y)]/h, B=[f(x,y+k)-f(x,y)]/k, according to my textbook. Right? How am I supposed to show that such approaches 0 is h,k approach zero?

2. Relevant equations

They're scattered around the assignment

3. The attempt at a solution

The only one worth showing my work is Problem 1. I used the theorem on the front.

grad(F)=<1, 3y^{2}, z^{3}>

grad(G)=<x^{2}, y^{2}, z^{2}>

grad(F), then, is never the zero vector.

grad(G) is at the point (0,0,0).

If I make grad(F) a scalar multiple of grad(G), my system of equations looks like

1=ßx^{2}

3y^{2}=ßy^{2}

z^{3}=ßz^{2}

x^{2}+y^{2}+z^{2}=1.

------> 1/ß + y^{2}+ z^{3}/ß = 1 -----> ß^{2}+ 3y^{2}+ ßz^{2}=1.

Now, how do I solve for the 13 other points with that equation????

Thanks in advance.

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# Homework Help: Adv Multi V Calc questions

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