- #1

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## Homework Statement

.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?

## Homework Equations

They're scattered around the assignment

## 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.