.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)| / √(x2+y2) = 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?
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, 3y2, z3>
grad(G)=<x2, y2, z2>
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/ß + y2 + z3/ß = 1 -----> ß2 + 3y2 + ßz2=1.
Now, how do I solve for the 13 other points with that equation????
Thanks in advance.