Question

advanced calculus

Answer 1

let \[f(x,y)= xy((x^2-y^2/x^2+y^2) \] if \[x^2+y^2\neq0\] and define f(0,0)=0. Show that \[f_x (0,y)=-y\] and \[f_y (x,0) = x\] for all x and y. Then show that \[f_yx (0,0) = -1 \] and \[f_xy(0,0) = 1\].

Answer 2

f_xy are partials with respect to x and y. they just wouldn't let me double up on the underscore.

Answer 3

\[f_{xy}(0,0)=1\]

f_{xy}(0,0)=1

Answer 4

this is a standard result that can easily be found using goggle.

Answer 5

like I said...2 sec on google...

http://www.math.uconn.edu/~leibowitz/math2110f09/mixedpartials.pdf

same function and everything

Answer 6

Thank you

Answer 7

Hail Zarkon!

Answer 8

I showed the same problem to my multivariate calc students this semester :)

Answer 9

someone is mean. :D