How do I find the limit of
lim
(x,y)->(0,0)
( x - xy + 3 ) / ( (x^2)y + 5xy - y^3 )
I know I have to use
lim
h->0
( f(0,h) - f(0,0) ) / h
but I get 3/0
You have tried only the direction parallel to the y-axis. There are infinitely many pathways to approach (0,0).
Take a shot at the x-direction. Get really creative and try the direction defined by x = y.
I thought it was fun to convert it to polar coordinates and then think about 'r' as it approaches zero. You can pick an angle you like for any approach.
What makes you think your result is inappropriate?