Prove the multivariable does not exist?

[youngronn]

1. I know both dne but how can i prove it? I am not getting any solid answers? help please!

(x,y) to (0,0)
1. ((x^2)y+x(y^2))/((x^2)-(y^2))
2. (x+y)/((x^2)+y+(y^2))

2. 1. Simplified down to xy/(x-y)
2. Simplified down to x/(x^2+y^2+y) + 1/((y+1)+x^2)

 

[Ray Vickson]

1. I know both dne but how can i prove it? I am not getting any solid answers? help please!

(x,y) to (0,0)
1. ((x^2)y+x(y^2))/((x^2)-(y^2))
2. (x+y)/((x^2)+y+(y^2))

2. 1. Simplified down to xy/(x-y)
2. Simplified down to x/(x^2+y^2+y) + 1/((y+1)+x^2)

What would need to happen in order for xy/(x-y) to have a limit as (x,y) → (0,0)? Does that happen in this case?

So, your very first step is to make sure you understand what is meant by a function going to a limit---if you do not understand that you are defeated right from the start.