Limit of x^2/(y^2+x^2) at (0,0): Calculus Homework Solution

[superdave]

Homework Statement

Show that the following limit does not exist:

lim (x,y) --> (0,0) of x^2 / (y^2 + x^2)

Homework Equations

The Attempt at a Solution

I think it involves using l'hospitals rule and using partial derivatives, but I really don't know.

 

[Office_Shredder]

For a limit to exist in multiple dimensions, it must be the same no matter which path you approach the point from. So if (x,y) travels over, say, y=x to (0,0), if the limit exists, it must be the same as if (x,y) travels over y=0 to (0,0).

So try two paths, show the limit is different depending on how you approach (0,0), and you're done

 

[superdave]

I'm not really sure how to go about that

 

[superdave]

I know how to take partial derivatives and directional derivatives...

 

[pki15]

Set y=x, and see what the limit is when x->0. Then try setting y=0, and see what the limit is as x->0. This is the idea for proving any limit in multiple variables does not exist, just go along different lines, if you get different answers, the limit does not exist.

 

[superdave]

Ah, I ge tit now, thanks