Problem:Find the following limit, assuming that it exists. |
> ;
2 2
x y
lim -------
x, y -> (0, 0) 2 2
x + y
|
|
Solution:
| If the limit exists then the function approaches the same value along any path to (0,0). In particular if we take y=x we obtain, |
> Limit(`x^2*x^2`/`(x^2+x^2)`,x=0) = Limit(x^2*x^2/(x^2+x^2),x=0);
x^2*x^2 2
lim --------- = lim 1/2 x = 0
x -> 0 (x^2+x^2) x -> 0