Find the limit if it exists. lim as (x,y)--> (0,0) of ((x+y)^2)/(x^2+y^2)?

0 ⤊

2007-09-24 21:24:53 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

Along the trajectory y=0:
x^2 / x^2 = 1
Along the trajectory y=x:
(2x)^2 / (2x^2) = 2
So the limit does not exist.

2007-09-24 21:29:02 · answer #1 · answered by Scarlet Manuka 7 · 0⤊ 0⤋

as (x,y)--> (0,0), x-->y
So, ((x+y)^2)/(x^2+y^2) becomes

(x+x)^2/(x^2 + x^2)
4x^2/2x^2
4/2
2

The limit is 2

2007-09-25 04:35:16 · answer #2 · answered by Christine P 5 · 0⤊ 1⤋