Limit of serverable variables,

[th3plan]

Homework Statement

(x,y)---> (0,0)
x²+y²/√(x²+y²+1) - 1

the -1 isn't in the square root, so people know

The Attempt at a Solution

i let y=o and got 2, and y=x² and x=y² and got 2, so how can i be sure this limit is 2, what other method must i try to be sure ?

 

[rocomath]

What exactly is the limit going to? And your problem is very hard to interpret ... might want to re-type that with proper parenthesis.

let x=y

 

[HallsofIvy]

Homework Statement

(x,y)---> (0,0)
x²+y²/√(x²+y²+1) - 1

the -1 isn't in the square root, so people know

But is it in the denominator? Is this $(x^2+ y^2)/(\sqrt{x^2+ y^2})+ 1$ or $(x^2+ y^2)/(\sqrt{x^2+ y^2}+ 1)$ ?

The Attempt at a Solution

i let y=o and got 2, and y=x² and x=y² and got 2, so how can i be sure this limit is 2, what other method must i try to be sure ?[/QUOTE]
One way to check is to change to polar coordinates. Since only r measures "distance to (0,0), if the limit, as r goes to 0, does not depend on $\theta$, that is the limit.