- #1
oreosama
- 51
- 0
Homework Statement
lim (x,y) -> (0,0) xy/sqrt(x^2+y^2) = 0
The Attempt at a Solution
my understanding of my actual goal here is kind of poor
given ε>0 there exist ∂>0 s.t. 0 < sqrt(x^2 + y^2) < ∂ then 0<|f(x,y) - L| < ε
| xy/sqrt(x^2 + y^2) - 0 | < ε
(xy * sqrt(x^2 + y^2)) / (x^2 + y^2) < ε
|xy|/|(x^2 + y^2)| * sqrt(x^2 + y^2) < ε
so some number always less than one(i think?) times ∂ < ε. I can't say i know where I am going with this at all. oh god please help.