## Calculus 8th Edition

$\frac{2}{3}$
From direct substitution, we have $\lim\limits_{(x,y) \to (1,1)}\frac{2xy}{x^2+2y^2}=\frac{2(1)(1)}{(1)^2+2(1)^2}$ $=\frac{2}{3}$