6. 求下列各极限:(1) lim_((x,y)to(0,1))(1-xy)/(x^2)+y^(2);(3) lim_((x,y)to(0,0))(2-sqrt(xy+4))/(xy);(5) lim_((x,y)to(2,0))(tan(xy))/(y);

(1) 直接代入 $(x, y) = (0, 1)$，得
$\lim_{(x,y)\to(0,1)}\frac{1-xy}{x^2+y^2} = \frac{1-0}{0+1} = 1$
答案： $\boxed{1}$

(3) 有理化分子，得
$\lim_{(x,y)\to(0,0)}\frac{2-\sqrt{xy+4}}{xy} = \lim_{(x,y)\to(0,0)}\frac{-1}{2+\sqrt{xy+4}} = -\frac{1}{4}$
答案： $\boxed{-\frac{1}{4}}$

(5) 利用等价无穷小替换 $\tan(xy) \sim xy$（当 $y \to 0$），得
$\lim_{(x,y)\to(2,0)}\frac{\tan(xy)}{y} = \lim_{(x,y)\to(2,0)}\frac{xy}{y} = 2$
答案： $\boxed{2}$