1
lim x→0y→2 sin(xy)/x
=lim x→0y→2 (xy)/x
=lim x→0y→2 y
= 2
2
lim x→0y→0 (2-√(xy+4))/xy
= lim x→0y→0 (4-(xy+4))/[(xy)·(2+√(xy+4))]
= lim x→0y→0 -(xy)/[(xy)·(2+√(xy+4))]
= lim x→0y→0 -1/[(2+√(xy+4))]
= -1/4