求下列极限 1.lim x→0y→2 sin(xy)/x 2.lim x→0y→0 (2-√(xy+4))/xy
3.lim x→0y→0(x^2y)/(x^3-y^3) 4.limx→0y→1 xy*sin(1/(x^2+y^2))
lim x→0y→2 sin(xy)/x
=lim x→0y→2 (xy)/x
=lim x→0y→2 y
= 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
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