求下列各式的极限.
(1)limx→0,y→0xy/√(1+xy)-1
(2)limx→0,y→0sinxy/x
(1)limx→0y→0xy/√(1+xy-1)= limx→0y→0xy(√1+xy+1)/(1+xy-1) =lim(√1+xy+1)=2. (2)limx→0y→0 sinxy/x=limx→0y→0 [(sinxy)/xy]y =1•0 =0
求下列各式的极限.
(1)limx→0,y→0xy/√(1+xy)-1
(2)limx→0,y→0sinxy/x
(1)limx→0y→0xy/√(1+xy-1)= limx→0y→0xy(√1+xy+1)/(1+xy-1) =lim(√1+xy+1)=2. (2)limx→0y→0 sinxy/x=limx→0y→0 [(sinxy)/xy]y =1•0 =0