企源知识库

求下列各式的极限．
(1)lim_x→0,y→0xy/(√1+xy)-1；
(2)lim_x→0,y→0sinxy/x
【正确答案】：(1)lim_x→0,y→0xy/(√1+xy)= lim_x→0,y→0xy((√1+xy)+1)/(1+xy-1)= lim_x→0,y→0[(√1+xy)+1] (2)lim_x→0,y→0sinxy/x=lim_x→0,y→0(sinxy/xy)y=1•0=0．