如何求Lim[2-(xy+4)^1/2]/xy x→0 ,y→0 和Lim sin(xy)/x x→0,y→0 这两道的极限值,求解题过程!谢谢
问题描述：
如何求Lim[2-(xy+4)^1/2]/xy x→0 ,y→0 和Lim sin(xy)/x x→0,y→0 这两道的极限值,求解题过程!谢谢
答
l第一题把上下底同时乘以2+（xy+4）^1/2得到lim(x,y)->(0,0)（-1*xy）/((2+(xy+4)^1/2)*xy)所以就等于-1/(2+4^1/2)=-1/4
答
1
Lim[2-(xy+4)^(1/2)]/xy
= -Lim[( (xy/4) +1)^(1/2) -1]/(xy/2)
= -Lim[e^( (1/2)·ln( (xy/4) +1) ) -1] /(xy/2)
= -Lim[(1/2)·ln( (xy/4) +1) ] /(xy/2)
= (-1/2)· Lim[(xy/4) ] /(xy/2)
= (-1/2)· (1/2)
= -1/4
2
Lim sin(xy)/x x→0,y→0
= Lim (xy)/x x→0,y→0
= Lim y x→0,y→0
= 0