问题标题：
【如何求Lim[2-(xy+4)^1/2]/xyx→0,y→0和Limsin(xy)/xx→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]/xyx→0,y→0和Limsin(xy)/xx→0,y→0这两道的极限值,求解题过程!谢谢
白鹏翔回答：
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
Limsin(xy)/xx→0,y→0
=Lim(xy)/xx→0,y→0
=Limyx→0,y→0
=0
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