求极限lim(x,y)→(0,0) [1-cos(xy)]/xy^2.
问题描述：
求极限lim(x,y)→(0,0) [1-cos(xy)]/xy^2.
求极限lim(x,y)→(0,0) [1-cos(xy)]/xy^2,麻烦写下过程
答
lim(x,y)→(0,0) [1-cos(xy)]/xy^2
=lim(x,y)→(0,0)( x²y²/2)/xy^2..
=lim(x,y)→(0,0)x
=0利用上册的等价无穷小 因为(1－cosx)等价于x²/2 所以 [1-cos(xy)]等价于( x²y²/2)