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

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/06 04:34:54
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,麻烦写下过程求极限lim(x,y)→(0,0)[1-cos(xy

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
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

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
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

利用单变元时的x趋于0时有lim (1-cosx)/x^2=1/2,
因此极限等于lim (1-cosxy)/(x^2y^2) * lim x
=1/2*0=0