Question

一个简单的求极限问题

1-cos(xy)/(sqrt(2-e^xy)-1)，当x,y→0时等于多少

Answer 1

lim((x,y)->(0,0) ) [ 1-cos(xy) ] / { √[(2-e^(xy)] -1 }
=lim((x,y)->(0,0) ) [ 1-cos(xy) ] . { √[(2-e^(xy)] +1 } / [2-e^(xy) -1 ]
=lim((x,y)->(0,0) ) [ 1-cos(xy) ] . { √[(2-e^(xy)] +1 } / [1-e^(xy) ]
=2lim((x,y)->(0,0) ) [ 1-cos(xy) ] / [1-e^(xy) ]
=2lim((x,y)->(0,0) ) (1/2)(xy)^2 / (xy)
=2lim((x,y)->(0,0) ) (1/2)(xy)
=0

Answer 2

会者不难，难者不会

Answer 3

=0
方法如下所示。
请认真查看。
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