作业帮Lim(Sinx-siny/x-y)极限
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Lim(Sinx-siny/x-y)极限
Lim(Sinx-siny/x-y)极限
Lim(Sinx-siny/x-y)极限
lim(x->y)[(sinx-siny)/(x-y)]=lim(x->y)[2cos((x+y)/2)sin((x-y)/2)/(x-y)] (应用和差化积公式)
=lim(x->y)[cos((x+y)/2)]*lim(x->y)[sin((x-y)/2)/((x-y)/2)]
=cosy*1 (应用重要极限lim(z->0)(sinz/z)=0)
=cosy ；
另一解法：原式=lim(x->y)(cosx) (0/0型极限,应用罗比达法则)
=cosy.
Lim(Sinx-siny/x-y)极限
求极限lim[(sinx-siny)/(x-y)]x趋向y
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证明sin(x+y)sin(x-y)=sinx-siny
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证明：对x≠y,恒有|sinx-siny|
为什么sinx*cosy-cosx*siny=sin(x-y)
证明.（sinx+siny)/cosx-cosy=ctg(y-x)/2
x+y=pai/3,sinx*siny的最小值在线